Question

A total of 678 women, who got pregnant under planned pregnancies, were asked how many cycles it took them to get pregnant. The women were classified as smokers and nonsmokers; it is of interest to compare the association between smoking and probability of pregnancy. The following table (Weinberg and Gladen, 1986, “The Beta-Geometric Distribution Applied to Comparative Fecundability Studies”, Biometrics 42(3): 547–560) summarises part of the data (essentially, women who had used the pill as a contraceptive are excluded).

a) Fit a geometric model, Geom(pi) to each group and compare the estimated probability of pregnancy per cycle.

b) Is there any evidence that there is an association between smoking and the probability of pregnancy? Justify your answer.

Cycle	Smokers	Non-smokers
1	29	198
2	16	107
3	17	55
4	4	38
5	3	18
6	9	22
7	4	7
8	5	9
9	1	5
10	1	3
11	1	6
12	3	6
>12	7	12

Answer 1

a)

We insert all data into excel and arrange data as a ascending order and then compute geometric model and its probability as

Geometric sequence = {1, 2, 4, 8, 16, 32, ......, 4096}

and its probability is as ={0.000122, 0.000244, 0.000488, ....... , 0.500061}

Here we see that probability of smokers(for cycle 1 and 3) and non-smokers(for cycle 1 and 2) are greater than Geometric probability for 2 cycle periods.

b)

Here we calculate correlation between probability of smokers and Non-smokers with geometric probability (P) is as using excel command ... =CORREL(Array1, array2)

We see that the correlation between Smokers and Geometric is -0.2099 and Non-smokers and Geometric is -0.2868. So we conclude that, there is a low negative correlation(Association) between smoking and the probability of pregnancy.