Six Sigma Study Guide

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Ted Hessing

Critical to X (CTX)

Posted by Ted Hessing

Critical to X (CTX) requirements are elements of a project that are important to the end customer.

As an example, think about going to buy a burger. There are several factors that you probably won’t think about much when ordering. However, you expect them in your order:

Critical to X. Photo by Scott Ogle

  • Quality : You expect an edible, tasty burger.
  • Cost : You expect to pay a certain amount for your burger.
  • Delivery : You expect to receive that burger fairly quickly.
  • Safety : You expect the result will not give you food poisoning.

These are all Critical to X (CTX) requirements.

Types of Critical to X (CTX) Requirements

Five labelled circles. Critical to X is surrounded by Critical to Quality, Critical to Cost, Critical to Delivery, and Critical to Safety.

These vary in terminology depending on whose articles you read. Some include Critical to Process requirements or leave out Critical to Safety. You’ll also find that sometimes discussions of CTX requirements waver between focusing on the customer and focusing on the workplace. This is understandable but leads to losing customer orientation, which is crucial in these requirements.

There are four basic Critical to X (CTX) factors:

CTQ: Critical to Quality

Ctc: critical to cost, ctd: critical to delivery.

  • CTS: Critical to Safety

Critical to Quality (CTQ) is like a compass for any organization seeking to achieve true customer satisfaction. It’s not just about meeting some generic standard; it’s all about the exact attributes of your product, process, or service that are absolutely essential for your customers. CTQ s can include physical measurements such as weight, height, length, depth, etc.

Identifying CTQs involves listening intently to the customer requirements. What are their needs, preferences, and pain points? What aspects, if not addressed, would instantly turn them away? By gathering this crucial intel, you can translate those often unspoken desires into concrete, measurable CTQs.

CTQs are often determined through interactions with customers and stakeholders, considering their needs, preferences, and specifications. These critical characteristics are the factors that, if not met at the desired level, would result in dissatisfaction or a failure to meet the intended purpose.

Critical to Cost (CTC) encompasses the elements influencing how costs affect customers. While resembling one of the CTX, CTQs, customers distinguish CTC s to articulate their precise requirements. For example, the weight of a product: if a customer expects a product’s weight to fall within the range of 50 to 60 pounds, any deviation beyond these limits is perceived as negatively impacting their specified requirements.

Critical to Cost (CTC) pertains to the factors or components within a product, process, or service that substantially influences its overall cost. Recognizing what is critical to cost is imperative for businesses to oversee expenditures and allocate resources judiciously and proficiently. Concentrating on the elements that wield the greatest impact on costs empowers organizations to make well-informed decisions, leading to the optimization of both their processes and products.

Critical to Cost Example

For example, take a business that manufactures sheet metal. The following costs to its customers apply:

  • The wholesale price for 0.5-inch thick hot-rolled, uncoated raw steel is $100-120/sheet.
  • Delivery costs are $100 per 100 sheets.
  • If the customer uses one of the company’s resellers, they’ll pay a 7-10% markup.
  • Customers must perform sampling and inspections on each load to ensure quality control. The estimated cost–materials, labor, and time–for this QC is $100 per 100 sheets.
  • Because it provides wholesale products only, and most customers are in the same country, there are minimal taxes and duties.
  • Most of its customers use only one or two resellers for their sheet metal, so the cost of procurement is not high.

Critical to delivery (CTD) are the requirements stated by customers, specifically concerning product or service delivery. Customers often identify and articulate CTD requirements to ensure that the delivery meets their expectations and organization needs. Organizations can prioritize and optimize their processes to meet customer expectations, minimize delays, and enhance overall satisfaction by identifying and understanding what is critical to delivery.

A few examples of Six Sigma projects that address one of the CTX: Critical to Delivery requirements are:

  • Improving a process to decrease time wastage (faster production).
  • Researching courier companies with the end goal of offering a same-day delivery service.
  • Changing the packaging products used to decrease parcel breakages in transit.

CTS: Critical to Safety .

Critical to Safety, or CTS, refers to the elements that, if not executed accurately or if they falter, have the potential to result in substantial injury, loss of life, or environmental harm. This applies to everything from products and processes to systems and even human actions. In other words, Critical to Safety requirements are based on the safety concerns of customers. These might include industry safety standards and workplace health and safety (OH&S) rules.

Examples of Critical to Safety Requirements

We can use the customer drivers mentioned above to create example CTS requirements:

  • Make all toy parts from fabric, no hard plastics.
  • Minimum machine bench height of 4′.
  • You can package multiple order items in the same box if the combined weight of items, box, and padding does not exceed 30 pounds.

Critical to X (CTX) and Six Sigma

Six Sigma projects can aim to improve any of the Critical to X (CTX) requirements. For example, a project might improve a process and decrease the end cost of a product by 10%. Hence, it would meet a Critical-to-Cost requirement. Or, it might focus on finding a new supplier for a key material, decreasing production costs. As a result, it could also decrease the end product’s price, again meeting a CTC requirement.

Keep in mind that these are customer-centric requirements. That means you need to be able to show a clear benefit to the customer. This includes any project that is supposed to address CTX.

Other helpful Critical to X (CTX) Links

  • Critical to Quality

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Comments (5)

Do u have CSSBB quesition bank for practicing purpose.

Actually, yes, I do have a question bank that I am getting ready to release. Make sure that you are on the email list (see sign up on the right side of the website) so that you are the first to know once it goes live.

In the meantime, I have links to several other free CSSBB question banks here .

Let me know how else I can help.

I completely agree with the author’s argument that CTX is a crucial factor in determining the success of a project. As a project manager myself, I have seen firsthand how a lack of clear goals and priorities can lead to confusion and waste of resources. I appreciate the author’s insight into this topic and look forward to seeing more of their work in the future.

Thanks for the kind words.

Great blog post on CTX! I completely agree with your point about the importance of X. As someone who has worked in the field for a while, I can attest to the challenges that arise when X is not properly addressed. Your insights into how to overcome these challenges are invaluable. Thank you for sharing your expertise!

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Critical Analysis in Composition

Glossary of Grammatical and Rhetorical Terms

  • An Introduction to Punctuation
  • Ph.D., Rhetoric and English, University of Georgia
  • M.A., Modern English and American Literature, University of Leicester
  • B.A., English, State University of New York

In composition , critical analysis is a careful examination and evaluation of a text , image, or other work or performance.

Performing a critical analysis does not necessarily involve finding fault with a work. On the contrary, a thoughtful critical analysis may help us understand the interaction of the particular elements that contribute to a work's power and effectiveness. For this reason, critical analysis is a central component of academic training; the skill of critical analysis is most often thought of in the context of analyzing a work of art or literature, but the same techniques are useful to build an understanding of texts and resources in any discipline.

In this context, the word "critical" carries a different connotation than in vernacular, everyday speech. "Critical" here does not simply mean pointing out a work's flaws or arguing why it is objectionable by some standard. Instead, it points towards a close reading of that work to gather meaning, as well as to evaluate its merits. The evaluation is not the sole point of critical analysis, which is where it differs from the colloquial meaning of "criticize."

Examples of Critical Essays

  • "Jack and Gill: A Mock Criticism" by Joseph Dennie
  • "Miss Brill's Fragile Fantasy": A Critical Essay About Katherine Mansfield's Short Story "Miss Brill" and "Poor, Pitiful Miss Brill"
  • "On the Knocking at the Gate in Macbeth " by Thomas De Quincey
  • A Rhetorical Analysis of Claude McKay's "Africa"
  • A Rhetorical Analysis of E B. White's Essay "The Ring of Time"
  • A Rhetorical Analysis of U2's "Sunday Bloody Sunday"
  • "Saloonio: A Study in Shakespearean Criticism" by Stephen Leacock
  • Writing About Fiction: A Critical Essay on Hemingway's Novel The Sun Also Rises

Quotes About Critical Analysis

  • " [C]ritical analysis involves breaking down an idea or a statement, such as a claim , and subjecting it to critical thinking in order to test its validity." (Eric Henderson, The Active Reader: Strategies for Academic Reading and Writing . Oxford University Press, 2007)​
  • "To write an effective critical analysis, you need to understand the difference between analysis and summary . . . . [A] critical analysis looks beyond the surface of a text—it does far more than summarize a work. A critical analysis isn't simply dashing off a few words about the work in general." ( Why Write?: A Guide to BYU Honors Intensive Writing . Brigham Young University, 2006)
  • "Although the main purpose of a critical analysis is not to persuade , you do have the responsibility of organizing a discussion that convinces readers that your analysis is astute." (Robert Frew et al., Survival: A Sequential Program for College Writing . Peek, 1985)

Critical Thinking and Research

"[I]n response to the challenge that a lack of time precludes good, critical analysis , we say that good, critical analysis saves time. How? By helping you be more efficient in terms of the information you gather. Starting from the premise that no practitioner can claim to collect all the available information, there must always be a degree of selection that takes place. By thinking analytically from the outset, you will be in a better position to 'know' which information to collect, which information is likely to be more or less significant and to be clearer about what questions you are seeking to answer." (David Wilkins and Godfred Boahen, Critical Analysis Skills For Social Workers . McGraw-Hill, 2013)

How to Read Text Critically

 "Being critical in academic enquiry means: - adopting an attitude of skepticism or reasoned doubt towards your own and others' knowledge in the field of enquiry . . . - habitually questioning the quality of your own and others' specific claims to knowledge about the field and the means by which these claims were generated; - scrutinizing claims to see how far they are convincing . . .; - respecting others as people at all times. Challenging others' work is acceptable, but challenging their worth as people is not; - being open-minded , willing to be convinced if scrutiny removes your doubts, or to remain unconvinced if it does not; - being constructive by putting your attitude of skepticism and your open-mindedness to work in attempting to achieve a worthwhile goal." (Mike Wallace and Louise Poulson, "Becoming a Critical Consumer of the Literature." Learning to Read Critically in Teaching and Learning , ed. by Louise Poulson and Mike Wallace. SAGE, 2004)

Critically Analyzing Persuasive Ads

"[I]n my first-year composition class, I teach a four-week advertisement analysis project as a way to not only heighten students' awareness of the advertisements they encounter and create on a daily basis but also to encourage students to actively engage in a discussion about critical analysis by examining rhetorical appeals in persuasive contexts. In other words, I ask students to pay closer attention to a part of the pop culture in which they live. " . . . Taken as a whole, my ad analysis project calls for several writing opportunities in which students write essays , responses, reflections, and peer assessments . In the four weeks, we spend a great deal of time discussing the images and texts that make up advertisements, and through writing about them, students are able to heighten their awareness of the cultural 'norms' and stereotypes which are represented and reproduced in this type of communication ." (Allison Smith, Trixie Smith, and Rebecca Bobbitt, Teaching in the Pop Culture Zone: Using Popular Culture in the Composition Classroom . Wadsworth Cengage, 2009)

