When the subjects are paired or matched in some way samples are considered to be?

This test is used for either of two types of comparisons.

• Pre-post Comparisons: One sample of subjects is measure twice under two different conditions, e.g., before and after receiving a drug.
• Comparison of Matched Samples: Two samples of pair-matched subjects, e.g., siblings or twins, or subjects matched by age and hospital ward

Example: Does a training intervention increase HIV knowledge?

Early in the HIV epidemic, there was poor knowledge of HIV transmission risks among health care staff. A short training was developed to improve knowledge and attitudes around HIV. Was the training effective in improving knowledge?

One could address this question with either two independent samples or with one dependent sample, but a single dependent sample would be a more efficient approach and it would have greater statistical power, i.e., ability to detect a significant difference if it exists. The illustration below outlines both approaches.

Two Independent Sample Option: We could enroll 30 subjects and randomly assign them to one of two groups. The 15 subjects in Group 1 would take the test of HIV knowledge without the training session, and 15 different subjects would receive the training and then be tested. These are two independent groups and we would compute the mean test score for each group and compare the means with a t-test for independent groups as discussed in the previous section. Results are shown under the independent option. The mean score in Group 1 was 17.2±4.7, and the mean score in Group 2 was 20.2±4.7. The difference in means is 3.0, and the p-value is 0.09, so the difference did not reach the 0.05 criterion for statistical significance.

Dependent Sample Option: The other option would be to enroll just 15 subject, but test them each twice. They would be tested initially, then they would be trained, and then they would be tested again after the training. So, for each subject, we have a pair of scores, pre-test and post-test. With this design, we are interested in the change in score for each subject, as shown in the dependent results on the right side of the figure. The t-test for a dependent or matched sample like this, computes the difference in scores for each and tests the null hypothesis that the mean difference is 0. In fact, the mean difference in scores is 3.0, and this is statistically significant with p=0.001. This design has greater statistical power, because each subject seves as their own control, greatly diminishing the person-to-person variability seen with the independent design.

The equation for the t-test for dependent groups is:

\(t-statistic=\frac{x_{diff}-\mu_{diff}}{\displaystyle\frac{s_{diff}}n}\;\;\;\;\;\;\;\;\;\;\;degreesoffreedom=n-1\)

where \(\mu_{diff}\) = the null hypothesis

In most circumstances, you are testing for any change in the paired measures, then the null hypothesis is that \(\mu_{diff}\)=0, but if you want to test whether the mean difference is different from a certain amount, plug that into \(\mu_{diff}\). If you are doing the usual paired t-test for which the null hypothesis is that the mean difference is 0, then you can just use the methods described in Epi-Tools. XLSX.

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Statistics Definitions > Matched Samples

What are Matched Samples?

• The same study participants are measured before and after an intervention.
• The same study participants are measured twice for two different interventions.

The opposite of a matched sample is an independent sample, which deals with unrelated groups. While matched pairs are chosen deliberately, independent samples are usually chosen randomly (through simple random sampling or a similar technique).

Purpose

The purpose of matched samples is to get better statistics by controlling for the effects of other “unwanted” variables. For example, if you are investigating the health effects of alcohol, you can control for age-related health effects by matching age-similar participants.

Tests

When you run a hypothesis test, you have to choose a test specifically for either independent samples or dependent (paired) samples. Paired samples can be analyzed with the following specific tests:

• The McNemar test is a non-parametric (distribution free) test for paired nominal data.
• The paired sample t test (also called a “related measures” t-test or dependent samples t-test) compares the means for the two groups to see if there is a statistical difference between the two.
• The Wilcoxon signed rank testis non-parametric alternative to the t-test. Note that this test doesn’t compare means, it compares mean ranks.

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