Core Concepts
| Item | Description |
|---|
H0 (Null Hypothesis) | The default assumption — 'no effect', 'no difference' |
H1/Ha (Alternative) | What you're trying to prove — 'there IS an effect' |
p-value | Probability of observing data at least as extreme, assuming H0 is true |
Alpha (Significance Level) | Threshold to reject H0 — commonly 0.05 (5%) |
One-tailed vs Two-tailed | One-tailed: tests direction (greater/less); Two-tailed: any difference |
Power = 1 - Beta | Probability of correctly rejecting H0 when H1 is true |
Type I & Type II Errors
| Decision | H0 is True | H0 is False |
|---|
| Reject H0 | Type I Error (alpha) | Correct (Power) |
| Fail to Reject H0 | Correct (1-alpha) | Type II Error (beta) |
T-Tests
| Item | Description |
|---|
One-Sample t-test | Compare sample mean to known population mean: t = (xbar - mu0) / (s/sqrt(n)) |
Independent Two-Sample | Compare means of two independent groups; check equal variance assumption |
Paired t-test | Compare means of same subjects before/after — analyzes differences |
Welch's t-test | Two-sample t-test WITHOUT assuming equal variances — safer default |
Assumptions | Normality (or n>30), independence, continuous data |
Cohen's d = (xbar1 - xbar2) / s_pooled | Effect size for t-tests: 0.2=small, 0.5=medium, 0.8=large |
Chi-Square & ANOVA
| Item | Description |
|---|
Chi-Square Test of Independence | Tests association between two categorical variables |
Chi-Square Goodness of Fit | Tests if observed frequencies match expected distribution |
Chi-Square Statistic: X^2 = Sum((O-E)^2 / E) | Sum of squared standardized differences |
One-Way ANOVA | Compare means of 3+ groups — tests if at least one differs |
F = Between-group variance / Within-group variance | Larger F suggests real group differences |
Post-Hoc Tests (Tukey HSD) | After ANOVA: find WHICH groups differ — control familywise error |
Pro Tip: A p-value is NOT the probability the null is true. It's P(data this extreme | null is true). A small p-value means surprising data under H0, not that your hypothesis is correct.