A computational tool that determines the probability of obtaining test results at least as extreme as the results actually observed, assuming the null hypothesis is correct, given a calculated test statistic. For instance, if a t-statistic of 2.5 is derived from a dataset, this tool calculates the probability of observing a t-statistic of 2.5 or greater (in the case of a one-tailed test) or 2.5 or greater in absolute value (in the case of a two-tailed test) if the null hypothesis is true.
This calculation offers significant value in hypothesis testing, facilitating informed decisions regarding the rejection or acceptance of the null hypothesis. It simplifies the process of statistical inference by automating a complex calculation, thereby saving time and reducing the potential for errors. Historically, these calculations were performed using statistical tables, a process that was both time-consuming and prone to inaccuracies. The advent of computerized calculators and statistical software has streamlined this process, making statistical analysis more accessible and efficient.