Overview
The Analyze phase converts the baseline from Measure into evidence about causes. Exploratory data analysis uses multi-vari studies to see whether variation is positional, cyclical or temporal, and correlation and simple linear regression to quantify relationships between an input and an output. Hypothesis testing provides the formal decision: setting null and alternative hypotheses, choosing a significance level, and selecting the right test for means, variances or proportions, including paired comparisons, one-way ANOVA and chi-square tests.
The section also covers additional analysis methods: root cause analysis tools such as the 5 whys, cause-and-effect diagrams and fault tree analysis, gap analysis between current and desired states, and waste analysis using lean categories. Candidates must pick valid tests, read p-values and regression output correctly, and keep correlation separate from causation before Improve acts on the findings.
How it's tested
Analyze questions usually present a data situation and ask which test or tool to use, how to state the hypotheses, or how to interpret output such as a p-value, correlation coefficient or R-squared. Expect some short calculations of test statistics or degrees of freedom, and several BEST-tool questions for root cause work.
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Select the right test
The stem describes the data type, number of groups and whether samples are paired, and you choose among t-tests, paired t, ANOVA, F-test, proportion tests and chi-square.
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Interpret the output
A p-value, confidence interval, correlation coefficient or regression equation is given and you decide whether to reject the null hypothesis or what the slope and R-squared mean in plain terms.
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Pick the root cause tool
A team situation, such as many possible causes or a chain of events behind a single failure, asks which tool to use: cause-and-effect diagram, 5 whys, fault tree analysis or Pareto chart.
A team compares defect rates (pass/fail) from three suppliers and asks whether they differ. A candidate reaches for ANOVA because there are three groups. But ANOVA compares means of continuous data; here the data are categorical counts in a supplier-by-outcome table. The correct choice is a chi-square test of independence, which compares observed counts with those expected if supplier and outcome were unrelated.
Topics 3
Official topics from the ASQ outline, in outline order.
4.1 Exploratory data analysisMulti-vari studies, correlation and simple linear regression.
- What it means
- Exploratory data analysis looks for patterns before formal testing. A multi-vari study splits variation into positional (within a part or across machines), cyclical (between consecutive units or batches) and temporal (over time) families. Correlation measures the strength and direction of a linear relationship; simple linear regression fits y = b0 + b1x to predict an output from an input.
- What to understand
- The correlation coefficient r ranges from -1 to +1; R-squared (the coefficient of determination) is the share of variation in y explained by the model, so r = 0.8 gives R-squared = 0.64. The slope b1 is the change in y per unit change in x. Residuals should be random, roughly normal and of constant spread for the model to be trusted.
- How it shows up
- Regression output is given and you interpret the slope, predict a value, or say what share of variation is explained; or a multi-vari chart is described and you name the dominant family of variation.
- Common confusion
- A strong correlation does not prove causation, since a lurking variable can drive both; candidates use r alone to justify changing an input.
4.2 Hypothesis testingHypothesis test logic, errors and power, and tests for means, variances and proportions, paired comparisons, ANOVA and chi-square.
- What it means
- A hypothesis test decides whether observed differences are larger than chance would explain. The null hypothesis states no difference or no effect; the alternative states the difference of interest. The significance level alpha is the accepted risk of a type I error (rejecting a true null); beta is the risk of a type II error (missing a real difference), and power is 1 - beta.
- What to understand
- Reject the null when the p-value is below alpha. Choose the test by data type and design: one- or two-sample t for means, paired t for before-and-after on the same units, F-test for two variances, one-way ANOVA for three or more means, proportion tests for one or two proportions, and chi-square for counts in categories. Larger samples increase power, and practical significance must still be judged.
- How it shows up
- Stems describe a comparison and ask which test fits, how to phrase the hypotheses, or what conclusion follows from a given p-value and alpha.
- Common confusion
- Failing to reject the null is not proof that the null is true; candidates write 'accept the null' and conclude the groups are identical.
4.3 Additional analysis methodsGap analysis, root cause analysis and waste analysis.
- What it means
- Beyond statistics, Analyze uses structured methods to confirm causes. Gap analysis compares current performance with a target or desired state to size what must change. Root cause analysis uses tools such as the 5 whys, cause-and-effect (fishbone) diagrams, fault tree analysis and Pareto charts. Waste analysis applies lean waste categories to find non-value-added time and effort.
