A test for "independence." You want to know if death within five years from a certain type of cancer is independent of gender. If the patient survives the first five years, she is considered "recovered." Consider the data: The logic for this test follows the pattern of the goodness-of-fit test. Here's how you do it: (a) Suppose that 84% of persons suffering from this type of cancer are still living after five years and that half are male and half female. This is our first approach to this data; the usual "test of independence" would not make these two assumptions. Determine the expected number, Ei , for each category under the assumption that recovery is independent of gender. (b) Evaluate Pearson's X2 statistic for part (a). (c) Based on part (b), does the data suggest that death rate for this cancer is independent of gender? (d) In part (b), what else does the data suggest beyond just independence? (e) Suppose you had not known the recovery rate for this type of cancer. What would you do? (f) Now we'll do the usual "test of independence," where the recovery rate and the proportion of male victims are estimated from the data . Suppose the recovery rate for patients stricken with this type of cancer is not known and you suspect the population of victims is not divided SO/50 between men and women. Would the data still suggest that recovery is independent of gender? (g) Does the data really seem to suggest, as we noted in part (f), that this type of cancer is dependent on gender?
A test for "independence." You want to know if death within five years from a certain type of cancer is independent of gender. If the patient survives the first five years, she is considered "recovered." Consider the data:
The logic for this test follows the pattern of the goodness-of-fit test. Here's how you do it:
(a) Suppose that 84% of persons suffering from this type of cancer are still living after five years and that half are male and half female. This is our first approach to this data; the usual "test of independence" would not make these two assumptions. Determine the expected number, Ei , for each category under the assumption that recovery is independent of gender.
(b) Evaluate Pearson's X2 statistic for part (a).
(c) Based on part (b), does the data suggest that death rate for this cancer is independent of gender?
(d) In part (b), what else does the data suggest beyond just independence?
(e) Suppose you had not known the recovery rate for this type of cancer. What would you do?
(f) Now we'll do the usual "test of independence," where the recovery rate and the proportion of male victims are estimated from the data .
Suppose the recovery rate for patients stricken with this type of cancer is not known and you suspect the population of victims is not divided SO/50 between men and women. Would the data still suggest that recovery is independent of gender?
(g) Does the data really seem to suggest, as we noted in part (f), that this type of cancer is dependent on gender?
Step by step
Solved in 9 steps with 38 images
