P-value
The probability of obtaining results at least as extreme as those observed if the null hypothesis were true; small values cast doubt on the null.
A p-value expresses how compatible your data are with the null hypothesis. Formally, it is the probability of observing a test statistic at least as extreme as the one you obtained, assuming the null hypothesis is true. A small p-value, conventionally below 0.05, suggests the data would be unlikely under the null, so researchers reject it. A p-value is not the probability that the null hypothesis is true, and it is not the probability that the result occurred by chance.
Thesis writers rely on p-values to report hypothesis tests, but examiners expect more than a bare threshold. Report exact p-values where possible, pair them with effect sizes and confidence intervals, and avoid describing nonsignificant results as proof of no effect. Interpreting p-values carefully, including their dependence on sample size, is a mark of statistical literacy in a results chapter.
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