t-Test (Are Two Groups Really Different?)

When you have two groups (two machines, two shifts, before vs after a change) and want to know if their averages truly differ — not just by luck — you use a t-test.

It returns a p-value:

• p < 0.05 → the difference is statistically significant (real)
• p ≥ 0.05 → not enough evidence; the gap could be random noise

Use the paired version when the two columns are the same items measured twice (e.g. each part before & after). Use the normal (Welch) version for two independent groups. For 3+ groups, use ANOVA instead.