# Dependent and independent samples

What is the difference between a dependent sample and an independent sample? And why is it important to know the difference? Whether the data at hand are from a dependent or an independent sample determines which hypothesis test is used.

If your data are independent, for example, an independent samples t-test or an ANOVA without repeated measures is calculated. If your data are dependent, a t-test for dependent samples or an ANOVA with repeated measures is calculated.

## Example Independent and Dependent Variable

Let's say you want to find out whether holidays have an effect on people's stress levels. To find out, you have created a small online survey on datatab.net that allows you to measure people's stress levels. In the survey, you ask people about their stress levels before and after their holiday. You now have two options:

In the left case you would have an independent sample, because the people you interviewed before the holiday have nothing to do with the people you interviewed after the holiday.

In the right case you would have a dependent sample, you would interview people before the holiday and interview the same people after the holiday, so the measures are always available in pairs. In this case, this is the preferred solution for this research question!

## Dependent sample

In a dependent sample, the measures are related. For example, if you take a sample of people who have had a knee operation and interview them before and after the operation, this is a dependent sample. This is because the same person was interviewed at two different times.

Of course, there does not necessarily need to be a before-and-after relationship to be studied.

For example, if you want to investigate whether a new baseball bat has an effect on batting performance, and the same people play once with the old bat and once with the new one, then you have a dependent sample. In this case, the measurements are also available in pairs, each player has used both bats, so there are two measurements for each player.

And it does not have to be the same person. For example, if you wanted to find out whether, in a relationship between men and women, women do more gardening than men, you would also have a dependent sample. You would have two measures that always go together in pairs, always one woman and one man.

## Independent sample

In independent samples, the values come from two or more different groups. For example, if the men's group and the women's group are asked about their income, independent samples exist. In this case, a person from one sample cannot be assigned to a person from the other sample.

## More than two dependent or independent samples

Of course, in the case of independent and dependent sampling, there can be more than two samples. The important thing is that in the case of independent sampling, the individual groups or samples have nothing to do with each other, and in the case of dependent sampling, a respondent appears in all groups.

## Hypothesis testing for dependent and independent samples

In general, there is always a hypothesis test for independent samples and a counterpart for dependent samples. Instead of the term dependent and independent, paired and unpaired are often used in the case of analysis of variance with and without repeated measures, and paired and unpaired in the case of the t-test.

Dependent sample Independent sample
t-test for dependent samples t-test for independent samples
ANOVA with repeated measurement ANOVA without repeated measurement
Wilcoxon-Test Mann-Whitney U-Test
Friedman Test Kruskal-Wallis Test

In DATAtab you can choose with one click whether you want to calculate the respective hypothesis test for dependent or independent samples.

Depending on the format in which you insert your data, a variant is pre-selected. Usually, a series is a respondent or, more generally, a case. Therefore, metric values that are in a series are initially considered dependent.

If a metric and a categorical variable are clicked, the respective independent test is automatically selected.

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