In Hypotheses and Controlled Experiments you wrote a hypothesis as a testable prediction. Statistics adds a careful twist: we do not test our idea directly. We test the boring alternative, that nothing is going on, and ask whether the data make it hard to believe.
- Null hypothesis ($H_0$): there is no effect or no difference. "The fertilizer does not change plant height." "The offspring fit a 3 : 1 ratio."
- Alternative hypothesis ($H_a$): there is an effect or a difference. "The fertilizer changes plant height." "The offspring do not fit 3 : 1."
Key idea
A test asks: if the null hypothesis were true, how likely would data this extreme be? That chance is the p-value. Biologists usually reject $H_0$ when $p < 0.05$. A test weighs evidence against the null; it never proves either hypothesis.
Why it works
Why test the null instead of our own idea? Because the null makes an exact prediction we can calculate with: no difference, or exactly a 3 : 1 ratio. "The fertilizer helps" does not say how much, so it predicts no single number. Random chance always makes samples differ a little. The test measures whether the difference we saw is bigger than chance alone would usually make.
| Result | What you say | What you do not say |
|---|---|---|
| p < 0.05 | Reject the null. The data are evidence of an effect. | The alternative is proven. |
| p ≥ 0.05 | Fail to reject the null. The data do not show a clear effect. | The null is true. There is no effect. |
Worked examples
Worked example: Writing the hypotheses
A student thinks that brine shrimp eggs hatch better in warmer water. She hatches eggs at 20 °C and at 28 °C. Write the null and alternative hypotheses.
- The null says the treatment does nothing: temperature does not change the hatching rate.
- The alternative says it does: the hatching rate differs between 20 °C and 28 °C.
- Her own idea ("warmer is better") is a kind of alternative, but the null is what gets tested.
Answer: $H_0$: hatching rate is the same at 20 °C and 28 °C. $H_a$: hatching rate differs between them.
Worked example: Reading a p-value
The test gives p = 0.21. What should she conclude?
- 0.21 is larger than 0.05.
- A difference this big would happen by chance about 21% of the time even if temperature had no effect.
- That is too common to rule out chance.
Answer: Fail to reject the null. The data do not show that temperature matters. They also do not prove it does not; a bigger experiment might show an effect.
Common mistake
Saying "we proved the null" when $p \ge 0.05$, or "we proved our hypothesis" when $p < 0.05$. Science reports evidence, not proof. Even a real effect can hide in a small sample, and about 1 time in 20 a true null will give $p < 0.05$ by chance alone. That is why results are repeated.
The 0.05 cutoff is a convention, not a law of nature. Some fields use stricter levels. What matters on the AP exam is to state it and use it the same way every time.