Critically Analyzing Video Games

 "When dealing with a game's significance, one could analyze the themes of the game be they social, cultural, or even political messages. Most current reviews seem to focus on a game's success: why it is successful, how successful it will be, etc. Although this is an important aspect of what defines the game, it is not critical analysis . Furthermore, the reviewer should dedicate some to time to speaking about what the game has to contribute to its genre (Is it doing something new? Does it present the player with unusual choices? Can it set a new standard for what games of this type should include?)." (Mark Mullen, "On Second Thought . . ." Rhetoric/Composition/Play Through Video Games: Reshaping Theory and Practice , ed. by Richard Colby, Matthew S.S. Johnson, and Rebekah Shultz Colby. Palgrave Macmillan, 2013)

Critical Thinking and Visuals

 "The current critical turn in rhetoric and composition studies underscores the role of the visual, especially the image artifact, in agency. For instance, in Just Advocacy? a collection of essays focusing on the representation of women and children in international advocacy efforts, coeditors Wendy S. Hesford and Wendy Kozol open their introduction with a critical analysis of a documentary based on a picture: the photograph of an unknown Afghan girl taken by Steve McCurry and gracing the cover of National Geographic in 1985. Through an examination of the ideology of the photo's appeal as well as the 'politics of pity' circulating through the documentary, Hesford and Kozol emphasize the power of individual images to shape perceptions, beliefs, actions, and agency." (Kristie S. Fleckenstein, Vision, Rhetoric, and Social Action in the Composition Classroom . Southern Illinois University Press, 2010)

Related Concepts

  • Analysis  and  Critical Essay
  • Book Report
  • Close Reading
  • Critical Thinking
  • Discourse Analysis
  • Evaluation Essay
  • Explication
  • Problem-Solution
  • Rhetorical Analysis
  • Definition and Examples of Explication (Analysis)
  • Rhetorical Analysis Definition and Examples
  • Quotes About Close Reading
  • How to Write a Critical Essay
  • What Is a Critique in Composition?
  • Definition and Examples of Analysis in Composition
  • Definition and Examples of Evaluation Essays
  • Understanding the Use of Language Through Discourse Analysis
  • What Is a Written Summary?
  • Critical Thinking in Reading and Composition
  • Critical Thinking Definition, Skills, and Examples
  • Miss Brill's Fragile Fantasy
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Research Method

Home » Critical Analysis – Types, Examples and Writing Guide

Critical Analysis – Types, Examples and Writing Guide

Table of Contents

Critical Analysis

Critical Analysis


Critical analysis is a process of examining a piece of work or an idea in a systematic, objective, and analytical way. It involves breaking down complex ideas, concepts, or arguments into smaller, more manageable parts to understand them better.

Types of Critical Analysis

Types of Critical Analysis are as follows:

Literary Analysis

This type of analysis focuses on analyzing and interpreting works of literature , such as novels, poetry, plays, etc. The analysis involves examining the literary devices used in the work, such as symbolism, imagery, and metaphor, and how they contribute to the overall meaning of the work.

Film Analysis

This type of analysis involves examining and interpreting films, including their themes, cinematography, editing, and sound. Film analysis can also include evaluating the director’s style and how it contributes to the overall message of the film.

Art Analysis

This type of analysis involves examining and interpreting works of art , such as paintings, sculptures, and installations. The analysis involves examining the elements of the artwork, such as color, composition, and technique, and how they contribute to the overall meaning of the work.

Cultural Analysis

This type of analysis involves examining and interpreting cultural artifacts , such as advertisements, popular music, and social media posts. The analysis involves examining the cultural context of the artifact and how it reflects and shapes cultural values, beliefs, and norms.

Historical Analysis

This type of analysis involves examining and interpreting historical documents , such as diaries, letters, and government records. The analysis involves examining the historical context of the document and how it reflects the social, political, and cultural attitudes of the time.

Philosophical Analysis

This type of analysis involves examining and interpreting philosophical texts and ideas, such as the works of philosophers and their arguments. The analysis involves evaluating the logical consistency of the arguments and assessing the validity and soundness of the conclusions.

Scientific Analysis

This type of analysis involves examining and interpreting scientific research studies and their findings. The analysis involves evaluating the methods used in the study, the data collected, and the conclusions drawn, and assessing their reliability and validity.

Critical Discourse Analysis

This type of analysis involves examining and interpreting language use in social and political contexts. The analysis involves evaluating the power dynamics and social relationships conveyed through language use and how they shape discourse and social reality.

Comparative Analysis

This type of analysis involves examining and interpreting multiple texts or works of art and comparing them to each other. The analysis involves evaluating the similarities and differences between the texts and how they contribute to understanding the themes and meanings conveyed.

Critical Analysis Format

Critical Analysis Format is as follows:

I. Introduction

  • Provide a brief overview of the text, object, or event being analyzed
  • Explain the purpose of the analysis and its significance
  • Provide background information on the context and relevant historical or cultural factors

II. Description

  • Provide a detailed description of the text, object, or event being analyzed
  • Identify key themes, ideas, and arguments presented
  • Describe the author or creator’s style, tone, and use of language or visual elements

III. Analysis

  • Analyze the text, object, or event using critical thinking skills
  • Identify the main strengths and weaknesses of the argument or presentation
  • Evaluate the reliability and validity of the evidence presented
  • Assess any assumptions or biases that may be present in the text, object, or event
  • Consider the implications of the argument or presentation for different audiences and contexts

IV. Evaluation

  • Provide an overall evaluation of the text, object, or event based on the analysis
  • Assess the effectiveness of the argument or presentation in achieving its intended purpose
  • Identify any limitations or gaps in the argument or presentation
  • Consider any alternative viewpoints or interpretations that could be presented
  • Summarize the main points of the analysis and evaluation
  • Reiterate the significance of the text, object, or event and its relevance to broader issues or debates
  • Provide any recommendations for further research or future developments in the field.

VI. Example

  • Provide an example or two to support your analysis and evaluation
  • Use quotes or specific details from the text, object, or event to support your claims
  • Analyze the example(s) using critical thinking skills and explain how they relate to your overall argument

VII. Conclusion

  • Reiterate your thesis statement and summarize your main points
  • Provide a final evaluation of the text, object, or event based on your analysis
  • Offer recommendations for future research or further developments in the field
  • End with a thought-provoking statement or question that encourages the reader to think more deeply about the topic

How to Write Critical Analysis

Writing a critical analysis involves evaluating and interpreting a text, such as a book, article, or film, and expressing your opinion about its quality and significance. Here are some steps you can follow to write a critical analysis:

  • Read and re-read the text: Before you begin writing, make sure you have a good understanding of the text. Read it several times and take notes on the key points, themes, and arguments.
  • Identify the author’s purpose and audience: Consider why the author wrote the text and who the intended audience is. This can help you evaluate whether the author achieved their goals and whether the text is effective in reaching its audience.
  • Analyze the structure and style: Look at the organization of the text and the author’s writing style. Consider how these elements contribute to the overall meaning of the text.
  • Evaluate the content : Analyze the author’s arguments, evidence, and conclusions. Consider whether they are logical, convincing, and supported by the evidence presented in the text.
  • Consider the context: Think about the historical, cultural, and social context in which the text was written. This can help you understand the author’s perspective and the significance of the text.
  • Develop your thesis statement : Based on your analysis, develop a clear and concise thesis statement that summarizes your overall evaluation of the text.
  • Support your thesis: Use evidence from the text to support your thesis statement. This can include direct quotes, paraphrases, and examples from the text.
  • Write the introduction, body, and conclusion : Organize your analysis into an introduction that provides context and presents your thesis, a body that presents your evidence and analysis, and a conclusion that summarizes your main points and restates your thesis.
  • Revise and edit: After you have written your analysis, revise and edit it to ensure that your writing is clear, concise, and well-organized. Check for spelling and grammar errors, and make sure that your analysis is logically sound and supported by evidence.

When to Write Critical Analysis

You may want to write a critical analysis in the following situations:

  • Academic Assignments: If you are a student, you may be assigned to write a critical analysis as a part of your coursework. This could include analyzing a piece of literature, a historical event, or a scientific paper.
  • Journalism and Media: As a journalist or media person, you may need to write a critical analysis of current events, political speeches, or media coverage.
  • Personal Interest: If you are interested in a particular topic, you may want to write a critical analysis to gain a deeper understanding of it. For example, you may want to analyze the themes and motifs in a novel or film that you enjoyed.
  • Professional Development : Professionals such as writers, scholars, and researchers often write critical analyses to gain insights into their field of study or work.

Critical Analysis Example

An Example of Critical Analysis Could be as follow:

Research Topic:

The Impact of Online Learning on Student Performance


The introduction of the research topic is clear and provides an overview of the issue. However, it could benefit from providing more background information on the prevalence of online learning and its potential impact on student performance.

Literature Review:

The literature review is comprehensive and well-structured. It covers a broad range of studies that have examined the relationship between online learning and student performance. However, it could benefit from including more recent studies and providing a more critical analysis of the existing literature.

Research Methods:

The research methods are clearly described and appropriate for the research question. The study uses a quasi-experimental design to compare the performance of students who took an online course with those who took the same course in a traditional classroom setting. However, the study may benefit from using a randomized controlled trial design to reduce potential confounding factors.

The results are presented in a clear and concise manner. The study finds that students who took the online course performed similarly to those who took the traditional course. However, the study only measures performance on one course and may not be generalizable to other courses or contexts.

Discussion :

The discussion section provides a thorough analysis of the study’s findings. The authors acknowledge the limitations of the study and provide suggestions for future research. However, they could benefit from discussing potential mechanisms underlying the relationship between online learning and student performance.

Conclusion :

The conclusion summarizes the main findings of the study and provides some implications for future research and practice. However, it could benefit from providing more specific recommendations for implementing online learning programs in educational settings.

Purpose of Critical Analysis

There are several purposes of critical analysis, including:

  • To identify and evaluate arguments : Critical analysis helps to identify the main arguments in a piece of writing or speech and evaluate their strengths and weaknesses. This enables the reader to form their own opinion and make informed decisions.
  • To assess evidence : Critical analysis involves examining the evidence presented in a text or speech and evaluating its quality and relevance to the argument. This helps to determine the credibility of the claims being made.
  • To recognize biases and assumptions : Critical analysis helps to identify any biases or assumptions that may be present in the argument, and evaluate how these affect the credibility of the argument.
  • To develop critical thinking skills: Critical analysis helps to develop the ability to think critically, evaluate information objectively, and make reasoned judgments based on evidence.
  • To improve communication skills: Critical analysis involves carefully reading and listening to information, evaluating it, and expressing one’s own opinion in a clear and concise manner. This helps to improve communication skills and the ability to express ideas effectively.

