P-value - Coin Flipping Example

Coin Flipping Example

For example, an experiment is performed to determine whether a coin flip is fair (50% chance, each, of landing heads or tails) or unfairly biased (≠ 50% chance of either of the outcomes).

Suppose that the experimental results show the coin turning up heads 14 times out of 20 total flips. The p-value of this result would be the chance of a fair coin landing on heads at least 14 times out of 20 flips. The probability that 20 flips of a fair coin would result in 14 or more heads can be computed from binomial coefficients as

\begin{align} & \operatorname{Prob}(14\text{ heads}) + \operatorname{Prob}(15\text{ heads}) + \cdots + \operatorname{Prob}(20\text{ heads}) \\ & = \frac{1}{2^{20}} \left = \frac{60,\!460}{1,\!048,\!576} \approx 0.058 \end{align}

This probability is the (one-sided) p-value. It measures the chance that a fair coin would give a result at least this extreme.

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