Question

Suppose there was no correlation between the Test Screen and the medical assessment of disease (i.e. the test was not able to differentiate between those with or without the disease). Based on the table given above, how many true positives among the sample of 100 do you expect the Test Screen to reveal? Based on this outcome and the observed values given in the initial table above, comment on the association between Test Screen and disease status.

                                   Medical Assessment

Test Screen              Disease          No Disease Total

Possible Disease   30                    20                    50

No Disease              10                    40                    50

Total                          40                    60                    100

Answer 1

Claim: There is an association between test screen and disease status.

The null and alternative hypothesis is

H0: There is no association between the test screen and disease status.

H1: There is an association between test screen and disease status.

Level of significance = 0.05

Test statistic is

O: Observed frequency
E: Expected frequency.
E = ( Row total*Column total) / Grand total

Test screen	Disease	No Disease	Total
Possible Disease	30	20	50
No Disease	10	40	50
Total	40	60	100

O	E	(O-E)	(O-E)^2	(O-E)^2/E
30	20	10	100	5
20	30	-10	100	3.333333
10	20	-10	100	5
40	30	10	100	3.333333
			Total	16.667

Degrees of freedom = ( Number of rows - 1 ) * ( Number of column - 1) = ( 2 - 1) * (2 - 1) = 1 * 1 = 1

Critical value = 3.841 ( From chi-square table)

Test statistic > critical value we reject null hypothesis.

Conclusion:

There is an association between test screen and disease status.