Importance of Critical Analysis

Here are some specific reasons why critical analysis is important:

  • Helps to identify biases: Critical analysis helps individuals to recognize their own biases and assumptions, as well as the biases of others. By being aware of biases, individuals can better evaluate the credibility and reliability of information.
  • Enhances problem-solving skills : Critical analysis encourages individuals to question assumptions and consider multiple perspectives, which can lead to creative problem-solving and innovation.
  • Promotes better decision-making: By carefully evaluating evidence and arguments, critical analysis can help individuals make more informed and effective decisions.
  • Facilitates understanding: Critical analysis helps individuals to understand complex issues and ideas by breaking them down into smaller parts and evaluating them separately.
  • Fosters intellectual growth : Engaging in critical analysis challenges individuals to think deeply and critically, which can lead to intellectual growth and development.

Advantages of Critical Analysis

Some advantages of critical analysis include:

  • Improved decision-making: Critical analysis helps individuals make informed decisions by evaluating all available information and considering various perspectives.
  • Enhanced problem-solving skills : Critical analysis requires individuals to identify and analyze the root cause of a problem, which can help develop effective solutions.
  • Increased creativity : Critical analysis encourages individuals to think outside the box and consider alternative solutions to problems, which can lead to more creative and innovative ideas.
  • Improved communication : Critical analysis helps individuals communicate their ideas and opinions more effectively by providing logical and coherent arguments.
  • Reduced bias: Critical analysis requires individuals to evaluate information objectively, which can help reduce personal biases and subjective opinions.
  • Better understanding of complex issues : Critical analysis helps individuals to understand complex issues by breaking them down into smaller parts, examining each part and understanding how they fit together.
  • Greater self-awareness: Critical analysis helps individuals to recognize their own biases, assumptions, and limitations, which can lead to personal growth and development.

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Critical analysis is a formal evaluation of someone else’s work. In academia, this work is most often a book, article, poem, play or piece of visual art. However, in business, you might need to carry out a critical analysis of a proposal for a project or grant, a policy or white paper, an industry handbook or even a research study. Broadly speaking, critical analysis involves examining the work to see how well the author has carried out their purpose, or how well the project or policy will or does carry out its purpose.

Critical analysis is therefore an extension of both critical thinking and critical reading . Critical thinking is the ability to engage in reflective and independent thinking about the information that you encounter. Critical reading is engaging with what you read by asking yourself questions about the author’s intention and your reaction to that. Critical analysis is the formalisation of both these processes, coupled with a written analysis for others.

There are therefore two elements to critical analysis. The first is carrying out the analysis itself: deciding what you think. The second is writing up your findings and judgement for others.

Steps in a Critical Analysis

There are several steps that you need to take to carry out a critical analysis. These include:

1. Critical reading of your text or examination of your piece.

This is a matter of carefully reading your text, possibly several times.

As you do so, consider (and note down) what you think is important and relevant. It will also be helpful to note any controversial points, or areas where you disagree.

There is more about this process in our page on Critical Reading .

During this process, you should aim to identify the main thesis, point or purpose, and then sub-themes or issues.

In a piece of business writing or an essay, the purpose or thesis is usually set out early on, often in the introduction. In a piece of fiction writing, it may be necessary to read the text fully to identify themes and then highlight the most important theme.>

It is also worth taking note of any evidence that supports the themes and purpose.

Finally, it is worth writing yourself a one-paragraph summary of the text. This is likely to be a good starting point for your analysis, because your readers may not have read the text themselves.

2. Analysing the text or piece

The purpose of your analysis is to make an overall judgement about how well the text has met its objectives, based on the evidence available to you.

There are five useful aspects to consider in analysing the text or piece:

Your reaction to the text . This has two purposes. First, it affects how you approach the analysis. For example, if the ideas in the text make you angry, you will find it harder to see their benefits. Second, writers often want to evoke certain emotions in their audience. This is part of the purpose of the piece—and therefore assessing this issue is an important part of judging whether it has met its objectives.

The background to the text . It is worth considering the backdrop against which the text was written. For a policy paper, for example, what has gone before? How urgent is the need to address the situation? For a piece of creative writing, when was it written and what was happening in the world at the time? How might this have affected the way that the author was writing, or what they wanted to achieve?

The author’s background and the possible implications of this . The author’s background is likely to have informed their opinions and views—and therefore what they have written. It is worth considering the text in this light. This is part of the background, but specific enough to consider as a separate category.

The definitions and concepts in the text . Consider how well the author has defined concepts and ideas. It is much easier to assess ideas if they are clearly defined and described in simple language. Similarly, poor definitions may mean that the author is not clear about their own meaning, or that your understanding is different from theirs.

The use of evidence . You should consider the evidence presented in the text in two senses. First, examine its general validity and reliability. For example, in a proposal or paper, are the ideas supported by peer reviewed studies published in reputable journals? Second, you should consider how well the evidence supports the author’s points. It is also worth considering what evidence is NOT cited, but which might support or undermine the author’s points. It follows that you should also have evidence to support your own arguments in your analysis.

3. Writing up your analysis

The final stage of a critical analysis is to write up your analysis to present it to others.

The precise form that you use is likely to depend both on your preferences, and on any guidelines provided by your organisation or institution (see box).

TOP TIP! Check your guidelines

Your organisation or institution may have guidelines for carrying out a critical analysis. Check them carefully for the structure that you are expected to use, or any essential sections that must be included. For example, some organisations require a summary paragraph upfront (like an executive summary).

You are likely to need to include:

A brief summary of the text or proposal.

A brief summary of your assessment of the text . This should usually be structured around a main point or thesis against which you will consider various aspects of the text.

  • For example, if you are analysing a business proposal, you might be concerned that the concepts are not defined very clearly, and that this may demonstrate that the author has not clearly understood the issues. Your main thesis is therefore this lack of clarity.

A more expanded version of  your analysis, with the evidence for each of your points . Again, this should be structured around your main thesis. It should also set your analysis in the wider context, including what else is known about the subject.

  • The example from the previous bullet described concerns about the lack of clarity of definitions and therefore ambiguity. In this example, your expanded analysis would focus on areas that are not clear, and the problems that might arise from the ambiguity.

A conclusion that sums up your argument and reiterates your judgement on the text.

TOP TIP! You don’t have to write it in order—just sort it afterwards

It is often easier to prepare your introduction and conclusion once you have finished your analysis, and you are absolutely clear on the points you want to highlight.

It is also a good idea to use headings to show divisions between sections.

Summing Up Critical Analysis

Ultimately, critical analysis is about asking questions—and then setting the answers into context.

The most important questions are What, How, Why and So what? The answers will provide a clear and succinct critique of a text, project or idea, and allow you to form a judgement about the text.

Continue to: Critical Thinking and Fake News Analytical Skills

See also: Assessing Internet Information Styles of Writing Understanding and Addressing Conspiracy Theories

Critical Analysis

A critical analysis involves analysis and judgment. like a film review, that both deconstructs a film and tells us whether we should see it., what is critical analysis.

Critical analysis is a type of analysis. An important distinction between a typical analysis and a critical analysis is that critical analysis requires you to take a stance on the thing you're analyzing—you present an argument, backed by the analysis you’ve done, to judge (or recommend, or critique) the work.

Diagram for critical analysis: cartoon thumbs up and down next to the word "critique", underneath is a plus sign leading to the word "analysis", with a diagram for analysis underneath with a cartoon cookie with arrows leading out to different ingredients, such as flour, peanut butter, chocolate chips, and flour.

For example, if you're analyzing a film's theme, you might examine certain scenes and snippets of dialogue to explain how they further the film's message.

A critical analysis goes one step further—you'll also makes a judgement about that them, about whether it's "good" or "ethical," "well-developed" or "effective." You might say something about the impact it should have or whether audiences should see the film or skip it.

  • Analysis = Examine a "thing" to understand how it functions.
  • Critical Analysis = Examine a thing to understand how it functions and make a judgement about its impact or value.

So Where Do I Start?

One common place to start is to examine your subject closely—say, a book, an artwork, or a play—and decide what effect it has on you or on other people who experience it.

  • Does it give you a certain feeling?
  • Does it offer you information?
  • Does it send a message?
  • Does it try to persuade you to do something?
  • Is it moral?
  • Is it unethical?
  • Is it beautiful and well-constructed?
  • Is it worthwhile?
  • What consequence might it have on its peers? On consumers? Is that a good thing or a bad thing?

Any one of these questions can help you formulate your critical claim, the thesis you'll ultimately try to argue.

  • Example: "Schindler's List is a good film because it offers a profound and terrifying reminder of the dangers of complacency and racism."

Reminder: criticism can be subjective, especially when it involves your perception and interpretation. Not everyone agrees with every film critic, and that's okay. A critical analysis gives us a window into how you consume, experience, perceive, and value whatever it is you're analyzing, which then, hopefully, elevates our appreciation and understanding of the thing itself.

Reminder about Analysis

Since any critical analysis is an argument, it’s important to explain how and why you got to your conclusions. This is where analysis comes in.

Analysis is the process of breaking something into its parts and examining them to understand their function. For instance, for the thesis of a critical analysis on a film, you might say, “this film effectively portrayed the boredom of office life with its use of bleak gray colors, droning soundtrack, and dryly funny dialogue.”

Here, the colors, soundtrack, and dialogue are all parts of the film, and you’re making a claim about the effect they have. In the rest of the paper you’ll describe and explain this effect, using evidence from the film to make your connections. This requires you to clearly explain how and why bleak colors or a droning soundtrack actually do, in fact, portray the boredom of office life. If not, you're simply making claims and hoping your audience trusts you. Without analysis, you have no evidence.

To recap, critically analyzing something means identifying its value or impact, then breaking down its components to explain how and why those components contribute to value or impact you identified.

Doing so will allow you to better understand that specific thing, and allow you to contribute meaningfully to the conversation surrounding the thing itself.

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Short Review on Analysis

Longer Dive into Analysis

Are you ready to chat with us about critical analysis? Consider these questions to help you in your consultation:

  • Have I clearly identified a “whole”?
  • Have I clearly outlined the “parts” that make up the whole?
  • Have I clearly explained how each part “functions” in connection to the whole? Does my writing clearly show why that part matters, and

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How to write a critical analysis

How to write a critical analysis paper

Unlike the name implies a critical analysis does not necessarily mean that you are only exploring what is wrong with a piece of work. Instead, the purpose of this type of essay is to interact with and understand a text. Here’s what you need to know to create a well-written critical analysis essay.

What is a critical analysis?

A critical analysis examines and evaluates someone else’s work, such as a book, an essay, or an article. It requires two steps: a careful reading of the work and thoughtful analysis of the information presented in the work.

Although this may sound complicated, all you are doing in a critical essay is closely reading an author’s work and providing your opinion on how well the author accomplished their purpose.

