Statistics Cheat Sheet: Hypothesis Testing
Hypothesis testing trips people up because the logic feels backwards. You assume the null is true, then ask how surprised you'd be by your data. Here's the whole process, compressed.
The five steps
- State the hypotheses. Null (H₀): no effect. Alternative (H₁): there is an effect.
- Choose a significance level. Usually α = 0.05.
- Compute the test statistic. z, t, or χ² depending on the situation.
- Find the p-value. The probability of a result this extreme under H₀.
- Make a decision. Reject H₀ if p < α; otherwise fail to reject.
Which test to use
| Situation | Test |
|---|---|
| Sample mean vs population (σ known) | z-test |
| Sample mean vs population (σ unknown) | t-test |
| Two sample means | two-sample t-test |
| Categorical data (counts) | chi-square test |
The one sentence that explains p-values
P-value = "if nothing is really going on, how likely is a result this extreme?" Low p-value means your data is hard to explain by chance alone.
Remember: failing to reject H₀ doesn't prove H₀ is true. It just means the evidence wasn't strong enough. Absence of evidence isn't evidence of absence — that's the most common stats mistake on exams.
Need a chart for your stats homework?
The chart generator makes bar, line, and pie charts in seconds.
Chart Generator →