Question

Ms Mahon collected data on the treatment for eating disorders. She was interested in how likely participants were to remain in treatment or drop out, and she wanted to examine this with respect to the number of traumatic events they had experienced in childhood. Her general hypothesis was that participants who had experienced more traumatic events during childhood would be more likely to drop out of treatment.

The data from this study are shown below. I have taken the liberty of altering them slightly so that I don't have to deal with the problem of small expected frequencies at the same time that I am trying to show how to make use of the ordinal nature of the data. The altered data are still a faithful representation of the effects that she found.

                                                                                  Number of Traumatic Events                  

	0	1	2	3	4+
Dropout	25	13	9	10	6
Remain	31	21	6	2	3

1. State the hypotheses for this study
2. Using Excel, run the appropriate statistical test (Attach your Excel results)

c)  What is the p-value?

d)  What is the critical value?

e)  What is the Test statistic?

f)  Make a decision:

g) Draw a conclusion (in the context of the problem):

Answer 1

(a) The hypothesis being tested is:

H0: Participants who had experienced more traumatic events during childhood would be the same likely as the drop out of treatment

Ha: Participants who had experienced more traumatic events during childhood would be more likely to drop out of treatment

(b)

		0	1	2	3	4+	Total
Dropout	Observed	25	13	9	10	6	63
	Expected	28.00	17.00	7.50	6.00	4.50	63.00
	O - E	-3.00	-4.00	1.50	4.00	1.50	0.00
	(O - E)² / E	0.32	0.94	0.30	2.67	0.50	4.73
Remain	Observed	31	21	6	2	3	63
	Expected	28.00	17.00	7.50	6.00	4.50	63.00
	O - E	3.00	4.00	-1.50	-4.00	-1.50	0.00
	(O - E)² / E	0.32	0.94	0.30	2.67	0.50	4.73
Total	Observed	56	34	15	12	9	126
	Expected	56.00	34.00	15.00	12.00	9.00	126.00
	O - E	0.00	0.00	0.00	0.00	0.00	0.00
	(O - E)² / E	0.64	1.88	0.60	5.33	1.00	9.46
		9.49	critical
		9.46	chi-square
		4	df
		.0506	p-value

The p-value is 0.0506.

Since the p-value (0.0506) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that participants who had experienced more traumatic events during childhood would be more likely to drop out of treatment.

Please give me a thumbs-up if this helps you out. Thank you!