Question

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: (1 point)

Table 2. Biologics/Biosimilar and severity of adverse condition.

Severity of Condition	Biologics Abcdmab	Biosimilar Abcdmab1	Biosimilar Abcdmab2	Biosimilar Abcdmab3	Total
Absent	543	211	90	476
Mild	44	22	8	31
Severe	28	9	7	31
Total

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

The Observed value table with the total is below

Observed
	Abcdmab	Abcdmab1	Abcdmab2	Abcdmab3	Total
Absent	543	211	90	476	1320
Mild	44	22	8	31	105
Severe	28	9	7	31	75
Total	615	242	105	538	1500

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(a) The Hypothesis:

H0: Severity of Condition and Biologis/Biosimilar are independent

Ha: Severity of Condition and Biologis/Biosimilar are not independent.

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(b) The degrees of freedom, df = (r – 1) * (c -1) = (3 - 1) * (4 - 1) = 6

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(c) The Expected value data are in the table below. Each Cell = Row total * Column Total/N. N = 1500

Expected
	Abcdmab	Abcdmab1	Abcdmab2	Abcdmab3	Total
Absent	541.20	212.96	92.40	473.44	1320
Mild	43.05	16.94	7.35	37.66	105
Severe	30.75	12.10	5.25	26.90	75
Total	615	242	105	538	1500

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(d) The Test Statistic: The table below gives the calculation of .

#	Observed	Expected	(O-E)	(O-E)2	(O-E)2/E
1	543	541.20	1.80	3.24	0.005987
2	44	43.05	0.95	0.9025	0.020964
3	28	30.75	-2.75	7.5625	0.245935
4	211	212.96	-1.96	3.8416	0.018039
5	22	16.94	5.06	25.6036	1.511429
6	9	12.10	-3.1	9.61	0.794215
7	90	92.40	-2.4	5.76	0.062338
8	8	7.35	0.65	0.4225	0.057483
9	7	5.25	1.75	3.0625	0.583333
10	476	473.44	2.56	6.5536	0.013843
11	31	37.66	-6.66	44.3556	1.177791
12	31	26.90	4.1	16.81	0.624907
Total					5.116262

test = 5.12

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(e) If test is > c, then reject H0

Here since test (5.12) is < 10.645, We Fail to reject H0.

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(f) The Conclusion: There isn't sufficient evidence at the 95% level of significance to warrant rejection of the claim that Severity of Condition and Biologis/Biosimilar are independent.

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