Critical analyses are most frequently done in academic settings (such as a class assignment). Writing a critical analysis demonstrates that you are able to read a text and think deeply about it. However, critical thinking skills are vital outside of an educational context as well. You just don’t always have to demonstrate them in essay form.

How to outline and write a critical analysis essay

Writing a critical analysis essay involves two main chunks of work: reading the text you are going to write about and writing an analysis of that text. Both are equally important when writing a critical analysis essay.

Step one: Reading critically

The first step in writing a critical analysis is to carefully study the source you plan to analyze.

If you are writing for a class assignment, your professor may have already given you the topic to analyze in an article, short story, book, or other work. If so, you can focus your note-taking on that topic while reading.

Other times, you may have to develop your own topic to analyze within a piece of work. In this case, you should focus on a few key areas as you read:

  • What is the author’s intended purpose for the work?
  • What techniques and language does the author use to achieve this purpose?
  • How does the author support the thesis?
  • Who is the author writing for?
  • Is the author effective at achieving the intended purpose?

Once you have carefully examined the source material, then you are ready to begin planning your critical analysis essay.

Step two: Writing the critical analysis essay

Taking time to organize your ideas before you begin writing can shorten the amount of time that you spend working on your critical analysis essay. As an added bonus, the quality of your essay will likely be higher if you have a plan before writing.

Here’s a rough outline of what should be in your essay. Of course, if your instructor gives you a sample essay or outline, refer to the sample first.

  • Background Information

Critical Analysis

Here is some additional information on what needs to go into each section:

Background information

In the first paragraph of your essay, include background information on the material that you are critiquing. Include context that helps the reader understand the piece you are analyzing. Be sure to include the title of the piece, the author’s name, and information about when and where it was published.

“Success is counted sweetest” is a poem by Emily Dickinson published in 1864. Dickinson was not widely known as a poet during her lifetime, and this poem is one of the first published while she was alive.

After you have provided background information, state your thesis. The thesis should be your reaction to the work. It also lets your reader know what to expect from the rest of your essay. The points you make in the critical analysis should support the thesis.

Dickinson’s use of metaphor in the poem is unexpected but works well to convey the paradoxical theme that success is most valued by those who never experience success.

The next section should include a summary of the work that you are analyzing. Do not assume that the reader is familiar with the source material. Your summary should show that you understood the text, but it should not include the arguments that you will discuss later in the essay.

Dickinson introduces the theme of success in the first line of the poem. She begins by comparing success to nectar. Then, she uses the extended metaphor of a battle in order to demonstrate that the winner has less understanding of success than the loser.

The next paragraphs will contain your critical analysis. Use as many paragraphs as necessary to support your thesis.

Discuss the areas that you took notes on as you were reading. While a critical analysis should include your opinion, it needs to have evidence from the source material in order to be credible to readers. Be sure to use textual evidence to support your claims, and remember to explain your reasoning.

Dickinson’s comparison of success to nectar seems strange at first. However the first line “success is counted sweetest” brings to mind that this nectar could be bees searching for nectar to make honey. In this first stanza, Dickinson seems to imply that success requires work because bees are usually considered to be hard-working and industrious.

In the next two stanzas, Dickinson expands on the meaning of success. This time she uses the image of a victorious army and a dying man on the vanquished side. Now the idea of success is more than something you value because you have worked hard for it. Dickinson states that the dying man values success even more than the victors because he has given everything and still has not achieved success.

This last section is where you remind the readers of your thesis and make closing remarks to wrap up your essay. Avoid summarizing the main points of your critical analysis unless your essay is so long that readers might have forgotten parts of it.

In “Success is counted sweetest” Dickinson cleverly upends the reader’s usual thoughts about success through her unexpected use of metaphors. The poem may be short, but Dickinson conveys a serious theme in just a few carefully chosen words.

What type of language should be used in a critical analysis essay?

Because critical analysis papers are written in an academic setting, you should use formal language, which means:

  • No contractions
  • Avoid first-person pronouns (I, we, me)

Do not include phrases such as “in my opinion” or “I think”. In a critical analysis, the reader already assumes that the claims are your opinions.

Your instructor may have specific guidelines for the writing style to use. If the instructor assigns a style guide for the class, be sure to use the guidelines in the style manual in your writing.

Additional t ips for writing a critical analysis essay

To conclude this article, here are some additional tips for writing a critical analysis essay:

  • Give yourself plenty of time to read the source material. If you have time, read through the text once to get the gist and a second time to take notes.
  • Outlining your essay can help you save time. You don’t have to stick exactly to the outline though. You can change it as needed once you start writing.
  • Spend the bulk of your writing time working on your thesis and critical analysis. The introduction and conclusion are important, but these sections cannot make up for a weak thesis or critical analysis.
  • Give yourself time between your first draft and your second draft. A day or two away from your essay can make it easier to see what you need to improve.

Frequently Asked Questions about critical analyses

In the introduction of a critical analysis essay, you should give background information on the source that you are analyzing. Be sure to include the author’s name and the title of the work. Your thesis normally goes in the introduction as well.

A critical analysis has four main parts.

  • Introduction

The focus of a critical analysis should be on the work being analyzed rather than on you. This means that you should avoid using first person unless your instructor tells you to do otherwise. Most formal academic writing is written in third person.

How many paragraphs your critical analysis should have depends on the assignment and will most likely be determined by your instructor. However, in general, your critical analysis paper should have three to six paragraphs, unless otherwise stated.

Your critical analysis ends with your conclusion. You should restate the thesis and make closing remarks, but avoid summarizing the main points of your critical analysis unless your essay is so long that readers might have forgotten parts of it.

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Writing a Critical Analysis

What is in this guide, definitions, putting it together, tips and examples of critques.

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This guide is meant to help you understand the basics of writing a critical analysis. A critical analysis is an argument about a particular piece of media. There are typically two parts: (1) identify and explain the argument the author is making, and (2), provide your own argument about that argument. Your instructor may have very specific requirements on how you are to write your critical analysis, so make sure you read your assignment carefully.

critical x analysis

Critical Analysis

A deep approach to your understanding of a piece of media by relating new knowledge to what you already know.

Part 1: Introduction

  • Identify the work being criticized.
  • Present thesis - argument about the work.
  • Preview your argument - what are the steps you will take to prove your argument.

Part 2: Summarize

  • Provide a short summary of the work.
  • Present only what is needed to know to understand your argument.

Part 3: Your Argument

  • This is the bulk of your paper.
  • Provide "sub-arguments" to prove your main argument.
  • Use scholarly articles to back up your argument(s).

Part 4: Conclusion

  • Reflect on  how  you have proven your argument.
  • Point out the  importance  of your argument.
  • Comment on the potential for further research or analysis.
  • Cornell University Library Tips for writing a critical appraisal and analysis of a scholarly article.
  • Queen's University Library How to Critique an Article (Psychology)
  • University of Illinois, Springfield An example of a summary and an evaluation of a research article. This extended example shows the different ways a student can critique and write about an article
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4.3: Body of a Critical Analysis

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  • Stephen V. Poulter
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The Body of a Critical Analysis can be made up of one or more of the Critical Perspectives. What are the Critical Perspectives?

Critical Perspectives

There are generally four ways (or perspectives ) for analyzing a text: writing from the perspective of a reader , writing as if the text is an object of study, writing about or from the perspective of an author , and writing about where a text fits into a particular context .

Assuming you want to use all four of the Critical Perspectives in your essay, the body will have these four major sections:

Reader Analysis: A Reader’s Perspective

Writing from a reader’s perspective means that we seek to understand a text through our own experience, yet we try also to understand how others who may be very different from us seek to understand the same writing through their experience. We will explore this perspective by writing a first impression , writing about favorite lines , as well as writing from different perspectives and through selective reading .

Text Analysis: Text as Object

Writing about the text as an object is a perspective that highlights what makes up that text. We will construct this part of our paper by identifying the patterns , segments , and strategies (devices) in the writing you choose to analyze.

Author Analysis: Understanding Text through Author

Examining whatever we can about an author sometimes gives us another perspective with which to deepen our understanding of the writing we choose. We may look at his or her life, thought processes, behaviors, beliefs , and so on, in order to further understand his or her work.

Context: Text’s Place in History

The fourth perspective from which to view a work has to do with how it fits into a context . This context usually has to do with how a text compares to other texts and works and its effect upon history or society.

The Body of a Critical Analysis is further constructed with patterns in sections under each Perspective:

Reader Analysis patterns:

  • First Impression
  • Favorite Lines
  • Different Perspectives
  • Selective Reading

Text Analysis patterns:

  • Text Strategies
  • Literary Perspectives

Author Analysis patterns:

  • Biographical Information
  • Social Information
  • Literary Information

Context pattern:

  • Historical Information

Note that your instructor may, for example, want only a Reader Response (Reader Analysis) paper, or he or she may want some patterns and not others. However, we will go section-by-section and pattern-by-pattern to create a thorough and complete analysis of a work.


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Critical analysis: home.

  • Reading Critically

What is Critical Analysis?

Analysis is a word that is also often used when taking a critical approach to something. It could be that you look at some evidence and if you think it is good quality, you may choose to include that in your essay or writing to help support your argument. When you have analysed different sets of evidence you may  synthesize all the ideas gathered from multiple sources bringing together the relevant information into a different argument or idea. 

To evaluate something or someone, you think and consider it or them in order to make a judgment about it/them; this could be as simple as how good or bad they are. When you critically evaluate something or someone you consider how judgments vary from different perspectives and how some judgments are stronger than others. This often means creating an objective, reasoned argument for your overall case, based on the evaluation from different perspectives.

Taking a critical approach when you are studying involves constantly asking questions and keeping an open mind.

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This LibGuide introduces you to critical analysis, one of the most important aspects of studying at university, but also one of the most difficult to understand. This guide is designed to provide a conceptual overview of critical analysis, along with related concepts like evaluation, and then to give more practical guidance on how to introduce more critical thinking into your studies. 

