Table of Contents

## What is T-test?

T-test is used to draw a comparison between the means of the two groups, a statistical hypothesis test called a t-test is performed. The t-test is typically used when the sample size is limited, or the data distribution is not normal. T-tests come in two varieties. The independent t-test is used to compare the means of two separate groups, such as the difference in test scores between boys and girls.

When comparing the means of two related groups, such as the variation in test results before and after a training program, the paired t-test is utilized. The researcher must first identify the null and alternative hypotheses before conducting a t-test. The alternative hypothesis asserts a substantial difference between the means of the two groups, contrary to the null hypothesis, which claims that there is not.

The researcher then compiles data from each group and calculates the t-statistic and p-value. This results in the acceptance of the alternative hypothesis, and the null hypothesis is refuted if the p-value is less than the set level of significance, such as 0.05.

## What is an F-test?

It’s a statistical test that’s used to compare the variances of two groups. It’s usually used when you want to know if the spread of data within each group is similar or if there are significant differences between the variances. The F-test is actually a ratio of two variances, and it’s calculated using a formula that compares the variance within each group to the variance between the groups.

A high ratio indicates that the variances of the two groups differ significantly from one another. When the ratio is low, the deviations are more comparable. So, why is the F-test useful? Well, let’s say you have data on the heights of men and women in a certain population, and you want to know if there’s a significant difference in the spread of heights between the two groups.

You could use an F-test to compare the variance of the heights of men to the variance of the heights of women. If the F-test shows that the ratio of the variances is high, it would indicate that there’s a significant difference in the spread of heights between the two groups. On the other side, if the ratio is low, it may indicate that men and women have similar height ranges.

## Difference Between T-test and F-test

- T-test is used to compare two groups’ means, whereas the F-test is used to compare two groups’ variances.
- T-test has two types (independent t-test and paired t-test), whereas F-test only has one type.
- T-test compares the means of two groups under the null hypothesis of no significant difference, whereas F-test compares the variances under the null hypothesis of equal variances.
- T-test calculates the t-statistic and p-value, whereas F-test calculates the F-ratio.
- The result of a T-test is interpreted based on the p-value, whereas the result of an F-test is interpreted based on the F-ratio and the corresponding p-value.

## Comparison Between T-test and F-test

Parameters of Comparison | T-test | F-test |

Purpose | Comparing the Means of Two Groups | Comparing Variances of Two Groups |

Types | Independent T-test & Paired T-test | No Types |

Null Hypothesis | No Significant Difference | Equal Variances |

Calculations | T-statistic & P-value | F-ratio |

Interpretation | Based on the P-value | Based on the F-ratio & P-value |