Question

Q4. Researchers were interested in determining whether gender and/or the number of tours soldiers served affected the incidence of PTSD. The PTSD impact instrument was used and scores were recorded upon discharge.

1. State the null and alternate hypotheses. Include both interaction and main effect hypotheses (should be 3 null and 3 alternate hypotheses).
2. What is the total sample size?
3. Identify the independent and dependent variables
4. List the test statistic and p value for the all your hypotheses? (Hint, there should be 3)
5. What is your conclusion (assume α = .05)?
6. What are the effect sizes?

Gender	Number_tours	Mean	Std. Deviation	N
1	1	4.04	1.989	249
	2	4.80	1.367	249
	Total	4.42	1.747	498
2	1	4.39	2.061	249
	2	4.97	1.467	249
	Total	4.68	1.810	498
Total	1	4.21	2.031	498
	2	4.89	1.419	498
	Total	4.55	1.783	996

Tests of Between-Subjects Effects
Source	Type III Sum of Squares	df	Mean Square	F	Sig.	Partial eta squared
Corrected Model	131.285a	3	43.762	14.322	.000	.042
Intercept	20621.510	1	20621.510	6748.649	.000	.872
Gender	16.968	1	16.968	5.553	.019	.006
Number_tours	112.004	1	112.004	36.655	.000	.036
Gender * Number_tours	2.313	1	2.313	.757	.384	.001
Error	3031.205	992	3.056
Total	23784.000	996
Corrected Total	3162.490	995

Answer 1

a) For Gender:

Null Hypothesis H0:

Alternative Hypothesis Ha:

For Number of tour:

Null Hypothesis H0:

Alternative Hypothesis Ha:

For Interaction:

Null Hypothesis H0: There is no interaction effect.

Alternative Hypothesis Ha: There is an interaction effect.

b) Total sample size N= 996

c) Independent variable: Gender and number of tours

Dependent variable: Incidence of PTSD

d) Test statisic for Gender F= 5.553 and P value= 0.019

Test Statistic for Number tours F= 36.655 and P value= 0.000

Test Statistic for Interaction F= 0.757 and P value= 0.384

e) For Gender P value smaller than the level of Significance 0.05 therefore SIGNIFICANT. REJECT NULL HYPOTHESIS HO. WE CAN CONCLUDE THAT THERE IS DIFFERENCE IN MEANS.

For Number of tour P value SMALLER THAN THE LEVEL OF SIGNIFICANCE. REJECT NULL HYPOTHESIS H0. WE CAN CONCLUDE THAT THERE IS DIFFERENCE IN MEANS.

FOR INTERACTION EFFECT P VALUE 0.757 GREATER THAN THE LEVEL OF SIGNIFICANCE. DO NOT REJECT NULL HYPOTHESIS H0. WE DON'T HAVE SUFFICIENT EVIDENCE TO SHOW THAT THERE IS AN INTERACTION BETWEEN TWO VARIABLES.

f) EFFECT SIZE FOR GENDER IS 0.006 SMALL

EFFECT SIZE FOR NUMBER OF TOUR IS 0.036 SMALL.

Effect size for INTERACTION is 0.001 SMALL