Lesson 6 — Hypothesis Testing

I love being
rejected!

How we turn a hunch into statistical evidence — and why rejection is actually a win.

Two hypotheses

H₀ — Null hypothesis
No difference
Golden retrievers and pugs are the same height. Nothing interesting is happening.
Hₐ — Alternative hypothesis
There IS a difference
Golden retrievers and pugs have different heights. Something real is going on.

Why start with the null?

We can never prove something is true for all cases — we can only collect evidence that makes it unlikely to be false.

We test whether the data is so unlikely under the null that we can safely reject it. We can never be 100% certain — but we can be 95%, or 99%.

The p-value

The probability of getting our result by random chance alone, if the null were true.

p < 0.05Statistically significant — reject H₀
p ≥ 0.05Not significant — fail to reject H₀

0.05 means we accept a 5% chance of being wrong. That’s not zero — but it beats guessing!

Reject or fail to reject?

✔ p < 0.05 → Reject H₀ Evidence supports the alternative. The difference is real (probably).
⌛ p ≥ 0.05 → Fail to reject H₀ Not enough evidence yet. Doesn’t mean H₀ is true — just unproven.

Key: we never “accept” the null. We only reject it or fail to reject it.

Test statistics

Every test produces a test statistic — a single number that summarizes the data and maps to a p-value.

The test statistic follows a known distribution (z, t, F, χ²), so we can calculate exactly how rare our result is. The more extreme the statistic, the smaller the p-value.

The full workflow

Hypothesis testing in 5 steps

1. State H₀ & Hₐ
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2. Collect data
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3. Calculate test statistic
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4. Get p-value
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5. Reject or fail to reject H₀
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