A Stat 101 course will cover many hypothesis tests among which are the one-sample t-test, the two-sample t-test, the one and two sample p-tests, and ANOVA. All these different tests are in reality just linear regression.
To see the translation between regression and the sundry named tests, imagine some data with quantitative variables x and y, a zero-one variable z, and a categorical variable (with potentially many levels) g. Each named hypothesis test corresponds to a particular model specification.
- one-sample t-test:
y ~ 1and take the p-value from the intercept. - two-sample t-test:
y ~ gwhenghas just two levels. Take the p-value from thegcoefficient. - one-sample p-test:
z ~ 1and take the p-value from the intercept. - two-sample p-test:
z ~ gwhenghas just two levels. Take the p-value from thegcoefficient. - test on simple regression:
y ~ xand take the p-value from thexcoefficient. - “one-way” ANOVA:
y ~ gwhenghas more than two levels. There will be a p-value for each level ofg(except the reference level), but the p-value for this test is the one fromR2()oranova_summary(), which doesn’t refer to a particular coefficient.
There are many other “forms of ANOVA” that are not covered in Stat101. These all fit in with the linear regression framework. For instance:
- “two-way” ANOVA:
y ~ g1*g2and take the p-value from the interaction term in theanova_summary()report. - analysis of covariance (ANCOVA):
y ~ x + gand take the p-value from thegterm in theanova_summary()report.