Dependent and independent samples

What are dependent and independent samples?

The distinction between dependent and independent samples is important because it determines which hypothesis test you should use.

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 dependent and independent samples

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 numiqo.com to measure people's stress levels. In the survey, you ask people about their stress level before and after the 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 measurements always come in pairs. For this research question, that paired design is the better choice.

Dependent Samples

In a dependent sample, the measurements 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 if each woman is paired with her male partner. You would then have two measurements that go together in pairs, one from each partner.

Independent Samples

In independent samples, the observations in one group are unrelated to those in the other groups. For example, if separate groups of men and women are asked about their income, the samples are independent. In this case, each person belongs to only one group and cannot be paired with a person from the other group.

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 are unrelated. In dependent samples, the same respondent may appear in all groups, or observations may be related through matching or another form of pairing.

Hypothesis testing for Dependent and Independent Samples

Many common hypothesis tests have one version for independent samples and another for dependent samples. For t-tests, the terms paired and unpaired are also commonly used. For analysis of variance, the corresponding terms are with repeated measures and without repeated measures.

In numiqo 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 row represents a respondent or, more generally, a case. Therefore, multiple metric values within the same row are treated as repeated measures (dependent).

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