🎓 CSSGB Quest › Learn › Hypothesis testing

Hypothesis testing basics

Hypothesis testing is the statistical framework used in the Analyze phase to decide whether an observed difference or relationship in the data is real or due to chance. Green Belt exams test the structure of hypotheses, what a p-value means, and the two types of errors.

Hypothesis structure

Null hypothesis (H₀): The default position — no effect, no difference, no relationship. Example: “The new setting produces the same mean output as the old setting (μ_new = μ_old).”
Alternative hypothesis (H_a): What the team is trying to demonstrate. Example: “The new setting produces a different mean output (μ_new ≠ μ_old).”

The test either rejects H₀ (evidence is strong enough) or fails to reject H₀ (evidence is not strong enough). Failing to reject H₀ does not prove H₀ is true — it means the data didn’t provide enough evidence to reject it.

The p-value

The p-value is the probability of observing results at least as extreme as those in the data assuming H₀ is true. A small p-value means the results are unlikely under H₀, providing evidence against it.

Decision rule (α = 0.05 is most common):
p-value < α → Reject H₀ (statistically significant)
p-value ≥ α → Fail to reject H₀ (not statistically significant at this α level)

Common trap: “p = 0.03 means there is a 3% chance the null hypothesis is true.” This is wrong. p = 0.03 means there is a 3% chance of observing results this extreme if H₀ were true.

Type I and Type II errors

	H₀ is actually true	H₀ is actually false
Reject H₀	Type I error (α) — false positive; "false alarm"	Correct decision ✓
Fail to reject H₀	Correct decision ✓	Type II error (β) — false negative; "miss"

α (Type I error rate): Usually set to 0.05. Lower α = fewer false alarms, but harder to detect real effects.
β (Type II error rate): Related to power (Power = 1 − β). Higher power = better at detecting real effects. For a given α, a larger sample size increases power (lowers β).

Basic test selection

What are you comparing?	Data	Test
One mean vs. a target	Continuous	1-sample t-test
Two independent group means	Continuous	2-sample t-test
Before/after on the same units	Continuous	Paired t-test
Three or more group means	Continuous	One-way ANOVA
Two proportions	Attribute	2-proportion z-test
Two categorical variables	Attribute	Chi-square test

Test yourself

The free 20-question CSSGB diagnostic covers all six Body of Knowledge sections, with an explanation for every answer.

Take the free CSSGB diagnostic

CSSGB Quest by Bizarre Act. Original study material; not affiliated with ASQ. CSSGB is a certification of ASQ. Terms · Privacy