Question

What is the difference between a test of independent means and a test of dependent means, and when is each appropriate?

Answer 1

A hypothesis testing is used to evaluate two mutually exclusive statements about the population, and the purpose of hypothesis testing is to determine which statement (from the two) is best supported by the sample data. When data is sufficiently large, the Z-test will be used to test the difference between the mean.

Dependent and Independent Samples

When we are working with one sample, we know that we need to select a random sample from the population, measure that sample statistic and then make hypothesis about the population based on that sample. When we work with two independent samples we assume that if the samples are selected at random (or, in the case of medical research, the subjects are randomly assigned to a group), the two samples will vary only by chance and the difference will not be statistically significant. In short, when we have independent samples we assume that the scores of one sample do not affect the other.

Independent samples can occur in two scenarios.

Testing the difference of the means between two fixed populations we test the differences between samples from each population. When both samples are randomly selected, we can make inferences about the populations.

When working with subjects (people, pets, etc.), if we select a random sample and then randomly assign half of the subjects to one group and half to another we can make inferences about the populations.

Dependent samples are a bit different. Two samples of data are dependent when each score in one sample is paired with a specific score in the other sample. In short, these types of samples are related to each other. Dependent samples can occur in two scenarios. In one, a group may be measured twice such as in a pretest-posttest situation (scores on a test before and after the lesson). The other scenario is one in which an observation in one sample is matched with an observation in the second sample.

A test for independent means:-

When the given samples are independent and we want to check the mean difference is significant or not between the different independent groups, then a test of independent means is used.

For example, there are two groups one consisting of males and other consisting of females with a heart problem, we want to check the mean effect of yoga is the same or not for both males and females, then an independent means test would be used.

A test for dependent means:-

When the same sample is compared at different times to check the effectiveness or the significance, then a test of dependent means is used.

For example, 60 people with heart problems were randomly selected and we want to check the mean effect of yoga at the start and at the end (says 30 days) of the study, then a paired sample mean test would be used to compare the mean effect of yoga.