Introduction

A p-value is one of the most misunderstood concepts in statistics…

The Simple Explanation

If we assume the null hypothesis is true, the p-value tells us how likely we are to see results at least as extreme as ours.

Example

Suppose we test whether a coin is fair. We flip it 100 times and get 60 heads. Our p-value answers:

“If the coin were truly fair, how likely is it to get 60 or more heads just by chance?”

The Formula

The test statistic for this example:

$$z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$$

In Python

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from scipy import stats

observed_heads = 60
n_flips = 100
expected_prob = 0.5

stat, pvalue = stats.binom_test(observed_heads, n_flips, expected_prob)
print(f"P-value: {pvalue:.4f}")