- What to understand
- A fishbone diagram organizes many potential causes by category (such as methods, machines, materials, measurement, people and environment) but proves nothing; candidate causes must be verified with data. The 5 whys follows one causal chain; fault tree analysis works top-down from a failure event through AND/OR gates. A Pareto chart focuses effort on the vital few categories.
- How it shows up
- A scenario asks which tool to use after brainstorming many possible causes, or what to do next after building a fishbone diagram, where the answer is to verify the likely causes with data.
- Common confusion
- Candidates treat the top items on a fishbone or a 5 whys chain as confirmed root causes; they remain hypotheses until data confirm them.
High-yield concepts
The terms, rules and formulas this domain turns into questions most often.
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Type I and type II errors
A type I error (alpha risk) rejects a null hypothesis that is true, such as calling a good process changed; a type II error (beta risk) fails to reject a false null, missing a real change.
- Remember
- Power = 1 - beta; for a fixed alpha, increasing sample size raises power and lowers beta.
- Tested as
- Definition and consequence questions, and producer's versus consumer's risk analogies.
- Trap
- Thinking a smaller alpha reduces both errors; with sample size fixed, lowering alpha raises beta.
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p-value decision rule
The p-value is the probability of observing results at least as extreme as the sample if the null hypothesis were true.
- Remember
- If p is less than alpha, reject the null; if p is greater than or equal to alpha, fail to reject it.
- Tested as
- Output-interpretation questions give a p-value and alpha and ask for the conclusion.
- Trap
- Reading the p-value as the probability that the null hypothesis is true.
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Correlation coefficient (r) and R-squared
r measures the strength and direction of a linear relationship from -1 to +1; R-squared = r squared for simple regression and gives the proportion of variation in y explained by x.
- Remember
- r = -0.9 is a stronger relationship than r = +0.6; the sign shows direction only.
- Tested as
- Interpretation of scatter diagrams and regression output.
- Trap
- Treating a strong r as proof that x causes y, or ignoring a curved relationship that r understates.
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Simple linear regression
The least-squares line y = b0 + b1x predicts the output from one input; b1 is the change in y for each one-unit change in x.
- Remember
- Predictions are only reliable inside the range of x values used to build the model.
- Tested as
- Plugging a value into an equation and interpreting the slope or intercept.
- Trap
- Extrapolating far beyond the observed data range.
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Test selection by data type
Continuous outputs use t-tests, ANOVA and F-tests; discrete outputs use proportion tests and chi-square; paired data use the paired t-test.
- Remember
- Two means: two-sample t. Same units before and after: paired t. Three or more means: one-way ANOVA. Two variances: F-test. Counts in categories: chi-square.
- Tested as
- The most common Analyze question pattern.
- Trap
- Running several two-sample t-tests across three groups, which inflates the overall type I error rate.
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One-way ANOVA
ANOVA compares three or more group means by comparing between-group variation to within-group variation; F = mean square between / mean square within.
- Remember
- A significant F says at least one mean differs, not which one; follow-up comparisons identify it.
- Tested as
- Test choice and reading an ANOVA table, including degrees of freedom (k - 1 between, N - k within).
- Trap
- Concluding that all means differ from each other after a significant F.
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Chi-square test
Chi-square = sum of (observed - expected) squared / expected; the test of independence checks whether two categorical variables are related, and goodness-of-fit checks counts against an expected distribution.
- Remember
- Expected count for a cell = row total x column total / grand total; degrees of freedom = (rows - 1) x (columns - 1).
- Tested as
- Contingency-table scenarios and short expected-count calculations.
- Trap
- Using ANOVA on pass/fail counts because there are several groups.
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Paired t-test
Compares the mean of differences measured on the same units under two conditions, such as before and after training for each operator.
- Remember
- Pairing removes unit-to-unit variation and increases power when the pairing is real.
- Tested as
- Before-and-after scenarios on the same parts, people or machines.
- Trap
- Using a two-sample t-test on paired data, which treats the samples as independent and loses power.
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Multi-vari study
A graphical study that separates variation into positional, cyclical and temporal families to show where the largest variation lives.
- Remember
- It narrows the search for causes before detailed testing; it does not prove a cause.
