Basics

1. Establish two competing hypotheses (null & alternative) about the population
2. Compare your observed sample data to what you would expect to see if the null hypothesis were true
   1. If they are very different, then conclude that the null hypothesis isn’t true
   2. If they aren’t very different, then fail to conclude that the null hypothesis isn’t true

Components of hypothesis tests

Null hypothesis ($H_0$):

• a default/baseline belief about the population; assumed to be true unless sufficient evidence is provided to believe otherwise

Alternative hypothesis ($H_1$ or $H_a$ or $H_A$):

• a different (often complementary) belief about the population; only will be accepted if sufficient evidence is provided

One-Sample -Test for…

• $H_0$: hypothesized mean
• $H_1$: two-sided or one-sided

Test statistic:

• a value calculated from your sample data that is assumed to follow some probability distribution; measures the amount of evidence the sample provides against $H_0$

p-value:

• if $H_0$ is true, the probability of getting a test statistic at least as extreme as the one you got

test results v. possible errors

critical value(s):

• percentile(s) from the test statistic’s distribution, beyond which is a probability of, like would be used in calculating a CI [an alternative to using p-values]
  • if test statistic is more extreme than criticial value(s), reject $H_0$. We have sufficient evidence that $H_1$ is true
  • if test statistic is not more extreme than critical value(s), fail to reject $H_0$. we do not have sufficient evidence to prove $H_1$

Wilcoxon tests