Cohen’s d measures the strength of the comparison between two means. Since it measures the strength of a relationship between variables, Cohen’s d is an effect size. Cohen’s d is calculated by taking the difference of the means divided by the pooled standard deviation, as illustrated in the following equation:
$$d = \frac{M_1 - M_2}{\sqrt{\frac{SD_1^2+SD_2^2}{2}}}$$
The Cohen’s d can be categorized as small (\(d = 0.2\)), medium (\(d = 0.5\)) or large (\(d = 0.8\)) according to the arbitrary values suggested in the literature (Lakens, 2013). With this shiny app you’ll be able to calculate this measure of effect size and also to perform a t-test for the comparison of two independent groups.
The t-test (a parametric test of difference) is used to test a statistical hypothesis to compare the means of two groups (pairwise comparison). The t-test is used when the data: 1) are independent, 2) follows a normal distribution and 3) has a homogeneity of variance. Please note, that to compare three or more means an ANOVA must be used.
The output values of a t-test are the t-value and the degrees of freedom. The t-value is a ratio of the difference between the two samples’ means and the variation that exists within the sample sets. The equation for the t-value is shown below, where \(m =\) mean of sample 1, \(\mu =\) mean of sample 2, \(s =\) standard deviation of the differences of the paired data values, and \(n =\) sample size. Large values indicate large differences between the two sample sets.
$$t = \frac{m-\mu}{\frac{s}{\sqrt{n}}}$$
The degrees of freedom describe how many pieces of independent information were involved in calculating the estimate. The degrees of freedom are found with \(n - 1\), since one item in the sample is not free to vary. An example of this would be picking a set of three numbers that have a mean of 10. Once you have chosen the first two numbers, the third number is chosen out of obligation. You could no longer pick just any number as you did the first two if the specific mean is to be met! Hence, the degrees of freedom for a sample size of three is 2.
The result of a t-test is the t-distribution, a continuous probability distribution. The t-distribution represents the location of the sample mean relative to the true mean. The distribution is symmetric and bell-shaped. It also has heavy-tails, meaning that it is more susceptible to producing values far from its mean.
To calculate Cohen’s d click on the “Calculate” tab. Here, you can choose the “Calculate with Statistics” tab to enter the corresponding information about your dataset. Alternatively, you can upload your data under the tab “Upload Your Data Frame.” Have fun! ;)
Ursula Allvee, Ines Filipa Das Neves Antunes Ramalhete, Cheyenne Cavender, Julia Poeschko and Christian Ludwig
Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and ANOVAs. Frontiers in psychology, 4, 863.
https://www.scribbr.com/statistics/t-test/
https://www.statisticshowto.com/probability-and-statistics/hypothesis-testing/degrees-of-freedom/