# Dependent and independent samples

What is actually the difference between a dependent and an independent sample (paired or unpaired samples)? And why is it important to know the difference? Whether the data are from a dependent or independent sample determines which hypothesis test is used.

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

## Example Independent and Dependent Variable

Let's say you want to find out if vacations have an impact on people's stress levels. To find out, you have created a small online survey on datatab.de, with which you measure the stress level of people. With the survey you ask people before and after their vacation about their stress level. Now there are two possibilities:

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

In the right case, you would then have a dependent sample, we survey people before the vacation and survey the same people after the vacation, so the measurements are always in pairs. This is the preferred solution in this research question!

## Dependent sample

In a dependent sample (or paired sample), the measured values are connected. For example, if a sample is drawn of people who have knee surgery and the people in the sample are each interviewed before and after the surgery, it is a dependent sample. This is the case because the same person was interviewed at two points in time.

Of course, there does not necessarily have to be a before-after relationship that is to be investigated.

A dependent sample also exists if, for example, you want to test whether a new type of baseball bat has an influence on the striking characteristics and the same people play once with the old and once with the new bat. Then the measured values are also available in pairs, each player has used both bats and there are therefore two measured values from each player.

And it doesn't have to be the same person either. For example, if you wanted to find out whether in a relationship between women and men, women do more gardening than men, you would also have a dependent sample. You would have two measurements each, always in pairs, always one woman and one man.

## Independent sample

In independent samples (or unpaired sample), the values come from two or more different groups. For example, if the group of men and the group of women 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 samples, there can also be more than two samples. The important thing is that in the case of an independent sample, the individual groups or samples have nothing to do with each other, and in the case of a dependent sample, a respondent is present 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.

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