Statistic question?

Question

Can anyone, for the love of God, explain to me how you find the P-value in a two-tailed test? Please tell me before I go jump out of my window!

Answer 1

The p-value is the probability of obtaining a result at least as "impressive" as that obtained, assuming the truth of the null hypothesis that the finding was the result of chance alone.

For example, say an experiment is performed to determine if a coin flip is fair (50% chance of landing heads or tails), or unfairly biased toward heads (> 50% chance of landing heads). If we choose a two-tailed test then the null hypothesis is that the coin is fair, and that any deviations from the 50% rate can be ascribed to chance alone. 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 (as larger values in this case are also less favorable to the null hypothesis of a fair coin) or at most 6 times out of 20 flips. In this case the random variable, T, is a binomial distribution. The probability that 20 flips of a fair coin would result in 14 or more heads is 0.0577. Since this is a two-tailed test, the probability that 20 flips of the coin would result in 14 or more heads or 6 or less heads is 0.115.

Generally, the smaller the P value, the more people there are who would be willing to say that the results came from a biased coin.