Analyze Phase: Root Cause and Statistical Analysis
Domain 4 tests statistical inference and root-cause discipline. You must select the right test, read a p-value correctly, and confirm a cause with data before anyone changes the process.
Hypothesis testing
- H0 states no difference or no effect; Ha states the effect you suspect.
- α is the Type I risk (rejecting a true H0); β is Type II (missing a real effect); power = 1 − β, usually targeted at 0.8.
- Reject H0 when p < α. A p-value is the probability of data at least this extreme if H0 were true - not the probability that H0 is true.
- Test selection: 1-sample t (mean vs target), 2-sample t (two means), paired t (same units before and after), ANOVA (three or more means), chi-square (association between categorical variables), regression and correlation (relationship strength).
- Assumptions: independent observations, normality for small samples, equal variances; check residual and probability plots.
Root cause
- Fishbone (6M), 5 Whys, FMEA, multi-vari studies and stratification narrow the candidate Xs.
- Correlation is not causation: confirm with a designed comparison or a DOE.
Worked example
Cycle time on Line A (n = 30) averaged 12.4 min; Line B averaged 11.9 min; a two-sample t-test gave p = 0.03. At α = 0.05, reject H0 - the difference is statistically real. But the gap is 0.5 min while a line changeover costs 40 min, so it is not practically significant and the team investigates a larger X instead. The result also assumes random sampling and passes the equal-variance check.
Traps that cost marks
Treating "fail to reject H0" as proof of no difference; running multiple pairwise t-tests instead of ANOVA; testing unvalidated measurement data; letting a huge n make a trivial difference look important; ignoring practical significance.