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  • Introduction
  • Chapter 1: Humanistic Thinking
  • Deep Comprehension
  • Literature Toolkit
  • Poetry Toolkit
  • Visual Art Toolkit
  • Music Toolkit

Critical Analysis

  • Elements of Critical Analysis
  • Analyzing Arguments
  • Identifying Fallacies
  • Meaningful Contribution
  • Chapter 2: Growth, Obstacles, and Grit
  • The Garden of Eden
  • "Paradise Lost" by John Milton
  • "Invictus" by William Ernest Henley
  • Sonnet 116 by William Shakespeare
  • "Christ in the Storm on the Sea of Galilee," Rembrandt van Rijn
  • Chapter 3: Individual, Collective, and Identity
  • Republic, Plato
  • Apology, Plato
  • The Nicomachean Ethics, Aristotle
  • "Misery" by Anton Chekhov
  • "I am!" by John Clare
  • "Good Friday" by Christina Rossetti
  • "On a Columnar Self" by Emily Dickinson
  • "A Bar at the Folies-Bergère" by Édouard Manet
  • "Melancholy" by Edvard Munch
  • Chapter 4: Time, Memory, and Impermanence
  • "Now I Become Myself" by May Sarton
  • "The World is Too Much With Us" by William Wordsworth
  • "I Wandered Lonely as a Cloud" by William Wordsworth
  • "Loveliest of Trees" by A. E. Houseman
  • "Impression, Sunrise" by Claude Monet
  • "The Unanswered Question" by Charles Ives
  • Byzantine Iconoclasm
  • Christ as the Good Shepherd from the Mausoleum of Galla Placidia
  • The Lamentation from the Church of Saint Panteleimon
  • The Christ Pantocrator from St. Catherine's Monastery
  • Apse Semi-Dome of the Basilica of Sant'Appolinare
  • The Crucifixion of St. Catherine's Monastery
  • The Holy Doors Diptych: Annunciation from St. Catherine's Monastery
  • Virgin (Theotokos) and Child between Saints Theodore and George from St. Catherine's Monastery
  • Emperor Justinian Mosaic from San Vitale
  • Ontological Exploration on Virtue 1
  • Chapter 5: Life, Death, and Loss
  • "The Story of an Hour" by Kate Chopin
  • "To Autumn" by John Keats
  • "When I am dead, my dearest" by Christina Rossetti
  • "To Be or Not to Be," Hamlet by William Shakespeare
  • "Crossing the Bar" by Alfred Lord Tennyson
  • "Death, be not proud" by John Donne
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  • Chapter 6: Faith, Knowledge, and Inquiry
  • An Overview of the Trial of Galileo
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  • Beyond Good and Evil by Friedrich Nietzche
  • Truth—Is as Old as God— by Emily Dickinson
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  • We Shall Fight on the Beaches, Winston Churchill
  • "Quit India" by Mahatma Gandhi
  • The Lives of the Artists by Giorgio Vasari
  • Heiligenstadt Testament, Ludwig van Beethoven
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critical x analysis

Once you have gained the skills for deep comprehension, that you not only understand an idea, topic, or object superficially but in its complexity and can articulate that complexity to others, the next step is to understand critical analysis. Whereas deep comprehension is essentially the process of absorbing and recalling information (albeit very subtle and nuanced), critical analysis involves putting pressure on that information to test its integrity. In this stage, you begin to categorize the claims you have deeply comprehended by their truth or soundness.

To illustrate this point, let's look at an example.

Imagine that you have discovered a cave filled with treasures that appear to be from a lost civilization. Because you are equipped with the skills of deep comprehension, you begin to look carefully at each object, ensuring you absorb as much information as you can from each one. You find works of art and literature with nuanced meanings with subtexts that might be missed without your careful attention. But, at some point, an important and serious question begins to form in your mind. "Where did all of this come from?" "How do I know this is really from a lost civilization, not some elaborate and well-crafted hoax?" To answer these questions, you must engage in critical analysis. You return to each object (with which you are intimately familiar) and begin to ask different questions of each one. Instead of asking, "What does it mean" or "How does it transmit meaning?" you begin asking questions, like, "Are the claims this object makes (that it is from a lost civilization) logical?" and "Is there anything about this object that makes its arguments weak?" And so you begin. You rigorously test each object for coherence and consistency until you have uncovered enough evidence that you are convinced whether or not to believe the contents of the treasure hoard. 

This is the difference between deep comprehension and critical analysis. The first aims to understand the meaning, and the second aims to evaluate that meaning's worth. To do that, we need to understand the elements or the tools to use to put pressure on claims. Then we need to identify the core of the  argument , often called the premise. Finally, we must vigilantly beware of logical fallacies , accepted claims that distort an argument and make it appear to be sound when it is, in fact, not. 

This content is provided to you freely by BYU Open Learning Network.

Access it online or download it at .

critical x analysis

Y = f(x) Roadmap: Telling the DMAIC Story Using Xs and Ys

Published: February 26, 2010 by Arne Buthmann

critical x analysis

With its DMAIC (Define, Measure, Analyze, Improve, Control) roadmap, the Six Sigma methodology provides a structured and systematic approach to solve business and process problems. The related toolkit is a selection of proven tools and methods that– correctly applied – helps to determine, analyze and improve a problem. All well and good, however, inexperienced or newly trained Green Belts and Belt Belts tend to lose themselves in the application of individual tools. Each tool is used separately and sequentially rather than in the context of the overall purpose of the DMAIC approach.

In the worst case, Green Belts and Black Belts are just completing templates and do not achieve the desired outcome of a significantly improved process. An excellent way to overcome this problem is to always keep the concept of Y = f (x) in mind when applying specific tools along DMAIC phases. Here is the Y = f(x) story, phase by phase.

Y = f(x) : Process Outcome a Result of Process Inputs

The mathematical term Y = f(x) , which translates as simply “ Y is a function of x,” illustrates the idea that the important process outcomes ( Y s) are a result of the drivers ( x ‘s) within processes. The goal of DMAIC is to identify which few process and input variables mainly influence the process output measures. Each DMAIC phase can therefore be described by how it contributes to this goal:

  • Define: Understand the project Y and how to measure it.
  • Measure: Prioritize potential x ‘s and measure x ‘s and Y .
  • Analyze: Test x – Y relationships and verify/quantify important x ‘s.
  • Improve: Implement solutions to improve Y and address important x ‘s.
  • Control: Monitor important x ‘s and the Y over time.

Define: Understand Project Y and How to Measure It

Many projects start with a rather unspecific and undefined business or process problem. It is obvious that something has to be done, but where exactly to start and what exactly to achieve is often only poorly described. Multiple tools are used during the Define phase to get a clear understanding of the project Y ( i.e., what the process problem is in measurable terms and what the project goals are).

The project charter delivers the Y by clearly stating what the business or process problem is. It also expresses the Y as a measurable process metric that tells how well the process is performing today (the baseline) and how performance should be after process improvement (the goal). However, in order to reach this clear definition of the Y , the voice of the customer (VOC) and a SIPOC diagram are needed. The voice of the customer helps to define a measurable project Y by translating unspecific customer requirements into measurable critical-to-quality elements (also known as CTQs, which is another term for the Y ). In addition, VOC is used to verify the importance of the Y metric and to set specifications for the Y under consideration. The SIPOC (suppliers, inputs, process, outputs, customers) diagram clearly links the project Y to the process output. The output column of the SIPOC shows which Y is a result of the process.

Since the output column usually shows multiple Y s, VOC is again needed to determine which Y should be included in the project. In the input column, the SIPOC provides a list of potential X s.

The business case finally links the project Y to the so called “Big Y .” This means it shows how achieving the project Y contributes to higher-level business objectives like financial targets, customer satisfaction or strategically relevant goals (on time to market, on-time delivery, inventory level, etc.). The project team can close the Define phase when it has a measurable, clearly defined Y with set specifications that help to distinguish between desired and not desired process performance.

Measure: Prioritize Potential Xs, and Measure X’s and Y

The Measure phase usually starts with a fishbone diagram and/or a detailed process mapping. Given the clearly defined Y from the Define phase, the fishbone helps to identify all potential causes ( x ‘s) of this Y ; the detailed process mapping also shows which process x ‘s mostly influence the process Y . At the end of this step, the project team should have a full picture of potential x ‘s that it might next have to reduce to a manageable and measurable few. The prioritization matrix or simple multi-voting techniques help to achieve this.

It is always important to remember that the brainstorming, as well as the reduction of potential x ‘s, happens based on process expertise, not yet on facts and data. As the next step, the team sets up a data collection plan that allows for measuring both x ‘s and Y in such a way that the data collected can later be used to identify cause-and-effect (i.e., x – Y ) relationships with the help of graphical and statistical tools. Of course, for all x ‘s and Y s to be measured, an operational definition and – if possible – a gage R&R study should be conducted in order to guarantee reliable data.

Having the x ‘s and Y data collected, the team would now start identifying patterns in data. Usually control charts, time series plots, and frequency plots are used to separate common from special cause variation. X ‘s that influence special cause variation are identified, and if they can be explained and avoided in the future, they are removed from the data set. Additionally, Pareto analyses where the Y is stratified by categories of one  x help to further scope the project. The final step in the Measure phase is to determine the baseline capability of the process Y : Yield, C pk or process sigma values indicate how well the process Y is performing today. This also sometimes leads to re-setting the initially stated goals in the project charter.

The Measure phase ends with related data for the Y and the most important x ‘s, where x ‘s of special cause variation have already been removed from the data set.

Analyze: Test X-Y Relationships and Verify/Quantify Important X’s

In terms of x ‘s and Y s, the Analyze phase is quite simple: All graphical tools (e.g., stratified frequency plots, pie charts, scatter plots, etc.) and statistical tools (hypothesis tests, regression analysis, design of experiments) that Green Belts and Black Belts learn during training have just one goal: Verifying and quantifying x – Y relationships. The large number of different tools available is simply because different data types (continuous or discrete) of x and Y require different tools, as illustrated in the figure below. In addition to this data door, the tools of the process door (waste analysis, value-added analysis) supplement the quantitative data analysis with a more qualitative analysis and confirmation of important process x ‘s.

At the end of the Analyze phase, the critical few x ‘s that contribute most to the problem of the process Y are known.

Improve: Implement Solutions to Improve Y, Address Important Xs

Analog to the Measure phase, the Improve phase also starts with getting a full picture. This time it is a full picture of potential solutions that – by addressing the critical few x ‘s – can help improve the Y . Brainstorming and creativity techniques help to generate these potential solutions. In order to reduce these solutions to those that should be implemented, each solution is rated against specific criteria. Two important criteria are how much a solution contributes to improving the Y and how much it addresses specific x ‘s. (Of course other criteria, like easiness of implementation, costs, etc., also are important.) Before starting the implementation of the improved process, a failure modes and effect analysis helps to identify ways that the process Y can fail and the potential causes (newly or previously identified x ‘s) and how to prevent these failures from happening.

At the end of the Improve phase, short-term data (e.g., from a pilot program) demonstrates that the identified solution or solution package has really improved the Y .

Control: Monitor the Y and Important X s Over Time

The Control phase ensures that the new performance of the Y is sustained over time. In order to achieve this, a process management chart is developed that shows the new process flow, offers critical check points during the process, and has recommended actions in case the process does not continue on target. In a process management chart, the previously identified x ‘s are called leading indicators (i.e., checkpoints during the process) and the Y is the lagging indicator (i.e., the final checkpoint at the end of a process cycle). Additionally, a performance measurement and monitoring system or dashboard is established that helps the process owner to measure and control the critical leading ( x ‘s) and lagging ( Y ) indicators on a continuous base. Control charts are again the best tool to show the performance of the Y over time.

After the handover of these tools to the process owner, the project is closed by evaluating the achieved results in terms of x ‘s that were identified and the improvement in the Y .

