Question

The New Jersey Department of Public Health offers psychological support programs for substance abuse patients with depression. It is suggested that the type of depression varies by the type of substance abuse. If so, such a relationship might help the department better target treatments. They random sample 75 medically declared substance abusers with depression. (C15PROB7.SAV) (χ2 = 5.12, p=.077; V=0.26; Lambdarow= 0.11, p > .05

Substance Abuse	Clinical	Dysthymic	Manic
Alcohol	20	10	8
Drugs	10	15	12

Select and justify the best test(s). The chi-square, Phi, Yates, or Lambda (or even a combination) might be best for a problem given the data and research question. Do not assume the independent is always on the row.

 Provide the null and alternative hypotheses in formal and plain language for the appropriate test at the 0.05 significance level.

 Do the math and reject/retain null at a=.05. State your critical value.

 Explain the results in plain language.

Answer 1

The New Jersey Department of Public Health offers psychological support programs for substance abuse patients with depression. It is suggested that the type of depression varies by the type of substance abuse. If so, such a relationship might help the department better target treatments. They random sample 75 medically declared substance abusers with depression. (:C15PROB7.SAV) (χ2 = 5.12, p=.077; V=0.26; Lambdarow= 0.11, p > .05

Substance Abuse	Clinical	Dysthymic	Manic
Alcohol	20	10	8
Drugs	10	15	12

Select and justify the best test(s). The chi-square, Phi, Yates, or Lambda (or even a combination) might be best for a problem given the data and research question. Do not assume the independent is always on the row.

Since we want to test is there any association between type of depression and type of substance abuse, chi square test is appropriate.

· Provide the null and alternative hypotheses in formal and plain language for the appropriate test at the 0.05 significance level.

Ho: There is no association between type of depression and type of substance abuse

H1: There is an association between type of depression and type of substance abuse

· Do the math and reject/retain null at a=.05. State your critical value.

Chi-Square Test
Observed Frequencies
	Column variable					Calculations
Substance Abuse	Clinical	Dysthymic	Manic	Total		fo-fe
Alcohol	20	10	8	38		4.8000	-2.6667	-2.1333
Drugs	10	15	12	37		-4.8000	2.6667	2.1333
Total	30	25	20	75
Expected Frequencies
	Column variable
Substance Abuse	Clinical	Dysthymic	Manic	Total		(fo-fe)^2/fe
Alcohol	15.2	12.6667	10.1333	38		1.5158	0.5614	0.4491
Drugs	14.8	12.3333	9.8667	37		1.5568	0.5766	0.4613
Total	30	25	20	75
Data
Level of Significance	0.05
Number of Rows	2
Number of Columns	3
Degrees of Freedom	2
Results
Critical Value	5.991
Chi-Square Test Statistic	5.1209
p-Value	0.0773
Do not reject the null hypothesis

calculated chi square = 5.1209

critical chi square at 0.05 level with 2 Df = 5.991

Since calculated chi square 5.1209 < critical value at 0.05 level, 5.991.

Ho is not rejected.

· Explain the results in plain language.

We conclude that there is no association between type of depression and type of substance abuse.