In: Statistics and Probability
A sample of 150 was obtained of men with each of three types of cancer, and the following data show blood types for each. Use an appropriate test, determine if blood type of cancer type are related. (Contingency table )
Blood Type |
||||
Cancer Type |
O |
A |
B |
AB |
Colon |
61 |
65 |
18 |
6 |
Lung |
69 |
57 |
15 |
9 |
Prostate |
73 |
60 |
12 |
5 |
Claim: blood type of cancer type are related.
The null and alternative hypothesis is
H0: blood type of cancer type are not related.
H1: blood type of cancer type are related.
Level of significance = 0.05
Test statistic is
O: Observed frequency
E: Expected frequency.
E = ( Row total*Column total) / Grand total
Blood Type | |||||
Cancer Type | O | A | B | AB | Total |
Colon | 61 | 65 | 18 | 6 | 150 |
Lung | 69 | 57 | 15 | 9 | 150 |
Prostate | 73 | 60 | 12 | 5 | 150 |
Total | 203 | 182 | 45 | 20 | 450 |
O | E | (O-E) | (O-E)^2 | (O-E)^2/E |
61 | 67.66667 | -6.66667 | 44.44444 | 0.656814 |
65 | 60.66667 | 4.333333 | 18.77778 | 0.309524 |
18 | 15 | 3 | 9 | 0.6 |
6 | 6.666667 | -0.66667 | 0.444444 | 0.066667 |
69 | 67.66667 | 1.333333 | 1.777778 | 0.026273 |
57 | 60.66667 | -3.66667 | 13.44444 | 0.221612 |
15 | 15 | 0 | 0 | 0 |
9 | 6.666667 | 2.333333 | 5.444444 | 0.816667 |
73 | 67.66667 | 5.333333 | 28.44444 | 0.420361 |
60 | 60.66667 | -0.66667 | 0.444444 | 0.007326 |
12 | 15 | -3 | 9 | 0.6 |
5 | 6.666667 | -1.66667 | 2.777778 | 0.416667 |
Total | 4.14 |
Degrees of freedom = ( Number of rows - 1 ) * ( Number of column
- 1) = ( 3 - 1) * (4 - 1) = 2 * 3 = 6
Critical value = 12.592
( From chi-square table)
Test statistic < critical value we fail to reject the null hypothesis.
Conclusion:
Blood type of cancer type are not related.