Question

A study of drug use among 12,372 college students matriculating for the first time in Fall 2012 looked at whether students increase their use of alcohol and recreational drugs over the course of their college career. Drug and alcohol use was measured every semester from Fall 2012 to Spring 2020. Results were broken down by a number of demographic variables including sex.

Number of day using per month
2012 2020
Mean St. dev. Mean St. dev.
Men (n=5520) 6.7 1.9 5.3 1.9
Women (n=6852) .5 2.2 4.1 1.7
Instead of just taking Fall 2012 and Spring 2020 as convenient start and end points, I might use students' drug use scores for every semester. These could be displayed in a time graph. If I took this approach, I probably wouldn't use a t test. Instead, I'd probably use:

a. Mann-Whitney/Wilcoxon test
b. a ²χ² test of association
c. correlation
d. a paired samples test

Answer 1

A paired samples test, like the paired t-test or repeated measures ANOVA, is suitable for analyzing repeated drug use scores over time, accounting for within-subject correlation. Correlation could be used to measure the relationship between time and drug use scores.

Therefore, the correct answer is: option d. a paired samples test.

Step-by-step explanation:

If you were to examine students' drug use scores for every semester from Fall 2012 to Spring 2020, you'd likely be dealing with data that is collected repeatedly over time from the same subjects. For such data, a paired samples test or repeated measures analysis would typically be appropriate, as these can take into account the correlation between measurements taken from the same individual at different times.

When analyzing data over time, it is crucial to account for this within-subject correlation to draw accurate conclusions about changes in drug and alcohol use among college students. A paired samples test, such as the paired t-test or a repeated measures ANOVA, would help assess if there are statistically significant changes in usage over time.

On the other hand, correlation could be used to measure the strength and direction of the relationship between the time in college and the drug use scores, but it wouldn't test for changes over time unless specifically looking at serial correlation.