Question

Exercise 3

The following Two-way Table presents data on two variables, “Type of Surgery” and “Level of Complication”. There are three categories in Type of Surgery (Gastric-banding, Sleeve-gastrectomy and Gastric-bypass), and three categories in Level of Complication (Serious, Non-Life-Threat and None). The table presents the counts of patients in each level of Surgery by each level of Complication.

Type of Surgery	Level of Complication
	Non-Life-Threat	Serious	None
Gastric-Banding	81	46	5253
Sleeve-Gastrectomy	31	19	804
Gastric-bypass	606	325	8110

Are “Level-of-Complication” and “Type-of-Surgery” associated? explain your answer.

Answer 1

null hypothesis:Ho:“Level-of-Complication” and “Type-of-Surgery” are independent

Alternate hypothesis:Ha:“Level-of-Complication” and “Type-of-Surgery” are  associated

degree of freedom(df) =(rows-1)*(columns-1)=		4
for 4 df and 0.05 level , critical value       χ2=		9.488
Decision rule : reject Ho if value of test statistic X2>9.488

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	d	e	f	Total
	a	252.8900	137.3600	4989.7500	5380.00
	b	40.1400	21.8000	792.0500	853.99
	c	424.9700	230.8300	8385.1900	9040.99
	total	718.00	389.99	14166.99	15274.98
chi square    χ2	=(Oi-Ei)2/Ei	d	e	f	Total
	a	116.834	60.765	13.889	191.4874
	b	2.081	0.3596	0.1803	2.6211
	c	77.116	38.4178	9.0313	124.5649
	total	196.0310	99.5422	23.1002	318.673
test statistic X2 =		318.67

since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that Level-of-Complication” and “Type-of-Surgery” are associated