Question

A researcher conducts an independent-measures study. One sample of individuals serves as a control group and another sample serves as a treatment group. The researcher hypothesizes that the two samples will be different on the dependent variable.

The data are as follows:

Control	Treatment
n = 6	n = 9
M = 56	M = 62
SS = 470	SS = 700

α = .05, two-tailed

a.) Following the steps of a hypothesis test, first determine whether the two groups differ in terms of their sample means.

b.) Second, calculate Cohen’s d and r2.

c.) Finally, Write a sentence demonstrating how the results of the hypothesis test and the measure of effect size (use either d or r2) would appear in a research report.

Answer 1

(a) s1 = √(SS/(n - 1)) = √(470/5) = 9.695, s2 = √(700/8) = 9.354

Data:        

n1 = 6       

n2 = 9       

x1-bar = 56       

x2-bar = 62       

s1 = 9.695       

s2 = 9.354       

Hypotheses:        

Ho: μ1 = μ2        

Ha: μ1 ≠ μ2        

Decision Rule:        

α = 0.05       

Degrees of freedom = 6 + 9 - 2 = 13      

Lower Critical t- score = -2.160368652       

Upper Critical t- score = 2.160368652       

Reject Ho if |t| > 2.160368652       

Test Statistic:        

Pooled SD, s = √[{(n1 - 1) s1^2 + (n2 - 1) s2^2} / (n1 + n2 - 2)] =   √(((6 - 1) * 9.695^2 + (9 - 1) * 9.354^2)/(6 + 9 -2)) =     9.487

SE = s * √{(1 /n1) + (1 /n2)} = 9.48660453562731 * √((1/6) + (1/9)) = 4.999879599      

t = (x1-bar -x2-bar)/SE = -1.200028897       

p- value = 0.25154096       

Decision (in terms of the hypotheses):        

Since 1.200028897 < 2.160368652 we fail to reject Ho    

Conclusion (in terms of the problem):        

There is no sufficient evidence that the group means are different

(b)

Cohen's d = |(x1-bar - x2-bar)|/Pooled s = |(56 - 62)|/9.487 = 0.632

r^2 = (t^2)/(t^2 + df) = (-1.2)^2 / ((-1.2)^2 + 13) = 0.10

(c) Since the p- value for the hypothesis test is > the level of significance, there is no sufficient evidence that the group means are different. Both Cohen's d and r^2 indicate a medium effect for the treatment.