How would small sample sizes affect a t-test and its assumptions?

How would small sample sizes affect a t-test and its assumptions?

The smaller the sample size, the greater the influence of the values of individual samples on variance. This variability becomes stable as the sample size increases. If the sample sizes of the groups are different, then this difference in variability may result in different variances.

What is homogeneity of variance how does it influence Student’s t-test and Welch’s t-test?

Assumptions of normality and homogeneity of variance underlie this test. We show that the Welch’s t-test provides a better control of Type 1 error rates when the assumption of homogeneity of variance is not met, and it loses little robustness compared to Student’s t-test when the assumptions are met.

What happens when t-test assumptions are violated?

If the assumption of normality is violated, or outliers are present, then the paired t test may not be the most powerful test available, and this could mean the difference between detecting a true difference or not. A nonparametric test or employing a transformation may result in a more powerful test.

When to use Welch’s t test for variance?

Welch’s t-test: Assumes that both groups of data are sampled from populations that follow a normal distribution, but it does not assume that those two populations have the same variance. So, if the two samples do not have equal variance then it’s best to use the Welch’s t-test.

Which is more robust Welch t test or Student’s t test?

Furthermore, the power of Welch’s t-test comes close to that of Student’s t-test, even when the population variances are equal and sample sizes are balanced. Welch’s t-test can be generalized to more than 2-samples, which is more robust than one-way analysis of variance (ANOVA).

How did the Welch’s t test get its name?

Welch’s t -test. In statistics, Welch’s t-test, or unequal variances t-test, is a two-sample location test which is used to test the hypothesis that two populations have equal means. It is named for its creator, Bernard Lewis Welch, and is an adaptation of Student’s t-test, and is more reliable when the two samples have unequal variances…

How to determine equal or unequal variance in t tests?

1. Use the Variance Rule of Thumb. As a rule of thumb, if the ratio of the larger variance to the smaller variance is less than 4 then we can assume the variances are approximately equal and use the Student’s t-test. Sample 1 has a variance of 24.86 and sample 2 has a variance of 15.76.