Paired t-test
The paired t-test, also known as the dependent t-test, is a statistical method used to determine whether there are statistically significant differences between the means of two related groups. It is particularly useful when comparing the means of the same group under two different conditions or time points.
When to use paired t-test?
The paired t-test is appropriate when you have two related groups, such as repeated measures on the same individuals, matched pairs, or before-and-after measurements on the same subjects. This test is commonly employed in educational research to evaluate the effectiveness of teaching interventions or instructional methods.
Assumptions and Data Requirements:
Before conducting a paired t-test, several assumptions must be met:
Normality: The differences between paired observations should be approximately normally distributed.
Independence: The paired observations should be independent of each other.
Equality of variances: The variances of the differences between paired observations should be equal.
Additionally, the data required for a paired t-test should consist of continuous variables obtained from a random sample.
Writing the Hypothesis:
The null hypothesis (H0) for a paired t-test states that there is no significant difference between the means of the paired observations. The alternative hypothesis (H1) suggests that there is a significant difference between the means of the paired observations.
For example:
H0: There is no significant difference in the mean test scores before and after implementing a new teaching method.
H1: There is a significant difference in the mean test scores before and after implementing a new teaching method.
Sample Situation with Sample Data:
Suppose a researcher wants to assess the effectiveness of a new teaching method on student learning outcomes. A pre-test and post-test are administered to the same group of students to measure their knowledge before and after the intervention.
