Paired Samples Test

Definition

The paired samples test is a statistical method used to compare the means of two related or dependent samples. It is commonly employed in scenarios where the same individuals or subjects are measured under two different conditions or at different time points.

5 Must Know Facts For Your Next Test

1. The paired samples test is used to compare the means of two related or dependent samples, such as the same individuals measured under two different conditions or at different time points.
2. The test assumes that the differences between the paired observations follow a normal distribution.
3. The null hypothesis for the paired samples test is that the mean difference between the two samples is zero, indicating no significant difference.
4. The test statistic used in the paired samples test is the t-statistic, which follows a t-distribution and is used to determine the statistical significance of the difference between the means.
5. The paired samples test is commonly used in studies where researchers want to assess the impact of an intervention or treatment on the same group of individuals.

Review Questions

• Explain the purpose of the paired samples test and when it would be appropriate to use this statistical method.
  • The paired samples test is used to compare the means of two related or dependent samples, such as measurements taken from the same individuals under two different conditions or at different time points. This test is appropriate when the observations in the two samples are paired or matched, and the researcher wants to assess whether there is a significant difference between the means of the two samples. The paired samples test assumes that the differences between the paired observations follow a normal distribution, and the null hypothesis is that the mean difference between the two samples is zero, indicating no significant difference.
• Describe the test statistic used in the paired samples test and explain how it is used to determine the statistical significance of the difference between the means.
  • The test statistic used in the paired samples test is the t-statistic, which follows a t-distribution. The t-statistic is calculated by dividing the mean difference between the two samples by the standard error of the mean difference. The t-statistic is then compared to the critical value from the t-distribution, based on the degrees of freedom and the chosen significance level. If the calculated t-statistic is greater than the critical value, the null hypothesis is rejected, and the researcher can conclude that there is a statistically significant difference between the means of the two samples.
• Analyze the potential implications of the paired samples test in the context of hypothesis testing for two means and two proportions.
  • $$ \text{The paired samples test is particularly relevant in the context of hypothesis testing for two means and two proportions when the samples are related or dependent.} \text{In the case of hypothesis testing for two means, the paired samples test can be used to compare the means of two related samples, such as measurements taken from the same individuals before and after an intervention.} \text{Similarly, in hypothesis testing for two proportions, the paired samples test can be used to compare the proportions of a binary outcome (e.g., success or failure) in the same group of individuals under two different conditions or time points.} \text{The use of the paired samples test in these contexts can provide more statistical power and precision in detecting significant differences, as it accounts for the correlation between the paired observations.} $$

Related terms

Dependent Samples:

Samples in which the observations are paired or matched, such as measurements taken from the same individuals before and after an intervention.

Null Hypothesis: The statistical hypothesis that there is no significant difference between the means of the two related samples.

t-statistic:

The test statistic used in the paired samples test, which follows a t-distribution and is used to determine the statistical significance of the difference between the means.