- Tested as
- Interpreting which family of variation dominates and where to look next.
- Trap
- Confusing cyclical (unit-to-unit or batch-to-batch) variation with temporal (time-to-time) variation.
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Root cause analysis tools
The cause-and-effect diagram organizes possible causes by category; the 5 whys traces one chain of causes; fault tree analysis models how events combine through AND/OR logic to produce a failure; a Pareto chart ranks categories by frequency or cost.
- Remember
- These tools generate and focus hypotheses; data must verify the cause before action.
- Tested as
- Tool-choice and next-step questions.
- Trap
- Implementing a fix for the cause named most often in brainstorming without verifying it.
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Statistical vs. practical significance
A statistically significant result shows a difference is unlikely to be chance; practical significance asks whether the difference is large enough to matter to the customer or business.
- Remember
- Very large samples can make tiny, unimportant differences statistically significant.
- Tested as
- Interpretation questions ask what to recommend after a significant but small effect.
- Trap
- Recommending expensive changes for a statistically significant but trivial difference.
Side by side
Concepts candidates mix up, compared on the point that decides the answer.
Two-sample t vs. paired t vs. one-way ANOVA vs. chi-square
| Concept | Meaning | Key difference | Common trap |
|---|---|---|---|
| Two-sample t-test | Compares means of two independent groups of continuous data | Independent samples, two groups | Using it for before-and-after on the same units |
| Paired t-test | Tests whether the mean difference between paired observations is zero | Same units measured twice | Pairing unrelated samples just because they are the same size |
| One-way ANOVA | Compares means of three or more groups of continuous data | One test controls the overall alpha | Running multiple t-tests instead |
| Chi-square test of independence | Tests whether two categorical variables are related using counts | Discrete data in a contingency table | Using ANOVA or t-tests on categorical outcomes |
Type I vs. type II error
| Concept | Meaning | Key difference | Common trap |
|---|---|---|---|
| Type I error (alpha) | Rejecting a null hypothesis that is actually true | A false alarm; you act on a difference that is not real | Thinking alpha is the probability the result is wrong overall |
| Type II error (beta) | Failing to reject a null hypothesis that is actually false | A miss; a real difference goes undetected | Forgetting that small samples make beta large |
Cause-and-effect diagram vs. 5 whys vs. fault tree analysis
| Concept | Meaning | Key difference | Common trap |
|---|---|---|---|
| Cause-and-effect diagram | Organizes many potential causes into categories for one effect | Broad; captures many hypotheses at once | Treating it as proof of the root cause |
| 5 whys | Asks why repeatedly to follow a single chain from symptom to cause | Deep but narrow; one path at a time | Stopping at a person ('operator error') instead of a process cause |
| Fault tree analysis | Top-down logic diagram linking a failure to contributing events through AND/OR gates | Shows how combinations of events cause a failure | Confusing it with FMEA, which works bottom-up from each failure mode |
Exam traps
Each trap is an answer that looks right. Learn the clue that should change your mind.
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Correlation as causation
- What candidates pick
- Change the input with the highest correlation to the output.
- Why it looks right
- A high r looks like strong evidence.
- Why it's wrong
- Correlation shows association only; a lurking variable may drive both, so causation needs a designed experiment or strong process knowledge.
Clue to watch for Observational data and an option that jumps straight to changing the process.
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Multiple t-tests for several groups
- What candidates pick
- Compare each pair of four machines with two-sample t-tests.
- Why it looks right
- The t-test is familiar and each comparison seems simple.
- Why it's wrong
- Each test carries alpha risk, so six tests inflate the chance of a false alarm well above 5%; one-way ANOVA tests all means together.
Clue to watch for Three or more groups of continuous data.
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Accept the null
- What candidates pick
- With p = 0.20, conclude the two processes have the same mean.
- Why it looks right
- Not finding a difference feels like finding sameness.
- Why it's wrong
- A non-significant result means the data did not show a difference; the sample may have been too small to detect one. The correct wording is fail to reject.
Clue to watch for A p-value above alpha and an option claiming equality or proof.
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Independent test on paired data
- What candidates pick
- A two-sample t-test for before-and-after measurements on the same 15 operators.
- Why it looks right
- There are two sets of numbers to compare.