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For further queries or assistance in writing a critical analysis email Bill Wrigley .

What do you critically analyse?

In a critical analysis you do not express your own opinion or views on the topic. You need to develop your thesis, position or stance on the topic from the views and research of others . In academic writing you critically analyse other researchers’:

  • concepts, terms
  • viewpoints, arguments, positions
  • methodologies, approaches
  • research results and conclusions

This means weighing up the strength of the arguments or research support on the topic, and deciding who or what has the more or stronger weight of evidence or support.

Therefore, your thesis argues, with evidence, why a particular theory, concept, viewpoint, methodology, or research result(s) is/are stronger, more sound, or more advantageous than others.

What does ‘analysis’ mean?

A critical analysis means analysing or breaking down the parts of the literature and grouping these into themes, patterns or trends.

In an analysis you need to:

1. Identify and separate out the parts of the topic by grouping the various key theories, main concepts, the main arguments or ideas, and the key research results and conclusions on the topic into themes, patterns or trends of agreement , dispute and omission .

2. Discuss each of these parts by explaining:

i. the areas of agreement/consensus, or similarity

ii. the issues or controversies: in dispute or debate, areas of difference

ii. the omissions, gaps, or areas that are under-researched

3. Discuss the relationship between these parts

4. Examine how each contributes to the whole topic

5. Make conclusions about their significance or importance in the topic

What does ‘critical’ mean?

A critical analysis does not mean writing angry, rude or disrespectful comments, or  expressing your views in judgmental terms of black and white, good and bad, or right and wrong.

To be critical, or to critique, means to evaluate . Therefore, to write critically in an academic analysis means to:

  • judge the quality, significance or worth of the theories, concepts, viewpoints, methodologies, and research results
  • evaluate in a fair and balanced manner
  • avoid extreme or emotional language

strengths and weaknesses computer keys showing performance or an

  • strengths, advantages, benefits, gains, or improvements
  • disadvantages, weaknesses, shortcomings, limitations, or drawbacks

How to critically analyse a theory, model or framework

The evaluative words used most often to refer to theory, model or framework are a sound theory or a strong theory.

The table below summarizes the criteria for judging the strengths and weaknesses of a theory:

  • comprehensive
  • empirically supported
  • parsimonious

Evaluating a Theory, Model or Framework

The table below lists the criteria for the strengths and their corresponding weaknesses that are usually considered in a theory.

Critical analysis examples of theories

The following sentences are examples of the phrases used to explain strengths and weaknesses.

Smith’s (2005) theory appears up to date, practical and applicable across many divergent settings.

Brown’s (2010) theory, although parsimonious and logical, lacks a sufficient body of evidence to support its propositions and predictions

Little scientific evidence has been presented to support the premises of this theory.

One of the limitations with this theory is that it does not explain why…

A significant strength of this model is that it takes into account …

The propositions of this model appear unambiguous and logical.

A key problem with this framework is the conceptual inconsistency between ….

How to critically analyse a concept

The table below summarizes the criteria for judging the strengths and weaknesses of a concept:

  • key variables identified
  • clear and well-defined

Evaluating Concepts

Critical analysis examples of concepts

Many researchers have used the concept of control in different ways.

There is little consensus about what constitutes automaticity.

Putting forth a very general definition of motivation means that it is possible that any behaviour could be included.

The concept of global education lacks clarity, is imprecisely defined and is overly complex.

Some have questioned the usefulness of resilience as a concept because it has been used so often and in so many contexts.

Research suggests that the concept of preoperative fasting is an outdated clinical approach.

How to critically analyse arguments, viewpoints or ideas

The table below summarizes the criteria for judging the strengths and weaknesses of an argument, viewpoint or idea:

  • reasons support the argument
  • argument is substantiated by evidence
  • evidence for the argument is relevant
  • evidence for the argument is unbiased, sufficient and important
  • evidence is reputable

Evaluating Arguments, Views or Ideas

Critical analysis examples of arguments, viewpoints or ideas

The validity of this argument is questionable as there is insufficient evidence to support it.

Many writers have challenged Jones’ claim on the grounds that …….

This argument fails to draw on the evidence of others in the field.

This explanation is incomplete because it does not explain why…

The key problem with this explanation is that ……

The existing accounts fail to resolve the contradiction between …

However, there is an inconsistency with this argument. The inconsistency lies in…

Although this argument has been proposed by some, it lacks justification.

However, the body of evidence showing that… contradicts this argument.

How to critically analyse a methodology

The table below provides the criteria for judging the strengths and weaknesses of methodology.

An evaluation of a methodology usually involves a critical analysis of its main sections:

design; sampling (participants); measurement tools and materials; procedure

  • design tests the hypotheses or research questions
  • method valid and reliable
  • potential bias or measurement error, and confounding variables addressed
  • method allows results to be generalized
  • representative sampling of cohort and phenomena; sufficient response rate
  • valid and reliable measurement tools
  • valid and reliable procedure
  • method clear and detailed to allow replication

Evaluating a Methodology

Critical analysis examples of a methodology

The unrepresentativeness of the sample makes these results misleading.

The presence of unmeasured variables in this study limits the interpretation of the results.

Other, unmeasured confounding variables may be influencing this association.

The interpretation of the data requires caution because the effect of confounding variables was not taken into account.

The insufficient control of several response biases in this study means the results are likely to be unreliable.

Although this correlational study shows association between the variables, it does not establish a causal relationship.

Taken together, the methodological shortcomings of this study suggest the need for serious caution in the meaningful interpretation of the study’s results.

How to critically analyse research results and conclusions

The table below provides the criteria for judging the strengths and weaknesses of research results and conclusions:

  • appropriate choice and use of statistics
  • correct interpretation of results
  • all results explained
  • alternative explanations considered
  • significance of all results discussed
  • consistency of results with previous research discussed
  • results add to existing understanding or knowledge
  • limitations discussed
  • results clearly explained
  • conclusions consistent with results

Evaluating the Results and Conclusions

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Critical analysis

What is "critical analysis".

"Critical analysis" is a desirable skill in all aspects of your university work, but what actually is it? As Brown and Keely discuss, analysing critically is a process of deconstructing what you read, write and listen to in a rational and logical manner (2012). It requires you to move beyond describing and analysing to evaluating, criticising and postulating on what you process.

However, while you are encouraged to critique, your response always has to be informed and well-grounded in research and wide reading. Critical analysis moves beyond simple description of a particular topic into the realms of analysis and evaluation, as visualised in the diagram below:

critical x analysis

Image transcription

Description: Who? What? Where? When?

Analysis: How? Why?

Evaluation: So What? What If? What Next?

As shown in the diagram, description and simple analysis must precede evaluation, which is where critical analysis lies. With your evaluative skills you must be able to ask yourself what all the description and analysis actually means, what it says about the author or topic and what its implications are.

Critical analysis is associated with a "deep approach" to your learning, which means that you relate new knowledge to what you already know. It also requires the examination of theoretical concepts and ideas; comparing and contrasting issues and perspectives to challenge your own understandings and to speculate and seek out implications. Furthermore, you must be able to distinguish between what is evidence and what is an argument. This involves questioning assumptions, recognising generalisations, and identifying bias in what you see, read and hear. Thinking critically helps you to uncover links across large and diverse bodies of knowledge enabling you to synthesise your own informed ideas.

Why is it so important?

At university, it is essential to think critically as it allows you to understand and analyse the evidence, ideas and claims within your particular field of study. Critical analysis allows you to have greater clarity on the issues and information you process. Academic disciplines are kept alive through constant reflection, debate and refinement of ideas. Critical analysis is thus crucial to the survival and renewal of all fields of enquiry.

How do I start to think and analyse "critically"?

In an academic context, critical analysis requires you to do the following in all your endeavours:

  • Provide informed reasoning backed by evidence and ideas from trustworthy academic resources such as books and peer-reviewed journal articles.
  • Identify context, background and/or bias that may lead to distortion within what you read and hear.
  • Identify and question unfounded assumptions.
  • Explain the significance and consequences of particular data, arguments and conclusions made by others (Drew & Bingham 2001, pp. 281 - 282)

Questions to ask when critically analysing information

  • What do I already know?
  • What do I need to work out?
  • Is this fact or opinion?
  • What evidence do they use to back their claim?
  • What are the stated and unstated assumptions in this information?
  • Are there other ways we can think about this?
  • Is it convincing and relevant?

Further resources

  • What is critical thinking (PDF)
  • How to read and take notes critically (PDF)
  • How to write critically (PDF)
  • Effective Reading
  • Peer-assessment & Self-evaluation

Browne, M & Keeley, S 2012, Asking the right questions: a guide to critical thinking, 10th edn, Prentice-Hall, Upper Saddle River, NJ. Drew, S & Bingham, R 2001, The Student Skills Guide, 2nd edn, Gower, Aldershot, UK.

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Critical analysis

What is it.

Critical analysis is the in-depth examination of an argument, situation, or problem, once it has been broken down into different parts. We critically analyse things for many reasons, such as checking for accuracy, forming our own opinions, understanding and improving a situation or process, solving problems, and making decisions. To do this, we use analytical thinking skills.

When we critically analyse an argument, situation, or problem, we examine the components of information, which might be in the form of text, numbers, images, or procedures. We systematically break down and interpret these components, examining them individually and looking at the relationships between them. The insights gained from this process give us the understanding we need to then critically evaluate the whole. This is called analytical thinking.

Critical analysis is one step in a critical thinking process which includes first gathering information, then critically analysing and evaluating it, and then making a decision.

critical x analysis

Analytical thinking in everyday life

While the phrase ‘analytical thinking’ may sound daunting, we actually do this sort of thinking in our everyday lives when we brainstorm, budget, detect patterns, plan, compare, do puzzles, play games, and make decisions based on multiple sources of information.

Think of the consideration that goes into the logistics of planning a birthday dinner — who to invite, what to cook, what music to play, space for everyone, invitation messages.

And if you’ve ever created a budget for yourself, you probably broke down expenses and spending into categories like bills, repayments, holiday savings, transport costs, groceries, streaming services, clothing, and avocados. Then, you thought about where you might be able to reduce costs and where you couldn’t. In other words, you analysed your finances!

Critical analysis at university

Whatever you’re studying, analytical skills will be highly beneficial at university. Through analysis, you gain the information you need to evaluate information, which leads to deeper understanding.

Depending on your discipline, you might need to analyse things like:

  • scientific data
  • legal case studies
  • historical events
  • political policies
  • mathematical theorems.

You’ll use critical analysis in your assessments, whether they’re essays, reports, reviews, proposals, research articles, reflective tasks, presentations, or portfolios.

When reading or writing about other people’s theories and arguments, you’ll likely need to complete an argument analysis. This involves examining the structure, validity, and effectiveness of arguments presented in various forms of discourse (like essays, academic articles, interviews, marketing copy, and speeches).

