Question

1. A research team studying the relationship between biologics/biosimilar chemotherapies and their severity of a certain adverse condition in a population collected data on 1500 subjects (patients) as displayed in the contingency table shown below. The researchers wished to know if these data were compatible with the hypothesis that severity of condition and biologics/biosimilar are independent. Please answer following questions: Total Biosimilar Abcdmab3 Table 2. Biologics/Biosimilar and severity of adverse condition. Biologics Biosimilar Biosimilar Severity of Abcdmab Abcdmab1 Abcdmab2 Condition Absent 543 211 90 Mild 44 22 8 Severe 28 9 7 Total 476 31 31 a) Please state your null hypothesis in text (not in symbol). b) Please calculate the degree of freedom. c) Please calculate the expected values for each cell. d) Please calculate the chi-square value. e) If the critical chi-square value is 10.645 at alpha level of 0.05, please state your statistical decision. f) State your conclusion.

Answer 1

a_)

Null hypothesis:Ho:   severity of condition and biologics/biosimilar are independent.

alternate hypothesis:Ha: severity of condition and biologics/biosimilar are dependent.

b)

degree of freedom(df) =(rows-1)*(columns-1)=(3-1)*(4-1)=

6

c)below is expected value table:

Expected	Ei=row total*column total/grand total	Biologics	Biosimilar 1	Biosimilar 2	Biosimilar 3	Total
	Absent	541.2000	212.9600	92.4000	473.4400	1320
	Mild	43.0500	16.9400	7.3500	37.6600	105
	Severe	30.7500	12.1000	5.2500	26.9000	75
	total	615	242	105	538	1500

d)

Applying chi square test of independence:

chi square    χ2	=(Oi-Ei)2/Ei	Biologics	Biosimilar 1	Biosimilar 2	Biosimilar 3	Total
	Absent	0.006	0.018	0.062	0.014	0.1002
	Mild	0.021	1.511	0.057	1.178	2.7677
	Severe	0.246	0.794	0.583	0.625	2.2484
	total	0.2729	2.3237	0.7032	1.8165	5.1163
test statistic X2=		5.1163

e)

since test statistic does not falls in rejection region we fail to reject null hypothesis

f)

we do not have have sufficient evidence to reject the hypothesis that severity of condition and biologics/biosimilar are independent.