- Why it's wrong
- The measurements are linked by operator; a paired t-test analyzes the differences and removes operator-to-operator variation, giving more power.
Clue to watch for The same units, people or parts measured under both conditions.
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ANOVA on counts
- What candidates pick
- One-way ANOVA to compare defective rates from three suppliers.
- Why it looks right
- Three groups suggests ANOVA.
- Why it's wrong
- Pass/fail outcomes are categorical; a chi-square test of independence or a test of proportions fits discrete data.
Clue to watch for Outcomes reported as counts of good and bad or yes and no.
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Fishbone as proof
- What candidates pick
- Implement a fix for the cause the team voted most likely on the cause-and-effect diagram.
- Why it looks right
- The team agreed, and action feels productive.
- Why it's wrong
- Brainstormed causes are hypotheses; Analyze requires verification with data, such as a hypothesis test, regression or a check of the process, before Improve.
Clue to watch for The question asks what to do NEXT after creating a fishbone or 5 whys chain.
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Extrapolating regression
- What candidates pick
- Use the regression equation to predict output at a setting far above any tested value.
- Why it looks right
- The equation produces a number for any x.
- Why it's wrong
- The relationship is only established within the observed range; outside it the true relationship may curve or break down.
Clue to watch for A predicted x value well beyond the minimum and maximum in the data.
Answer framework
For Analyze phase questions about tests, output or root causes, apply these steps in order.
- Identify the output data type and the number of groups or variables, and note whether samples are paired or independent.
- Write the null and alternative hypotheses in words before choosing a test, so the comparison is explicit.
- Match the test: t or paired t for means, ANOVA for three or more means, F for variances, proportions or chi-square for counts.
- Compare the p-value with alpha, then state reject or fail to reject the null, and check whether the effect is large enough to matter in practice.
- For root cause questions, treat tools as hypothesis generators and choose the option that verifies the cause with data before Improve.
Practice question
Want more like this? The CSSGB practice test has questions for every domain.
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Study strategy
Start with hypothesis testing logic rather than individual tests: null and alternative hypotheses, alpha and beta, power and the p-value rule. Once that frame is solid, build a single test-selection flowchart keyed on data type, number of groups and pairing, and practice it on twenty short scenarios until you can choose a test in under thirty seconds.
Next cover exploratory data analysis. Interpret regression output, including slope, R-squared and residual patterns, and practice reading multi-vari charts. Then move to additional analysis methods, focusing on which root cause tool fits each situation and on the rule that brainstormed causes must be verified.
Commonly underestimated areas are the wording of conclusions (fail to reject, not accept), the chi-square expected-count calculation, and paired designs, which candidates miss because the stem hides the pairing in a phrase such as 'the same operators'. After this section, take a timed Analyze set that mixes test selection and interpretation, then move to Improve, where the causes you verified become the factors in designed experiments and lean solutions.
FAQ
How many Analyze questions are on the CSSGB?
ASQ lists 15 of the 100 scored questions for this section.
How do I choose the right hypothesis test quickly?
Ask three questions: is the output continuous or discrete, how many groups are compared, and are the observations paired? Those answers point to t-tests, paired t, ANOVA, F-tests, proportion tests or chi-square.
What does a p-value of 0.03 mean at alpha 0.05?
The p-value is below alpha, so you reject the null hypothesis and conclude the evidence supports a difference or effect. It does not mean there is a 3% chance the null is true.
What is the difference between r and R-squared?
r measures the strength and direction of a linear relationship; R-squared, which equals r squared in simple regression, is the proportion of variation in the output explained by the input.
Is a fishbone diagram enough to identify the root cause?
No. It organizes possible causes so the team can decide what to investigate; the likely causes must then be confirmed with data before Improve acts.
How long should I spend on Analyze?
Plan roughly 15–20 hours within a 120-hour plan, most of it on test selection, output interpretation and regression practice.
How does Analyze connect to Improve?
The vital few inputs confirmed in Analyze become the factors in Improve's designed experiments or the targets of lean solutions, so a weak Analyze leads to experiments on the wrong variables.
Other Quality Management certifications
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Test your Domain 4 knowledge
You have covered multi-vari studies, regression, test selection and root cause tools. Check whether you can choose the right test and conclusion on timed questions.