Critical analysis in the workplace

Employers specifically look for candidates with analytical skills because they need to know employees can use clear and logical thinking to resolve conflicts. Some industries even have specific, structured analyses that professionals in those fields need to understand in order to do their jobs, such as a cost analysis, risk analysis, or environmental impact analysis.

Here are some examples of the type of critical analyses professionals in different industries might need to do:

Starting your analysis: identifying the component parts

Component parts refer to the separate elements of an argument, situation, or problem. This might include the evidence provided, the people involved, the weather, market fluctuations, or any number of other characteristics of the situation you’re examining. If you don’t identify all the parts, you risk ignoring a critical element when you form your opinion or offer a solution.

Critically analysing an argument

When you come across an argument, you might immediately have an opinion. However, in order for you to get a comprehensive understanding of the accuracy of the argument, and explain your logic to others, you first need to critically analyse the argument by looking at its component parts.

To learn more about argument analysis, check out this tutorial on RMIT Learning Lab which includes pages on the key steps to analysing an argument, identifying strong and weak evidence and persuasive language techniques, and includes examples of argument analyses.

Critically analysing a process

Breaking something down into its component parts isn’t just used for arguments. We can also use it to analyse problems and find the root causes of issues with processes and services.

Here’s an example:

Sarawut, a nutrition consultant, has been hired by an aged care facility to review their nutritional assessment process. There are concerns that the current process isn’t adequately addressing the individual dietary needs of residents and may be negatively affecting wellbeing and nutrition.

Sarawut’s task is to provide advice on how the facility can improve the process to meet the specific needs of the residents and promote good health. Before he can offer any recommendations, he needs to find the flaws in the process. Here are some of the component parts that Sarawut plans to analyse:

  • Current assessment procedures: Sarawut will review how nutritional assessments for residents entering the facility have been conducted up until now. He’ll consider how comprehensive the information is and whether it meets public health guidelines. He’ll examine the initial procedures to see where there may be flaws.
  • Tools used to assess nutrition: He will consider the tools they use to screen nutrition, how sensitive they are, check that they’re working properly, are well maintained and modern. This will help him understand whether the staff have accurate information about the nutritional health of the residents.
  • Current dietary plan procedures: These plans are formulated for residents based on their initial assessment, so if the assessment is flawed, the dietary plans are, too. Sarawut will investigate how the plans are developed and the level of personalisation and research that goes into them. He’ll also consider how often those plans are monitored or updated.
  • Staff awareness and training: It’s the staff members who carry out the process that Sarawut is analysing and improving. He needs to check their understanding of the assessment process, make sure they’ve received adequate training, and find out how well equipped they are to address the nutritional concerns of the residents.
  • Communication between health professionals: It’s important for Sarawut to evaluate the communication between staff at the facility. Are they sharing relevant information regarding the residents’ health and nutrition through the right channels? A breakdown in communication about a resident’s health could have serious consequences.

In addition to the five mentioned above, there are some more component parts on Sarawut’s list.

Can you think of anything else he should examine in order to get a comprehensive understanding of the facility’s nutritional assessment process?

Expand the section below for examples:

Now that you know how thinking analytically can help identify problems in a process or service, check out the case study below, which demonstrates how this approach can lead to innovative solutions.

Analytical thinking solves problems – a case study

In the 1960s, companies in the US didn’t have a fast, reliable, and cost-effective way to deliver urgent documents or packages. The standard mail system was slow but inexpensive, and the only alternative was a private courier, which was prohibitively expensive. That’s when Frederick W. Smith came up with the idea of a national, overnight delivery service as a part of an assignment in his undergraduate economics class at Yale University.

As the story goes, Smith received only an average grade, evidently his professor wasn’t all that impressed with the concept, but after critically analysing the current system, thinking through his original ideas more fully, and refining his business plan, Smith launched FedEx — now the largest, global, overnight delivery service in the world.

Thinking can create change and always has. As with Smith’s overnight delivery service, any service we now use and any problem we may still face provides thinkers with opportunities to critically reflect and use analytical thinking to generate solutions and viable options for improvement.

Source Bloomberg Business Week. (2004). Online extra: Fred Smith on the birth of FedEx.

Reflect on your own analytical thinking

As we mentioned at the start of this page, critical analysis is an important step in a critical thinking process. To continue building your skills check out the following page in this chapter to learn about the next step: evaluating information critically.

This page includes content adapted from Analytical Thinking by OpenStax (original) and Kristin Conlin, licensed under a CC BY-NC-SA 4.0, except where otherwise noted.

Key Transferable Skills Copyright © 2024 by RMIT University Library is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Mathematics > Analysis of PDEs

Title: on the number of bound states for fractional schr{ö}dinger operators with critical and super-critical exponent.

Abstract: We study the number $N_{<0}(H_s)$ of negative eigenvalues, counting multiplicities, of the fractional Schrödinger operator $H_s=(-\Delta)^s-V(x)$ on $L^2(\mathbb{R}^d)$, for any $d\ge1$ and $s\ge d/2$. We prove a bound on $N_{<0}(H_s)$ which depends on $s-d/2$ being either an integer or not, the critical case $s=d/2$ requiring a further analysis. Our proof relies on a splitting of the Birman-Schwinger operator associated to this spectral problem into low- and high-energies parts, a projection of the low-energies part onto a suitable subspace, and, in the critical case $s=d/2$, a Cwikel-type estimate in the weak trace ideal $\mathcal{L}^{2,\infty}$ to handle the high-energies part.

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Ground State Solutions of Nehari-Pohozaev Type for Schrödinger–Poisson–Slater Equation with Zero Mass and Critical Growth

  • Published: 09 May 2024
  • Volume 34 , article number  221 , ( 2024 )

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  • Yu Gu 1 &
  • Fangfang Liao 1  

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In this article, we study the Schrödinger–Poisson–Slater type equation with the critical growth and zero mass:

where \(3<p<6\) and \(\mu >0\) . By combining a new perturbation method and the mountain pass theorem, Liu et al. [J. Diff. Eq., 266 (2019), 5912–5941] prove that the above equation has at least one positive ground state solution for \(p \in (4, 6)\) and \(\mu >0\) or \(p \in (3, 4]\) if \(\mu \) is sufficiently large. By using a much simpler method than the ones used in the above mentioned paper, together with subtle estimates and analyses, we obtain better results on the existence for a ground state solution of Nehari-Pohozaev type.

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Ground State and Sign-Changing Solutions for Critical Schrödinger–Poisson System with Lower Order Perturbation

Ground state sign-changing solution for schrödinger-poisson system with critical growth, ground state solutions of nehari-pohozaev type for a fractional schrödinger-poisson system with critical growth, data availability.

There are no relevant data in our paper.

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How to Use Z Critical Value Calculator in Excel – Step by Step Guide

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Navigating statistical analysis in Microsoft Excel requires a grasp of crucial concepts like the Z critical value. This value acts as a threshold for statistical significance, guiding your interpretation of data in the realm of standard normal distributions. Whether you’re delving into research, business analysis, or any field reliant on data-driven decisions, understanding how to use Z critical value calculator is indispensable.

Key Takeaways:

  • Significance Threshold: The Z critical value sets the boundary for determining whether your results are statistically significant, aiding in decision-making processes.
  • Standardization with Z Scores: Z scores offer a standardized way to compare data points across different scales, facilitating insightful analysis regardless of original units of measurement.
  • Calculation in Excel: Excel’s built-in functions, like NORM.S.INV, streamline the process of computing Z critical values, providing a user-friendly platform for statistical analysis.
  • Interpretation Insights: Interpreting Z critical values accurately is crucial; they indicate the significance of test results within the chosen confidence level, guiding your conclusions.

Table of Contents

Introduction to Z Critical Value in Excel

Understanding the z critical value.

When you dive into the world of statistics , certain terms might seem confusing at first, but they’re crucial for precise data analysis. One such term is the Z critical value, which is what statisticians refer to when they’re dealing with standard normal distributions.

In simpler terms, it’s the threshold at which your results can be considered statistically significant. It helps you understand the ‘rareness’ of the result within the context of your data. If you’re someone who regularly uses Excel for statistical analysis, knowing how to find the Z critical value is an essential skill.

The Importance of Z Scores in Statistical Analysis

In statistical analysis, Z scores are incredibly important. They provide a clear, standardized method of comparison between different data points or sets. A Z score expresses the number of standard deviations a data point is from the mean. By converting raw scores into Z scores, you can understand a data point’s position relative to the overall dataset irrespective of the original units of measurement.

This becomes particularly useful in scenarios where you are comparing scores from different tests or measurements that may not use the same scale. With Z scores, these disparate sets of data can be normalized, enabling you to compare apples to oranges, so to speak. Additionally, Z scores are used in various statistical tests, such as the Z-test, to assess whether there is a significant difference between sample and population means.

Understanding Z scores equips you with the ability to identify outliers, understand the data distribution, and make informed decisions backed by statistics. Given the utility and versatility of Z scores, it’s evident why they are a cornerstone in the world of analytics.

Getting Started with Your Z Critical Value Calculator

Requirements for using a z critical value calculator in excel.

Before you jump into calculating the Z critical value in Excel, there are a few prerequisites. First and foremost, you need a version of Excel that supports the statistical functions you’re planning to use. This usually means having the latest updates installed, which will ensure access to all the necessary features.

Second, a little background in statistics can go a long way. At a minimum, you should understand what a Z critical value is and why it’s significant for your analysis. You should also be familiar with terms like “confidence level,” “standard deviation,” and “mean” as they are key components of the calculation.

Lastly, ensure your data is ready for analysis. This means it should be inputted into Excel in a clean, organized manner – no missing values, and ideally, in a single column or row for easy reference. With these requirements in place, you’ll be set to compute the Z critical value smoothly and with confidence.

Step-by-Step Guide to Accessing the Functions

If you’ve got your data organized and a grasp on the basics of Z scores, accessing the functions in Excel needed for calculating the Z critical value is your next step. Here’s how to do just that:

STEP 1: Click on the cell where you would like to display your Z critical value.

Z Critical Value Calculator

STEP 2: Now, go to the ‘Formulas’ tab on Excel’s Ribbon, which is the toolbar you see at the top of Excel’s interface.

Z Critical Value Calculator

STEP 3: From there, look for the ‘Function Library’ group – this is where you’ll find built-in functions for various forms of analysis. Click on ‘More Functions,’ then hover over ‘Statistical’ to see a dropdown list of statistical functions.

Z Critical Value Calculator

STEP 4: From the list, you will choose the function that corresponds to the Z critical value calculation; often, this is the ‘NORM.S.INV’ or ‘NORM.INV,’ depending on the specific analysis you’re conducting.

Z Critical Value Calculator

Remember that different versions of Excel may use slightly different paths or names for these functions. If you’re in doubt, the search feature in Excel’s ‘Help’ menu can be a quick way to find the proper function and how to use it for your version of Excel.

