The student in Question 5 from Module 18
decides to conduct the same study using a
within-participants design in order to control
for differences in cognitive ability. He
selects a random sample of participants and
has them study different material of equal
difficulty in both the music and no music
conditions. The data appear below. As
before, they are measured on an intervalratio
scale and are normally distributed.
Music No Music
6 10
7 7
6 8
5 7
6 7
8 9
8 8
a. What statistical test should be used to
analyze these data?
b. Identify H0 and Ha for this study.
c. Conduct the appropriate analysis.
d. Should H0 be rejected? What should the
researcher conclude?
e. If significant, compute the effect size and
interpret.
f. If significant, draw a graph representing
the data.
a. To analyze these data, a paired-sample t-test should be used. A paired-sample t-test is appropriate when you want to compare the means of two related groups.
b. H0 (null hypothesis): There is no difference in the mean scores between the music and no music conditions.
Ha (alternative hypothesis): There is a difference in the mean scores between the music and no music conditions.
c. To conduct the paired-sample t-test, first calculate the differences between the paired observations (music - no music). Then, calculate the mean and standard deviation of these differences. Finally, use these values to perform the t-test.
d. To determine whether H0 should be rejected, compare the obtained t-value with the critical t-value at a given significance level (e.g., α = 0.05). If the obtained t-value is greater than the critical t-value, H0 can be rejected, indicating a significant difference between the means. If the obtained t-value is not greater than the critical t-value, H0 should not be rejected, suggesting no significant difference between the means.
e. If H0 is rejected, compute the effect size using Cohen's d. This is calculated by dividing the mean difference by the pooled standard deviation of the differences. The magnitude of Cohen's d can be interpreted as small (d = 0.20), medium (d = 0.50), or large (d = 0.80).
f. To draw a graph representing the data, you can create a paired bar graph or a line graph. Each point on the graph represents one participant's pair of scores, with one bar or point representing the music condition and the other representing the no music condition. The graph can visually illustrate the differences or changes between the two conditions.