What are the assumptions made when conducting a t-test?

When conducting a t-test, it is assumed that the data is normally distributed, independent, and has equal variances.

A t-test is a statistical test that is used to compare the means of two groups to determine if they are significantly different from each other. It is based on certain assumptions that need to be met for the test to be valid and reliable.

The first assumption is that the data is normally distributed. This means that the distribution of the data should resemble a bell curve, with most of the data points clustered around the mean and fewer data points as you move away from the mean in either direction. This assumption is crucial because the t-test is a parametric test, which means it makes assumptions about the underlying distribution of the data. If the data is not normally distributed, the results of the t-test may not be valid.

The second assumption is that the data is independent. This means that the data points in one group do not depend on the data points in the other group. In other words, the outcome of one observation does not influence the outcome of another observation. This assumption is important because if the data points are not independent, it could lead to a violation of the assumption of independence, which could affect the validity of the t-test.

The third assumption is that the variances of the two groups are equal. This is also known as the assumption of homogeneity of variances. This assumption is important because the t-test compares the means of two groups, and if the variances are not equal, it could affect the accuracy of the test. If this assumption is violated, a different version of the t-test, such as the Welch's t-test, may be used instead.

In conclusion, when conducting a t-test, it is important to check these assumptions to ensure the validity and reliability of the test results. If these assumptions are not met, the results of the t-test may not be accurate, and alternative statistical tests may need to be considered.