Analyze: Root Cause and Hypothesis Testing
Analyze: Root Cause and Hypothesis Testing
Analyze narrows candidate causes to verified ones using data. The exam tests graphical analysis, FMEA, hypothesis-test selection, p-values, confidence intervals, power, and regression or ANOVA interpretation.
Core rules and concepts
- Root-cause tools: process map, value-stream map, multi-vari study, Ishikawa, and 5 Whys. Verify with data, not consensus.
- FMEA: RPN = Severity x Occurrence x Detection; high severity or detection scores need action even when RPN is moderate.
- Hypotheses: H0 is no difference or no effect; H1 is the claim. Alpha is Type I error (false alarm); beta is Type II (missed effect); power = 1 - beta.
- Decision rule: reject H0 when p is less than or equal to alpha. A p-value is not the probability that H0 is true.
- Test selection: continuous outcome uses one-sample t, two-sample t, paired t, or ANOVA; categorical uses chi-square; association uses regression or correlation. Check independence, normality, and equal variance; use Welch or nonparametric alternatives when violated.
- Practical significance: compare the confidence interval to a business threshold.
Worked example
Two suppliers' lead times (n = 30 each) give a two-sample t-test p = 0.028 and a 95% CI for the difference of 0.4 to 6.2 days. Reasoning: p < 0.05, so the difference is statistically significant; the CI excludes zero. But if the practical threshold is 2 days, the lower bound (0.4) is below it, so the evidence is not strong enough for a switch without a pilot. Check equal variance; if violated, use Welch's test.
Traps that cost marks
Saying p = 0.05 proves H0; accepting H0 as proof of no difference; ignoring power and sample size; multiple comparisons without correction; correlation presented as causation; using an independent t-test on paired data; extrapolating regression beyond the data range.