Question

A therapist measures the relationship between a patient's expectations that therapy will be successful and the actual success of the therapy. The following table shows the results of this hypothetical study using a sample of 50 clients.

		Therapy Successful
		Yes	No	Totals
Client expects success	Yes	22	8	30
	No	4	16	20
	Totals	26	24

(a) Compute the phi correlation coefficient. (Round your answer to three decimal places.)
  

(b) Using a two-tailed test at a 0.05 level of significance, state the decision to retain or reject the null hypothesis. Hint: You must first convert r to χ².

Retain the null hypothesis

.Reject the null hypothesis.     

Answer 1

Using Excel<data<megastat<chisquare test

The output is as follows:

Chi-square Contingency Table Test for Independence
			Yes	No	Total
	Yes	Observed	22	8	30
		O - E	6.40	-6.40	0.00
		(O - E)² / E	2.63	2.84	5.47
	No	Observed	4	16	20
		O - E	-6.40	6.40	0.00
		(O - E)² / E	3.94	4.27	8.21
	Total	Observed	26	24	50
		O - E	0.00	0.00	0.00
		(O - E)² / E	6.56	7.11	13.68
			13.68	chi-square
			1	df
			.0002	p-value
			.523	Phi coefficient

a) phi correlation coefficient=0.523

b) pvalue =0.00<0.05(alpha)

Since p value is less than alpha we reject the null hypothesis.

Please upvote if this helps you out. Please do the comment for any doubt or clarification. Thank You!