# Effect size for independent t-test

The effect size basically indicates how strong an observed effect is. Depending on which hypothesis is tested, effect stands for relationship or correlation, for example.

• How strong is the relationship/difference?
• How strong is the correlation?

The t-test for independent checks whether there is a difference between two independent groups. The effect size in the independent t-test now tells how strong the difference between the groups is. In the independent t-test, this is done by comparing differences in means.

This allows different studies to be compared using the effect size.

## Difference effect size and p-value

The p-value says nothing about the size of the effect or difference and depends very much on the sample size.

What does this mean? If there is a difference in the population, the larger the sample, the more clearly it is indicated in the p-value. If the sample is very large, very small differences in the population can also be detected. These small differences may no longer be relevant at all.

In the left study in the upper graph, we will get, with the same difference, a larger p-value than in the right study. Simplified, this is due to the fact that more people were interviewed in the right study and therefore smaller differences are significant than in the left study.

To standardize this, the effect size is used in addition to the p-value.

## Effect size of the t-test for independent samples

As already said, the p-value says nothing about the strength of the difference, but only whether the difference is significant or not. The independent t-test compares differences in means. One question could be whether there is a mean difference in the salary of men and women. To make these differences comparable across several studies, the effect size is needed.

## Calculate effect size in t-test for independent samples

The effect size for a t-test for independent samples is usually calculated using Cohen's d.To calculate the effect size, the mean difference is standardized i.e. divided by the standard deviation.

However, the standard deviation of the population is not known. In order to estimate the effect size with full confidence, the hedges g, also often just called d, is used. With hedges g, only parameters of the sample are used.

The hedges g or the d can now be transformed even further so that it can be calculated quite easily if a t-test for independent samples has been calculated.

In the literature, a variety of different names and symbols are used for the different effect sizes. A detailed discussion on the topic of different effect size measures for the difference of means from two independent groups can be found here: Enzmann, D. (2015). Notes on Effect Size Measures for the Difference of Means From Two Independent Groups: The Case of Cohen's d and Hedges' g (Technical Report).

## Interpret effect size

The resulting values of the hedge g or d and Cohen's d can be interpreted using Cohen's table below.

d
Small effect 0,2
Medium effect 0,5
Great effect 0,8

For example, an effect of 0.5 is a medium effect and means that the difference between the two groups is equal to half a standard deviation. If the effect size is in the middle of two values, the result is a small to medium effect or a medium to large effect.

## Calculate effect strength with DATAtab

On DATAtab in the independent t-test calculator, the effect size can easily be calculated online. Simply select a metric and a categorical variable and click on effect size.

Cite DATAtab: DATAtab Team (2023). DATAtab: Online Statistics Calculator. DATAtab e.U. Graz, Austria. URL https://datatab.net