Question

Hospital administrators at a local hospital are interested in quality of care. As such, they ask a random sample of patients that have used the hospital's health care services to fill out a questionnaire. The questionnaire has questions about the patient's worry (negative, positive), the hospital staff's communication skills (low, medium, high), and satisfaction with medical care. The administrators are interested in how patient's worry and their assessment of the hospital staff's communication impact their satisfaction with medical care. The survey data are below. What can the administrators conclude with an α of 0.05?

	Communication
Worry	low	med	high
negative	7 6 8 6 8	8 4 5 4 5	6 7 4 6 5
positive	8 6 6 7 7	7 8 6 8 7	7 8 6 6 6

a) What is the appropriate test statistic?
(na, one-way ANOVA ,within-subjects ANOVA ,two-way ANOVA )

b) Compute the appropriate test statistic(s) to make a decision about H₀.
Worry: p-value =    
Communication: p-value =   
Interaction: p-value =     


c) Using the SPSS results, compute the corresponding effect size(s) and indicate magnitude(s).
Worry: η² =   ;  -(na, trivial effect. small effect. medium effect, large effect)  
Communication: η² =   ; (na, trivial effect, small effect, medium effect, large effect)  
Interaction: η² =   ; ( na, trivial effect, small effect, medium effect, large effect)  

Answer 1

a)

two-way ANOVA

b)

Applying two way ANOVA:

Source of Variation	SS	df	MS	F	P-value	F crit
Worry	6.5333	1	6.5333	5.4444	0.0283	4.2597
Communication	3.8000	2	1.9000	1.5833	0.2260	3.4028
Interaction	6.0667	2	3.0333	2.5278	0.1009	3.4028
Within	28.8000	24	1.2000
Total	45.2000	29

Worry: p-value = 0.0283
Communication: p-value = 0.2260
Interaction: p-value = 0.1009

c)

Worry: η² = SS(worry)/SS(total) =6.5333/45.2000=0.1445 , medium effect

Communication: η² =3.80/45.20 =0.0841 , small effect

Interaction: η² = 6.0667/45.20 =0.1342 medium effect