Student's t-Test

The t-test is the go-to method for comparing processes in quality engineering. Did the new tool produce different dimensions than the old one? Is the morning shift mean statistically different from the afternoon shift? Has the supplier's material changed? These are all t-test questions.

In manufacturing, the one-sample t-test answers "is our process mean significantly different from the target?" — a question directly relevant to process centering. The two-sample t-test answers "did the process change after we adjusted the machine?" — critical for validating process improvements.

The practical challenge is that the t-test assumes normal distributions (or large enough samples for the Central Limit Theorem to apply). With the small samples common in quality work (5–20 measurements per group), the normality assumption matters. Non-normal data can inflate Type I error rates (false positives) or reduce test power (missing real differences). Engineers often apply the t-test blindly without checking assumptions, leading to unreliable conclusions.

EntropyStat enables process comparisons without the normality assumption that the t-test requires. Instead of comparing means under a Gaussian model, EntropyStat compares entire distribution shapes using the EGDF. This captures differences in spread, skewness, and tail behavior that a comparison of means would miss entirely.

Consider two batches of parts with identical means but different distribution shapes — one symmetric, one right-skewed. A t-test would conclude "no significant difference." But the skewed batch might have a much higher tail probability beyond the upper specification limit, meaning more defects. EntropyStat's distribution-level comparison catches this because it compares the full EGDF, not just a single summary statistic.

For small-sample comparisons (5–15 measurements per group), the EGDF's entropy-based approach is especially valuable. The t-test's power drops sharply with small samples under non-normality, potentially missing real process changes. The EGDF produces stable distribution estimates with as few as 5–8 measurements, making meaningful before/after comparisons possible with the limited data typical of process improvement projects.