Homework SourseCigarette smoking has important health consequences and is p
Cigarette smoking has important health consequences and is positively associated with heart and lung diseases. Less well known are the consequences of quitting smoking. In one study, a group of 10 nurses initially aged 50-54, who smoked at least 1 pack per day and quit for at least 6 years reported their weight before and 6 years after quitting smoking. A commonly used measure of obesity that takes height and weight into account is the body mass index(BMI, where BMI = wt in kg/ ht2 in meter). The BMI of the 10 women before and 6 years after quitting smoking are given in the last two columns of 1. (Fundamentals of Bio-Statistics: Bernard Rosner, 6th edition).
Perform suitable parametric tests for the following. You must include a complete statistical analysis, including a discussion and full assessment of any assumptions you make. Be sure to include relevant SPPS or R output at the relevant place (and not as attachments) to support any claims you make.
(a) We need to examine whether there is a change in the mean BMI levels before and 6 years after quitting smoking among the women who are heavy smokers. What test would you recommend for this? Explain your choice clearly.
(b) Perform your test of choice for part(a) and report a two-tailed p-value and your conclusion.
One issue is that there has been an ongoing change in weight in society. For this purpose, a control group of 50-54 year-old never-smoking women were recruited to and their BMI was reported at baseline(age 50-54) and 6 years later at a follow-up visit. The results are given in the frst two columns of 1.
(c) Now we wish to test whether mean change in BMI over 6 years is different between women who quit smoking and women who have never smoked? What test would you recommend for this?
(d) Perform your test of choice for part(c) and report a two-tailed p - value value and your conclusion.
(e) Are there any reasons to question the validity of the parametric tests you performed in parts (b) and (d) above?
How would you address these question(s), if any? (If any alternate analyses are needed, you must include a full discussion and all relevant SPSS or R output.)
Table 1: BMI changes in 50 to 54-year old women over a 6-year period.
| ID | BMI at Baseline | BMI at 6 years of follow-up | ID | BMI at baseline | BMI at 6 years of follow-up |
|---|---|---|---|---|---|
| 1 | 26.5 | 29.3 | 11 | 25.6 | 31.1 |
| 2 | 33.8 | 32.9 | 12 | 24.4 | 27.6 |
| 3 | 27.6 | 25.5 | 13 | 31.1 | 36.6 |
| 4 | 24.4 | 28.3 | 14 | 20.4 | 20.8 |
| 5 | 21.6 | 23.3 | 15 | 22.3 | 23.2 |
| 6 | 32.3 | 37.1 | 16 | 22.2 | 23.8 |
| 7 | 31.9 | 35.4 | 17 | 20.8 | 26.1 |
| 8 | 23.0 | 24.8 | 18 | 23.5 | 31.0 |
| 9 | 31.2 | 30.4 | 19 | 26.6 | 29.2 |
| 10 | 36.3 | 37.1 | 20 | 23.0 | 24.0 |
Solution
Sol)
A) We need to examine whether there is a change in the mean BMI levels before and 6 years after quitting smoking among the women who are heavy smokers. What test would you recommend for this? Explain your choice clearly.
Sol) To Examine change in the mean BMI levels before and 6 years after quitting smoking among the women who are heavy smokers. We use t test for paired sample test.
b)
Null Hypothesis:There is no difference in mean BMI levels before and 6 years after quitting smoking among the women who are heavy smokers
Alternative Hypothesis:There is no difference in mean BMI levels before and 6 years after quitting smoking among the women who are heavy smokers
Level of significance=0.05
From SPSS output
Test Statistic t=2.146
and p value=0.060 alpha=0.05
P value > alpha we donot reject the null hypothesis.
Hence here is no difference in mean BMI levels before and 6 years after quitting smoking among the women who are heavy smokers
C) Now we wish to test whether mean change in BMI over 6 years is different between women who quit smoking and women who have never smoked? What test would you recommend for this?
Sol) We use paired t test
d)
Null Hypothesis:There is no difference in mean change in BMI over 6 years and women who quit smoking and women who have never smoked
Alternative Hypothesis:There is a difference in mean change in BMI over 6 years and women who quit smoking and women who have never smoked
Level of significance=0.05
From SPSS output
Test Statistic t= 1
and p value=0.343 alpha=0.05
P value > alpha we donot reject the null hypothesis.
There is no difference in mean change in BMI over 6 years and women who quit smoking and women who have never smoked
e) we use parametric test . To find the difference between two means we use parametric test only.
