Question

Researchers wants to know if taking the herbal supplement St. John's Wort will affect depression. First, they measure the depression level of a sample of n = 4 depressed people (Pre-Test Scores). Then after a week of taking St. John's Wort, they again measure the sample's depression levels (Post-Test Scores). Note that high scores on the depression measure indicate more depression, whereas low scores indicate less depression.

Participant	Pre-Test Scores	Post-Test Scores
A	9	6
B	12	5
C	13	8
D	11	9

(a) Identify the Independent Variable (IV):

Depression level

People taking not taking St. John's Wort   

People taking St. John's Wort

St. John's Wort

(b) Identify the Dependent Variable (DV):

Depression level

People taking not taking St. John's Wort  

  People taking St. John's Wort

St. John's Wort

(c) What is the null hypothesis (H₀) for a two-tailed test?

μ_D ≥ 0

μ_D ≤ 0

   μ_D = 0

μ_D ≠ 0

(d) What is the alternative hypothesis (H₁) for a two-tailed test?

μ_D ≥ 0

μ_D ≤ 0   

μ_D = 0

μ_D ≠ 0

(e) Compute df for the related samples t test.

df =

(f) Use the t distribution table in Appendix B to determine the critical value of t for a two-tailed test at the 0.05 level of significance. (Use 3 decimal places.)

t-critical = ±

(g) Calculate the difference scores and M_D.

Participant	Pre-Test Scores	Post-Test Scores	D	D2
A	9	6
B	12	5
C	13	8
D	11	9
			ΣD =	ΣD2 =

M_D =

(h) Compute the Sum of Squares, sample variance, and estimated standard error for the difference scores (D).

SSD =	(Use 3 decimal places.)
s2D =	(Use 3 decimal places.)
sMD =	(Use 3 decimal places.)

(i) Compute the t-statistic for your data. (Use 3 decimal places.)

t =

(j) What decision should be made about the null hypopthesis (H_o)?

Fail to reject the null hypothesis, there is no significant reduction in depression.

Reject the null hypothesis, there is no significant reduction in depression.

   Reject the null hypothesis, there is a significant reduction in depression

Fail to reject the null hypothesis, there is a significant reduction in depression.

(k) Calculate the estimated Cohen's d and r² to measure effect size for this study. (Use 3 decimal places.)

d =
r² =

(l) How would the results be presented in the literature?

Taking St. John's Wort reduced depression levels by an average of (M = -4.25, SD = 2.217). This treatment effect was not significant, t(3) = -3.833, p > 0.05.

Taking St. John's Wort reduced depression levels by an average of (M = -4.25, SD = 2.217). This treatment effect was significant, t(4) = -3.833, p < 0.05.  

  Taking St. John's Wort reduced depression levels by an average of (M = -4.25, SD = 2.217). This treatment effect was significant, t(3) = -3.833, p < 0.05.

Taking St. John's Wort reduced depression levels by an average of (M = -4.25, SD = 2.217). This treatment effect was not significant, t(4) = -3.833, p > 0.05.

Answer 1