Analyze Phase: Root Cause Analysis and Hypothesis Testing
What the exam tests
Analyze tests whether you can move from symptoms to verified causes. Expect root-cause tools, FMEA, hypothesis-test selection, p-values, confidence intervals, and the difference between statistical and practical significance.
Core rules
- Root-cause tools include 5 Whys, fishbone diagrams, process mapping, stratification, scatter plots, and FMEA for risk prioritization.
- State H0 and Ha before testing. Choose the test by data type and structure: one-sample t for a mean, two-sample t for two independent means, paired t for before/after on the same units, ANOVA for three or more means, chi-square for proportions or contingency tables, and F-tests or Levene for variances.
- Reject H0 when p is less than alpha. A p-value is the probability of data at least as extreme if H0 is true; it is not the probability that H0 is true.
- Check assumptions: independence, normality, and equal variance. With large samples, means tests are robust, but variance tests are not.
- Statistical significance is not business significance; compare the confidence interval with the practical threshold.
Worked example
Two lines are compared with a two-sample t-test: n = 30 each, difference in mean cycle time 4.8 minutes, 95% CI 1.2 to 8.5 minutes, p = 0.03, alpha = 0.05. Reject H0: the lines differ. The reasoning continues: if the team's practical threshold for action is 10 minutes, the entire CI lies below it, so the difference is real but not worth a capital project. Report both conclusions.
Traps
Saying p = 0.03 means a 3% chance H0 is true; running many pairwise t-tests instead of ANOVA; testing causes before the measurement system is validated; and ignoring non-normal data or unequal variances.