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In which of the following situations would it be appropriate to use a paired t-test to analyze the data? Check all that apply. A researcher was interested in the differences in attitudes towards saving money and eliminating debt between couples who are engaged to be married. As part of a premarital counseling program, 45 engaged couples filled out a survey that assessed their attitudes towards financial matters such as their priorities for saving money and eliminating debt. The researcher compared the scores of each member of the engaged couple to see if there was a mean difference in the couples’ attitudes towards saving money and eliminating debt. A biologist was interested in finding out whether rats who are littermates (siblings who are born at the same time) have similar abilities when learning how to run a maze. The biologists selected 50 pairs of littermates and tested how many trials it took for the rat to get to the end of the maze in less than 10 seconds. The null hypothesis was that there would be no mean difference in the number of trials that the rat and their litter mate would take to complete the maze in under 10 seconds. Each rat’s maze time was compared to his/her littermate. A medical researcher believes that a new drug will increase a patient’s red blood cell count at a higher rate than that achieved by an old drug currently in use. The researcher randomly assigns 50 patients to be in the “new drug” group and 50 patients to be in the “old drug” group, then compares the mean red blood cell count for the “new drug” group to the red blood cell count of the “old drug” group. A researcher is interested in determining the effects of caffeine on manual dexterity. The researcher recruits a sample of 60 participants and asks each participant to complete a manual dexterity task similar to the game “Operation.” Each participant completes the task twice: On Day 1, participants complete the task when they have not consumed any caffeine for at least 6 hours. On Day 2, the participants drink a beverage with 200 mg of caffeine 20 minutes before completing the task. The researcher compares each individual’s number of errors in the task with and without caffeine exposure and computes a mean difference.

Question

In which of the following situations would it be appropriate to use a paired t-test to analyze the data? Check all that apply. A researcher was interested in the differences in attitudes towards saving money and eliminating debt between couples who are engaged to be married. As part of a premarital counseling program, 45 engaged couples filled out a survey that assessed their attitudes towards financial matters such as their priorities for saving money and eliminating debt. The researcher compared the scores of each member of the engaged couple to see if there was a mean difference in the couples’ attitudes towards saving money and eliminating debt. A biologist was interested in finding out whether rats who are littermates (siblings who are born at the same time) have similar abilities when learning how to run a maze. The biologists selected 50 pairs of littermates and tested how many trials it took for the rat to get to the end of the maze in less than 10 seconds. The null hypothesis was that there would be no mean difference in the number of trials that the rat and their litter mate would take to complete the maze in under 10 seconds. Each rat’s maze time was compared to his/her littermate. A medical researcher believes that a new drug will increase a patient’s red blood cell count at a higher rate than that achieved by an old drug currently in use. The researcher randomly assigns 50 patients to be in the “new drug” group and 50 patients to be in the “old drug” group, then compares the mean red blood cell count for the “new drug” group to the red blood cell count of the “old drug” group. A researcher is interested in determining the effects of caffeine on manual dexterity. The researcher recruits a sample of 60 participants and asks each participant to complete a manual dexterity task similar to the game “Operation.” Each participant completes the task twice: On Day 1, participants complete the task when they have not consumed any caffeine for at least 6 hours. On Day 2, the participants drink a beverage with 200 mg of caffeine 20 minutes before completing the task. The researcher compares each individual’s number of errors in the task with and without caffeine exposure and computes a mean difference.

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Solution

The paired t-test would be appropriate in the following situations:

  1. The researcher studying differences in attitudes towards saving money and eliminating debt between couples who are engaged to be married. This is because the data is paired, with each pair being a couple, and the researcher is looking for a mean difference in attitudes within each pair.

  2. The biologist studying whether rats who are littermates have similar abilities when learning how to run a maze. Again, the data is paired (each pair being a set of littermates), and the biologist is looking for a mean difference in the number of trials it took each rat to complete the maze.

  3. The researcher studying the effects of caffeine on manual dexterity. In this case, the pairs are the same individuals tested under two different conditions (with and without caffeine). The researcher is looking for a mean difference in the number of errors made in the task under these two conditions.

The paired t-test would not be appropriate for the medical researcher studying whether a new drug increases a patient’s red blood cell count at a higher rate than an old drug. This is because the data is not paired; the patients in the "new drug" group are not in any way linked or paired with the patients in the "old drug" group. A different statistical test, such as an independent samples t-test, would be more appropriate in this situation.

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