A new medical condition known as Slipitosis has been discovered and is believed to relate to Banana consumption. A study is undertaken to confirm this. During the study, it is found that Females consume Bananas at a higher rate than males and the researchers are worried about Simpsons Paradox influencing the results if they leave out gender. They, therefore, undertake a Mantel-Haenszel analysis of the relationship between banana consumption and Slipitosis, conditional on gender.

Sliptosis
Gender Yes No Total
Female
Yes 81 47 128
No 428 392 820
Total 509 439 948
Male
Yes 14 46 60
No 500 2030 2530
Total 514 2076 2590

Test that combined OR = 1:
Mantel-Haenszel chi2 (1) = 5.213
Pr>chi2= 0.022
Test of homogeneity (B-D) chi2(1) = 0.48 Prychi2 = 0.503
(1) From the above cross-tabulation, we can calculate that among women, the odds ratio representing the association between eating more than 2 bananas and having Slipitosis is 1.58.
This means:

a) The odds of having slipitosis among women who eat more than 2 bananas is 1.58 times the odds of having slipitosis among women who eat no more than 2 bananas a week.
b) The odds of having slipitosis among women who eat no more than 2 bananas is 1.58 times the odds of having slipitosis among women who eat more than 2 bananas a week.
c) The probability of having slipitosis among women who eat more than 2 bananas is 1.58 times the probability of having slipitosis among women who eat no more than 2 bananas a week.
d) The probability of eating more than 2 bananas a week among women patients with slipitosis is 1.58 times the probability of eating more than 2 bananas a week among women patients without slipitosis.

(2) Mantel Haenszel statistics indicate:

a) That there is no relationship between banana consumption and slipitosis.
b) That the more bananas one eats the greater the prevalence of slipitosis.
c) That there is a relationship between banana consumption and slipitosis adjusting for gender effect.
d) That gender is more related to slipitosis than banana consumption.