Question

21. Consider the following data on recidivism as measured by the rearrest of persons who have committed at least one previous offense. There are a number of points on which you would wish to be reassured before drawing conclusions from such data. What are they? Assuming that your questions received satisfactory answers, what conclusions could you draw from the following data? Treatment Received No Therapy Group Therapy Individual Therapy 25 Back in prison within 1 year Back in prison in 1-10 years Never back in prison Total 12 61

Answer 1

There is association between therapy and prison

here we can test whether prison and therapy are independent or associated

so the null hypothesis H0: prison and therapy are independent

alternate hypothesis Ha: prison and therapy are not independent

we use here chi-square test and statistic chi-square=sum((O-E)²/E)=22.27 with (r-1)(c-1)=(3-1)(3-1)=4 df

typical critical chi-square(0.05,4)=9.49 is less than calculated/observed chi-square=22.27, so we reject the null hypothesis and conclude that there is association between therapy and prison.

	observed	Expected(E)	E	(O-E)	(O-E)2/E
	24	61*75/186	24.60	-0.60	0.01
	25	61*70/186	22.96	2.04	0.18
	12	61*41/186	13.45	-1.45	0.16
	10	43*75/186	17.34	-7.34	3.11
	13	43*70/186	16.18	-3.18	0.63
	20	43*41/186	9.48	10.52	11.68
	41	82*75/186	33.06	7.94	1.90
	32	82*70/186	30.86	1.14	0.04
	9	82*41/186	18.08	-9.08	4.56
sum=	186	0	186	0	22.27