Question

Example 16: A clinical psychologist compared the effectiveness of cognitive behavioral therapy (CBT) to the effectiveness of family therapy (FT) for treating women with anorexia nervosa. The psychologist randomly selected 28 women with anorexia nervosa. 17 of the 28 women were randomly assigned to CBT and the other 11 women were randomly assigned to FT. Each women's weight prior to therapy was subtracted from her weight 3 months after therapy/ Thus the greater the weight difference, the more effective the treatment. The mean weight difference and standard deviation were, respectively, 2.356 lbs and 5,889 lbs for the CBT sample and 8.199 lbs and 4.220 lbs for the FT sample/

P1: The set of weight differences if every woman on the planet with anorexia nervosa underwent CBT. The mean of this population is U1.

p2: The set of weight differences if every woman on the planet with anorexia nervosa underwent FT. The mean of this population is U2.

a) Using α = 0.01, what did the psychologist conclude? (i.e., perform an independent-samples t-test)

b) Construct a 99% confidence interval for the difference between the mean weight difference if every woman with anorexia nervosa underwent CBT and the mean weight difference if every woman with anorexia nervosa underwent FT.

c) Calculate Cohens' d.

Answer 1

a) Using α = 0.01, what did the psychologist conclude? (i.e., perform an independent-samples t-test)

The hypothesis being tested is:

H0: µ1 = µ2

H1: µ1 ≠ µ2

The p-value is 0.0050.

Since the p-value (0.0050) is less than the significance level (0.01), we can reject the null hypothesis.

Therefore, we can conclude that there is a difference in the effectiveness of cognitive behavioural therapy (CBT) to the effectiveness of family therapy (FT).

b) Construct a 99% confidence interval for the difference between the mean weight difference if every woman with anorexia nervosa underwent CBT and the mean weight difference if every woman with anorexia nervosa underwent FT.

The 99% confidence interval for the difference between the mean weight difference if every woman with anorexia nervosa underwent CBT and the mean weight difference if every woman with anorexia nervosa underwent FT is between -11.15 and -0.53.

c) Calculate Cohens' d.

Cohen's d = 1.06

CBT	FT
2.356	8.199	mean
5.899	4.22	std. dev.
28	11	n
	37	df
	-5.84	difference (CBT - FT)
	30.21	pooled variance
	5.50	pooled std. dev.
	1.96	standard error of difference
	0	hypothesized difference
	-2.988	t
	.0050	p-value (two-tailed)
	-11.15	confidence interval 99.% lower
	-0.53	confidence interval 99.% upper
	5.31	margin of error
	1.06	Cohen's d