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.

Read more about this topic:  P-value

Famous quotes containing the word coin:

    “It is not funny that a man should be killed, but it is sometimes funny that he should be killed for so little, and that his death should be the coin of what we call civilization.”
    —Raymond Chandler (1888–1959)