Below is a clear description of the difference between T Test Vs. F Test
T test is a statistical test that is used to compare two dependent/related samples. In other words, t-test analyses if there is a difference in mean between two sets of data. The test is also used to determine the significance of regression coefficients and the y-intercept in a regression model. Additionally, the t test is used to confirm if the slope of the regression line differs from zero. The formula for calculating the T test statistic is shown below where ẋ_{1} and ẋ_{2} are the means of the first and second datasets, S_{1} and S_{2} are the respective standard deviations and n_{1} and n_{2} are the sample sizes of the two datasets.
The test is used to test the claim that two populations have the same variance. It is also used to examine the overall significance/validity of a regression model. The F tests statistic is usually a ratio as shown below
T test | F test |
Used to test if two sample means are equal | Used to test if two normal population variances are equal. |
T test statistic follows student t- distribution with n-1 degrees of freedom | F-statistic follows a Scedecor F distribution with N_{1}-N_{2} degrees of freedom. |
Used when sample size is small and standard deviation is unknown | Used when population variances/standard deviations are known |
Contact us if you need help with your statistics tasks. Some of the commonly used statistical tests in hypothesis testing include the F test and the student’s t test. The two tests have proven to be confusing not only to novices but also to students. This is because people are under the impression that the two tests are similar while they are not. The only similarity between them is that they are both parametric tests which means that they make assumptions about the population from which the sample was drawn.