Hypothesis Testing and P Values
Hypothesis testing helps you judge whether sample evidence is unusual under a stated null claim. The p value is the probability of seeing a test statistic at least as extreme as the observed value, when the null hypothesis is treated as true. A small p value does not prove the alternative. It shows that the observed result would be rare under the null model.
Why This Calculator Helps
This calculator supports common test families used in statistics courses and reports. You can enter a z statistic for large sample normal tests. You can use a t statistic when a sample standard deviation and degrees of freedom matter. You can enter a chi square statistic for variance, fit, or independence tests. You can also enter an F statistic for ratio tests.
Tail Direction and Alpha
The tail choice is important. A left tailed test measures evidence in the lower tail. A right tailed test measures evidence in the upper tail. A two tailed test checks both directions. The calculator applies the selected tail rule and compares the p value with alpha.
Alpha is the chosen significance level. Common values are 0.10, 0.05, and 0.01. When the p value is less than or equal to alpha, the result is marked as reject the null hypothesis. When the p value is larger, the result is marked as fail to reject the null hypothesis. It avoids claiming that the null is proven.
Better Inputs and Exports
Use the statistic from the correct test. Match degrees of freedom to the selected distribution. Use positive values for chi square and F tests. Record the test direction before viewing the result. Changing the tail after seeing data can make the conclusion misleading.
The export buttons help study notes, worksheets, and trails. The CSV file opens in a spreadsheet. The PDF file gives a printable report. You can compare your work with those rows before using your numbers.
Final Interpretation
Always interpret the result with context. A p value is not the size of an effect. It is not the probability that the null hypothesis is true. It is evidence. Combine it with design quality, assumptions, sample size, and importance.