Calculating Z Critical Value: A Step-by-Step Process

Inputting data: where and how to start.

When you’re ready to calculate the Z critical value, your data must be accessible and neatly aligned. First things first – input your data. Usually, it’s best to place your data set in a single column for clarity and ease of use. Make sure there are no gaps or non-numeric entries that could skew your calculations.

After your data is in place, you need to define the significance level (alpha, α) for your analysis. This is the probability of rejecting the null hypothesis when it is actually true, and it’s commonly set at 0.05 for a 95% confidence level. However, the level you choose may vary based on the standards of your field or the specific requirements of your analysis.

With the significance level determined, you can now calculate the Z score that corresponds to that level. In Excel, you’ll likely use the NORM.S.INV function for this purpose. Here’s how you start:

STEP 1: Click on an empty cell where you want the Z critical value to appear.

Z Critical Value Calculator

STEP 2: Enter “=NORM.S.INV(α)” into the cell, replacing α with your chosen significance level. Press ‘Enter,’ and Excel will calculate the Z critical value for you.

Z Critical Value Calculator

If you’re conducting a right-tailed test with a 95% confidence level, use this formula –


Z Critical Value Calculator

If you’re conducting a two-tailed test with a 95% confidence level, replace α with 0.025 (since each tail represents 2.5% of the total area under the curve).

Z Critical Value Calculator

Remember, precise data input is key. Any error in your data could lead to incorrect conclusions, so take your time and check your work. With these steps, you’ve made headway in your statistical analysis using Excel.

Making Sense of Your Results

Interpreting z critical values in excel.

Once you’ve calculated the Z critical values in Excel, interpreting them correctly is essential to drawing accurate conclusions from your data. These values serve as the thresholds which determine the significance of your test results. Here’s what you need to keep in mind:

  • If your Z test statistic exceeds the Z critical value in absolute terms, you would typically reject the null hypothesis. This would indicate that the test result is statistically significant, meaning it is unlikely to have occurred by random chance.
  • In a one-tailed test, you compare your test statistic to one critical value on either the left or the right tail of the distribution, depending on your hypothesis.
  • For a two-tailed test, you have two critical values to consider, corresponding to both tails. Your test statistic should fall outside of these two values to be considered significant.

Always remember that the Z critical value is connected to the confidence interval you chose. The more stringent the confidence level (like 99% instead of 95%), the farther the Z critical value will be from zero, making it a tougher threshold for your test statistic to exceed.

Interpreting these results in the context of your research enables you to make informed decisions or inferences, so take the time to understand what these numbers are telling you about the data you are analyzing.

Mistakes to Avoid When Using the Z Critical Value Calculator

When using the Z critical value calculator in Excel, accuracy is everything. To reduce the likelihood of errors, here are common mistakes you’ll definitely want to steer clear of:

  • Using The Wrong Function: Make sure to use the appropriate statistical function for calculating Z critical values (NORM.S.INV for standard normal distributions). Using the wrong function will lead to incorrect results.
  • Misplacing the Confidence Level: It’s common to mistakenly input the confidence level percentage rather than the alpha level (significance level) in the function. Remember, alpha is typically 1 minus the confidence level (e.g., for 95% confidence, alpha is 0.05).
  • Incorrect Tail Selection: Confusing one-tailed and two-tailed tests can happen. Ensure you use the correct formula for the type of test you’re conducting; they are not interchangeable.
  • Ignoring Data Range: Not properly extending your function to include the entire range of data can skew results. Confirm that you’ve selected the full dataset before calculating.
  • Data Entry Errors: Double-check all data entered in Excel. Simple mishaps like typos or misplaced decimals can significantly alter your Z critical value and subsequent interpretations.

By avoiding these pitfalls, you can trust your Z critical value calculations to be a solid foundation for your statistical analysis. Remember, these mistakes are not just about Excel proficiency; they also pertain to your grasp of statistical principles.

Practical Applications of Z Critical Values

Examples in real-world scenarios.

Z critical values play an important role in many real-world scenarios, particularly in the fields of business, healthcare, and research:

  • In market research , Z critical values help to determine whether changes in consumer satisfaction scores after a product update are statistically significant or if they could be attributed to chance.
  • The healthcare industry relies on Z critical values to evaluate the effectiveness of new treatments. Researchers may utilize Z scores to decide if the recovery rates in the treatment group are significantly different from the recovery group under standard care.
  • In finance , analysts might use Z critical values to assess whether the average returns on an investment over time are significantly different from the market average, helping to guide investment decisions.

By applying Z critical values to these real-world situations, professionals can make data-driven decisions with greater confidence, mitigating risk and identifying true signals amid the noise.

Enhancing Data Analysis Skills with Z Critical Values

Understanding and utilizing Z Critical Values enhance your data analysis skills by adding depth to your interpretative abilities. When you’re proficient in calculating and interpreting Z scores, you develop a stronger command of the statistical analysis, which allows you to:

  • Make accurate predictions by setting appropriate confidence levels.
  • Quantify the uncertainty in your predictions and estimates.
  • Differentiate between random fluctuations in your data and meaningful patterns that warrant further investigation.
  • Design and evaluate experiments or studies with increased rigor and precision.

By incorporating Z critical values into your analytical toolbox, you’re not just crunching numbers—you’re translating them into actionable insights that can inform strategies and decisions across various domains. Whether you’re in academia, industry, or any field that relies on data, mastering Z critical values is a step toward sharper, more reliable analysis.

Frequently Asked Questions

How do you calculate zscore in excel.

To calculate a Z score in Excel:

  • Input your data in one column.
  • Calculate the mean of your data using the formula: =AVERAGE(range).
  • Calculate the standard deviation with: =STDEV.S(range) for a sample or =STDEV.P(range) for a population.
  • Use the Z score formula: =(X-μ)/σ, replace ‘X’ with the cell of the data point, ‘μ’ with the mean, and ‘σ’ with the standard deviation.

Enter and execute this formula for each data point to get their Z scores.

What Does the Z Critical Value Represent?

The Z critical value represents a threshold in the standard normal distribution beyond which the observed data is considered statistically significant. Specifically, it determines the point at which you would reject the null hypothesis in a hypothesis test based on the chosen confidence level.

How Can I Find Z Critical Value Tables in Excel?

To find Z critical value tables in Excel, you cannot access them directly, but you can calculate Z critical values for specific confidence levels using Excel functions like NORM.S.INV() .

Can I Use Z Critical Values for One-Tailed Tests?

Yes, Z critical values are used in one-tailed tests to determine the significance threshold. You use NORM.S.INV(1-α) for right-tailed tests and NORM.S.INV(α) for left-tailed tests, where ‘α’ is your significance level.

What Are Some Tips for Beginners Calculating Z Critical Values?

For beginners calculating Z critical values:

  • Understand the concept of Z scores and their role in hypothesis testing.
  • Learn the differences between one-tailed and two-tailed tests.
  • Familiarize yourself with Excel’s statistical functions.
  • Start with clean, well-organized data.
  • Practice with different data sets to reinforce your skills.

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John Michaloudis

John Michaloudis is a former accountant and finance analyst at General Electric, a Microsoft MVP since 2020, an Amazon #1 bestselling author of 4 Microsoft Excel books and teacher of Microsoft Excel & Office over at his flagship Academy Online Course .

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Reverse Engineering: Its Critical Role in Computer-Based Forensic Investigations; Bridging Socioeconomic Gaps: An Analysis of Persisting Inequity in the Education System

Educational inequities persist through our modern education system despite efforts to address them, and the gaps between groups of students are growing. Education is viewed as a critical pillar to society and is often perceived as one of the most efficacious equalizers for those under the poverty line. Despite its potential, it now often serves as a barrier instead due to a lack of equal access for students in minority groups and those of a lower socioeconomic (SES) background. The focus of the STS component of this project was to analyze educational inequity and factors that contribute to it. The technical aspect was unrelated to the general research problem, as it followed a CS Capstone approach, where I discussed my experiences in an internship project I partook in. The STS component of the project focuses on persistent inequities in the education system. First, it discusses the roots of inequity, in racial segregation of school systems. It goes on to explain how this inequality evolved into inequity, due to improper distribution of resources throughout the educational system. SES is found to be a factor that is strongly linked with education quality and outcome. A large contributor to SES’s correlative relationship is how it can influence access levels to technology, which in itself has an impact on a student’s education. There are also other struggles lower SES students face that are external stressors. The work goes on to use the Covid 19 Pandemic as a case study of how students of lower SES can be affected disproportionately by those external stressors. Many students lacked access to devices and the internet during the pandemic, which prevented them from completing their schoolwork effectively. Finally, the work examines some case studies of efforts being put forth to address inequity by nonprofit and for-profit companies across the US. My technical component of my project was less research based and more so describing a critical part of my education outside of school. It focused on a Reverse Engineering problem that I was tasked with at an internship I have been participating in for six years. I discussed how I broke down the problem, analyzed it systematically, and rebuilt the functional program by the end. I was tasked with determining the purpose of an unlabeled file. After finding it to be executable and disassembling it, I worked my way through the assembly code, slowly reverse engineering the program to determine its function and purpose. Eventually, I determined the program, and a set of files I found within it, were a corrupted Docker container. I rebuilt the program to a functional state and completed the project. The STS portion of my research does a good job contributing to the broad picture view of educational inequity. It lays out where inequity is stemming from and some of its negative effects; however, I think it should only serve as a starting point for further, more pointed research. It would be beneficial to continue with a higher level of specificity for many of the problems discussed in the original work. For example, when case studies are presented for current efforts in combating inequity, it would be beneficial to develop metrics and analyze how effective each of those efforts had been to compare and contrast them. Such research could lead to increasing the efficacy of the efforts seeking to aid in addressing issues with inequity. The technical component of the project did not embody research; it served more as a project for me to gain experience in my field. With that being said, the project made it clear that there is a need for a program capable of rebuilding Docker containers, something that proved to be painful to do manually. This may serve as grounds for future expansion on the work completed. I am thankful to Professor Peter Norton, who permanently altered my view of my role as an engineer in society and had a massive impact on my education. Professor Norton fostered a unique classroom environment that promoted positive discussion of ethical and social issues from diverse perspectives. He also aided in the preliminary pieces of research for the STS component of this project. I would also like to thank Professor Caitlyn Wylie who provided extensive feedback through multiple drafts of writing the STS research component of this project. That style of writing has never been something that came easily to me; she was extremely helpful in the organization and production of the STS paper. I would finally like to thank Ms. Rosanne Vrugtman, my technical writing instructor, who provided excellent feedback on the drafts of my technical paper.

School of Engineering and Applied Science

Bachelor of Science in Computer Science

Technical Advisor: Briana Morrison

STS Advisor: Caitlin Wylie


Uploaded: May 09, 2024

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