Question

3. (23 pts) The JASP file ‘sleep-spring2020.csv’ contains data representing the average number of hours of sleep in the last two nights by 8 depressed patients and 9 non-depressed patients. (Group 1 is ‘depressed’ and group 2 is ‘non-depressed.’) The researcher is interested in whether the two groups reliably differ in the amount of sleep they get.

Group	Sleep
1	7.5
1	7.9
1	7.7
1	8.4
1	7.4
1	6.7
1	7.3
1	8.5
2	7
2	6.2
2	5.9
2	6.5
2	7.6
2	7.2
2	6.6
2	7.4
2	6.9

a. (2 pts) What kind of statistical test is appropriate here? Why?

b. (4 pts) What are the null and alternative hypotheses? (Make these two-tailed.)

c. (4 pts) Report the mean and sample standard deviation for each sample.

d. (3 pts) What is t_obt? How many degrees of freedom are there? What is t_crit (a = 0.05_2tail)?

e. (1 pt) Report the p value of t_obt from JASP.

f. (2 pts) What is your conclusion about H₀, using a = .05_2tail? What is the basis for your decision, in terms of the decision rule?

g. (4 pts) By hand, calculate the size of the effect (omega squared) of the study and interpret the effect size. Show your work, including the formula for omega squared.

h. (3 pts) Based on the decision about the null hypothesis, the effect size estimate, and general considerations about statistical power, what should the researcher conclude about possible differences in sleep between depressed and non-depressed patients? Justify your answer in a few sentences.

Answer 1

Using Excel

data -> data analysis -> t-Test: Two-Sample Assuming Equal Variances

a) independent sample t-test

b)
Ho: mu1 = mu2
Ha: mu1 <> mu2

c)

d)
TS= 3.0905

e)
p-value = 0.0075

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