P-Value Calculator

A p-value is the probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is true. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis. A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.

A Z-test is used when you know the population standard deviation and have a large sample size (typically n > 30). A T-test is used when you don’t know the population standard deviation and must estimate it from your sample, or when you have a small sample size (typically n ≤ 30). The T-test uses the t-distribution, which has heavier tails than the normal distribution used in the Z-test.

A Chi-Square test is used for categorical data to assess whether there’s a significant association between categorical variables. It’s commonly used for tests of independence (to determine if two categorical variables are related) and goodness-of-fit tests (to determine if sample data matches a population with a specific distribution).

The significance level (α) is the threshold used to determine whether a p-value is statistically significant. Common significance levels are 0.01, 0.05, and 0.10. The choice depends on the consequences of making a Type I error (rejecting a true null hypothesis). In fields where false positives are costly (like medical research), a lower significance level (0.01) might be used. In exploratory research, a higher level (0.10) might be acceptable.

A one-tailed test tests for the possibility of an effect in one direction only, while a two-tailed test tests for the possibility of an effect in both directions. For example, a one-tailed test might test if a mean is greater than a hypothesized value, while a two-tailed test would test if the mean is different (either greater or less) from the hypothesized value. Two-tailed tests are more conservative and are generally preferred unless there’s a strong theoretical reason for a one-tailed test.