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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 marriage therapist believes that many couples have different perspectives regarding the state of their marriage prior to the start of couples therapy. In order to determine whether there is difference in marital satisfaction, prior to the start of couples therapy, each member of 30 married couples is individually given a marital satisfaction questionnaire. For each couple, the marital satisfaction scores of the wife and husband are compared to see if there is a difference in how they view the state of their marriage. A psychologist was interested in determining whether fraternal twins differ in terms the degree to which they are extroverts. A sample of 50 fraternal twins was given the Eysenck personality questionnaire to assess their levels of extraversion. Each twin’s extraversion score was compared to his/her fraternal twin. A psychiatrist believes that a new medication (New Drug) is more effective at reducing the symptoms of depression than a placebo, sugar pill (Placebo). Sixty people with depression were randomly assigned to one of two groups, (1) New Drug or (2) Placebo, and were given the assigned drug or sugar pill for 30 days. Each of the 60 participants then completed the Beck Depression Inventory and the mean depression score for the New Drug group is compared to the mean depression score for the Placebo group. A researcher is interested in determining the effects of sleep deprivation on the accuracy with which mazes are completed. Thirty people are given a test of mazes on Day 1 at 9 am and again on Day 2 at 9 pm after being kept awake for 36 hours. The researcher then compares the number of errors made on Day 1 to Day 2.

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 marriage therapist believes that many couples have different perspectives regarding the state of their marriage prior to the start of couples therapy. In order to determine whether there is difference in marital satisfaction, prior to the start of couples therapy, each member of 30 married couples is individually given a marital satisfaction questionnaire. For each couple, the marital satisfaction scores of the wife and husband are compared to see if there is a difference in how they view the state of their marriage. A psychologist was interested in determining whether fraternal twins differ in terms the degree to which they are extroverts. A sample of 50 fraternal twins was given the Eysenck personality questionnaire to assess their levels of extraversion. Each twin’s extraversion score was compared to his/her fraternal twin. A psychiatrist believes that a new medication (New Drug) is more effective at reducing the symptoms of depression than a placebo, sugar pill (Placebo). Sixty people with depression were randomly assigned to one of two groups, (1) New Drug or (2) Placebo, and were given the assigned drug or sugar pill for 30 days. Each of the 60 participants then completed the Beck Depression Inventory and the mean depression score for the New Drug group is compared to the mean depression score for the Placebo group. A researcher is interested in determining the effects of sleep deprivation on the accuracy with which mazes are completed. Thirty people are given a test of mazes on Day 1 at 9 am and again on Day 2 at 9 pm after being kept awake for 36 hours. The researcher then compares the number of errors made on Day 1 to Day 2.

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Solution

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

  1. The marriage therapist's study: This is because the same individuals (husbands and wives) are being measured twice - before the start of couples therapy. The scores of the wife and husband are dependent on each other, making this a paired sample.

  2. The psychologist's study on fraternal twins: Again, this is a case of dependent samples because the extraversion scores of each twin are being compared to their fraternal twin.

  3. The researcher's study on sleep deprivation: The same individuals are being tested on two different days, making this a paired sample. The number of errors made on Day 1 and Day 2 are dependent on each other.

The paired t-test would not be appropriate for the psychiatrist's study on the new medication. This is because the participants are divided into two independent groups (New Drug and Placebo), and the depression scores of individuals in one group are not dependent on the scores of individuals in the other group. This would require an independent samples t-test.

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