Analyze
Find the vital few X's
Analyze narrows many candidate causes to the proven few. Start graphically - Pareto, multi-vari, box plots, scatterplots, run charts, fishbone, 5 whys, FMEA - then confirm with statistical inference.
Inference essentials
Every test compares a statistic to a distribution under a null hypothesis. Type I error (α) rejects a true null, the producer's risk; Type II error (β) fails to reject a false null, the consumer's risk. Power = 1 − β and rises with larger sample size, larger effect, or less noise. Confidence intervals convey effect size and precision; a p-value alone does not.
Test selection: one-sample or paired t for means; two-sample t (or Mann-Whitney when assumptions fail) for two means; ANOVA (or Kruskal-Wallis) for three or more; chi-square for counts and independence; F or Levene for variances; proportion tests for rates. Check independence, normality or adequate n, and equal variance before trusting results.
Traps
“p = 0.06 proves there is no difference” - absence of evidence is not evidence of absence. Multiple unadjusted comparisons inflate α. Correlation is not causation. And a one-tailed test chosen after seeing the data is a red flag.
Rule of thumb: for a two-sample t-test at 80% power with α = 0.05, n ≈ 16(s/Δ)² per group; to double precision you need four times the data.