Analyze
Purpose of Analyze
Analyze proves which Xs actually drive the Y. Core tools are process mapping and value analysis, Pareto charts, fishbone diagrams, 5 Whys, FMEA, multi-vari studies, and inferential statistics.
Hypothesis testing basics
The null hypothesis states no difference or no effect. Alpha is the Type I error rate, rejecting a true null, usually set at 0.05. Beta is the Type II error rate, failing to reject a false null; power equals one minus beta. The p-value is the probability of seeing data at least this extreme if the null were true. It is not the probability that the null is true, and failing to reject is not proof of equality, only insufficient evidence. Traps love these distinctions, plus the claim that a small p-value measures the size of the effect.
Choosing a test
Use a one-sample, two-sample, or paired t-test for means, ANOVA for three or more means, chi-square for counts and independence, an F-test for variances, and regression or correlation for relationships. Check normality and equal variance; for non-normal continuous data use a transformation or a nonparametric alternative. Distinguish statistical from practical significance: with a large sample, a trivial difference can be significant.
Correlation and causation
A correlation coefficient r runs from -1 to 1, and r near zero means no linear relationship, not no relationship. Watch for confounding and lurking variables before declaring cause.
Worked example
Tensile strengths from two suppliers are compared and p = 0.03 with alpha 0.05. Reject the null: a real difference is detectable. Whether the difference matters is a separate engineering and cost judgment. If p were 0.12, the correct statement is that there is not enough evidence of a difference.