Question

Question: A study of racial differences of breast cancer diagnosis was done

	White	Black	Total
Local	45	13	58
Regional	76	9	85
Distant	35	7	42
total	156	29	185

1a)What is the conditional probability that the disease stage of a randomly selected patient is Regional, given that the patient is black?

1b)What is the conditional probability that a randomly selected patient is white, given that the patient has the disease stage Distant ?

1c)If you want to test within white breast cancer patients, are the disease stages equally distributed across “local”, “regional”, and “Distant” stages? What is the appropriate test to use:

- Two correlated sample- T test

- Two sample independent-T test

- X² test of independence

- X² goodness of fit test

1d)  If you want to test the disease stage and race are independent. Which of the following is the appropriate Test and test statistics value?

- X² test of independence: X² = 7.554

- X² test of independence: X² = 3.687   

- X² goodness of fit test: X² = 7.554

- X² goodness of fit test: X² = 3.687

1e) What is the P-value and df?

Answer 1

a) conditional probability that the disease stage of a randomly selected patient is Regional, given that the patient is black

=9/29=0.3103

b)conditional probability that a randomly selected patient is white, given that the patient has the disease stage Distant =35/42=0.8333

c)

-- X² goodness of fit test

d)

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	local	regional	distant	Total
	white	48.9100	71.6800	35.4200	156.01
	black	9.0900	13.3200	6.5800	28.99
	total	58.00	85.00	42.00	185.00
chi square    χ2	=(Oi-Ei)2/Ei	local	regional	distant	Total
	white	0.313	0.260	0.005	0.5779
	black	1.682	1.4011	0.0268	3.1097
	total	1.9944	1.6614	0.0318	3.688
test statistic X2 =		3.687

- X² test of independence: X² = 3.687    

e)

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

2

p value =

0.1582