In which of the following situations would it not be appropriate to use a paired t-test to
analyze the data?
A. A marriage therapist believes that many couples have different perspectives
regarding the state of their marriages, 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 thirty married couples were individually given a
marital satisfaction questionnaire. The mean marital satisfaction scores were then
separately calculated for the group of husbands and the group of wives.
B. 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.
C. 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.
D. 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.
What is (are) your question(s)?
a, b,c
b and c
A paired t-test is appropriate when comparing the means of two dependent groups, where each observation in one group is matched or paired with an observation in the other group. It is used to assess whether there is a statistically significant difference between the means before and after an intervention or treatment.
In the given situations, let's analyze each option to determine whether a paired t-test would be appropriate:
A. In this situation, the data are collected from married couples to compare the marital satisfaction scores of husbands and wives. Each member of the couples completes a questionnaire individually. Since the scores within each couple are not paired or dependent, a paired t-test would not be appropriate. Instead, an independent t-test could be used to compare the means of two independent groups (husbands and wives).
B. Here, the psychologist wants to assess the level of extraversion in fraternal twins. The twins are assessed individually using a personality questionnaire. As the observations are independent and not paired, a paired t-test would not be appropriate. Again, an independent t-test can be used to compare the means of twins.
C. In this case, the psychiatrist wants to compare the mean depression scores between two groups: the New Drug group and the Placebo group. The participants are randomly assigned to one of the two groups and complete the inventory individually. Since the observations in each group are independent and not paired, a paired t-test is not suitable. An independent t-test can be used to compare the mean depression scores between the two groups.
D. Here, the researcher wants to analyze the effect of sleep deprivation on maze completion. The same group of people is tested on two different occasions: Day 1 and Day 2 after 36 hours of sleep deprivation. The number of errors made on Day 1 is then compared to the number of errors made on Day 2. Since the observations are paired (each person's performance is measured twice), a paired t-test would be appropriate to assess whether there is a significant difference in maze completion between the two occasions.
Therefore, the situations where it would not be appropriate to use a paired t-test are options A, B, and C.