Stop 02 · Math FoundationsTopics · 5/9

Hypothesis Testing

In short

Conversions went from 4.1% to 4.4%. Real improvement or random wobble? Hypothesis testing is the standard way to decide, instead of going with whoever argues loudest.

A formal process for testing whether an observed effect is likely real or just random noise — starting with a null hypothesis and using data to decide whether to reject it.

The jaadu as a judge with a gavel weighs evidence folders on a balance scale.

Think of it like this

Innocent until proven guilty

A court starts by assuming the accused is innocent. Only strong evidence lets the judge reject that. Hypothesis testing works the same way: assume 'no effect' first, and only reject it if the data would be very surprising under that assumption.

Watch it happen

The steps of a test

H0 and H1

Set alpha

Collect

Test stat

p-value

Decide

1/6Null (H0): the new button changes nothing. Alternative (H1): it changes the conversion rate.

The big ideas

What you need to know

Null vs alternative

The null says 'nothing is going on'. You look for evidence strong enough to reject it.

Type I error

Rejecting a true null: a false alarm. Alpha is the rate you accept for this.

Type II error

Missing a real effect. Usually caused by too small a sample.

Pick the right test

t-test for means, chi-square for counts and categories, z-test for proportions with big samples.

See it in code

Walk through the code

python

1from scipy import stats2 3control   = [42, 38, 45, 40, 39, 44, 41]   # minutes on page4treatment = [47, 44, 49, 46, 43, 48, 45]5 6t_stat, p_value = stats.ttest_ind(treatment, control, equal_var=False)7print(round(t_stat, 2), round(p_value, 4))8 9if p_value < 0.05:10    print("Reject H0: the difference is unlikely to be chance")11else:12    print("Fail to reject H0")

1/3Two groups of measurements. Tiny here just to show the idea.

A Welch's t-test comparing two small groups. Real tests need far more data, planned in advance.

Save yourself the pain

Common mistakes

Oops

Saying 'we proved there is no difference' when p > 0.05.

Do this instead

Say 'we didn't find enough evidence of a difference'. A small sample can easily miss a real effect.

Oops

Choosing the test or the threshold after seeing the results.

Do this instead

Decide hypothesis, test and alpha up front, and write them down.

Your mission

Run a test in a sheet

~25 min

Quick check

Your test gives p = 0.21. What's the correct conclusion?

Go deeper

1State a null and alternative hypothesis for a simple, concrete question.
2Learn the correct interpretation of a p-value (and the common wrong ones).
3Walk through a worked hypothesis test example step by step.