State the null hypothesis (H_0) and alternative hypothesis (H_1)
Choose the appropriate test statistic (e.g., (z), (t), (chi^2), (F)) based on the test and assumptions
Collect the sample data and compute the test statistic
Determine the sampling distribution of the test statistic under (H_0)
Compute the observed test statistic value (e.g., (t_{text{obs}}), (z_{text{obs}}))
Select the test type: two-tailed, right-tailed, or left-tailed
Convert the observed statistic to a p-value using the CDF/survival function of the distribution under (H_0)
For a right-tailed test: (p = P(T ge t_{text{obs}}) = 1 – F(t_{text{obs}}))
For a left-tailed test: (p = P(T le t_{text{obs}}) = F(t_{text{obs}}))
For a two-tailed test: (p = 2 min{F(t_{text{obs}}), 1 – F(t_{text{obs}})})
If the test is based on a (chi^2) or (F) statistic, use the corresponding CDF/survival function similarly
Use software to compute p-values directly (e.g., R, Python, Excel) when available
Report the p-value as the probability (under (H_0)) of obtaining a result at least as extreme as the observed one