Question

In: Statistics and Probability

How do you interpret a t value? When would it be appropriate to use a t...

  1. How do you interpret a t value?
  2. When would it be appropriate to use a t test of dependent samples? Please provide an example.

Solutions

Expert Solution

dependent paired sample t test

What does this test do?

The dependent t-test (also called the paired t-test or paired-samples t-test) compares the means of two related groups to determine whether there is a statistically significant difference between these means.

What variables do you need for a dependent t-test?

You need one dependent variable that is measured on an interval or ratio scale (see our Types of Variable guide if you need clarification). You also need one categorical variable that has only two related groups.

Paired Sample T-Test

The paired sample t-test, sometimes called the dependent sample t-test, is a statistical procedure used to determine whether the mean difference between two sets of observations is zero. In a paired sample t-test, each subject or entity is measured twice, resulting in pairs of observations. Common applications of the paired sample t-test include case-control studies or repeated-measures designs. Suppose you are interested in evaluating the effectiveness of a company training program. One approach you might consider would be to measure the performance of a sample of employees before and after completing the program, and analyze the differences using a paired sample t-test.

One of the most common experimental designs is the "pre-post" design. A study of this type often consists of two measurements taken on the same subject, one before and one after the introduction of a treatment or a stimulus. The basic idea is simple. If the treatment had no effect, the average difference between the measurements is equal to 0 and the null hypothesis holds. On the other hand, if the treatment did have an effect (intended or unintended!), the average difference is not 0 and the null hypothesis is rejected.

The Paired-Samples T Test procedure is used to test the hypothesis of no difference between two variables. The data may consist of two measurements taken on the same subject or one measurement taken on a matched pair of subjects.

Additionally, the procedure produces:

  • Descriptive statistics for each test variable
  • The Pearson correlation between each pair and its significance
  • A confidence interval for the average difference (95% or a value you specify)

levels are measured before and after the study, and the physician wants to know if either set of measurements has changed.


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