In: Statistics and Probability
.4 Read the following excerpts from the University of Michigan News Service online article “Women need not lose sleep over menopause,U-M study says” (April 27,2004). ANNARBOR,Mich.—Can’tgetagoodnight’ssleep?Don’tbequicktoblameitonmenopause. Middle-aged women often complain that they sleep poorly,and both women and their health care providers point to menopause as the cause. But University of Michigan researchers Jane Lukacs and Nancy Reame say it may be time to put that assumption to rest.In an article in the justreleased April issue of the Journal of Women’s Health,Lukacs,an assistant research scientist at the U-M School of Nursing, under the direction of nursing professor Reame, tested the connection between the hormone estrogen and women’s sleep quality. Her conclusion:“Estrogen has been blamed for a lot,but that doesn’t seem to be what’s at work here.” To separate aging effects from menopause, Lukacs and her collaborators studied a group of women aged 20–52,and compared them to age-matched women who had gone through menopause, some of whom were using estrogen therapy.For example,she examined a 47-year-old woman still having regular menstrual cycles and compared her data to a 47-year-old woman who had not had regular cycles for 12 months. They found total sleep time,time spent awake during the night,and efficiency of sleep time all were worse for older women than younger women,regardless of whether the older women were still having menstrual cycles and regardless of whether they used estrogen therapy.While young women around age 24 slept about seven hours (416.9 minutes),all women in their 40s,regardless of their estrogen levels or menopause status, got only about six to six-and-a-half hours of sleep (354.9–377.8 minutes). Further, although many women have taken hormone replacement drugs to try to help their sleep,Lukacs and Reame found that for women who were not having hot flashes,there was little difference in sleep between post-menopausal women who were or were not taking estrogen supplements.“Our findings fail to support the popular view that estrogen plays an important role in sleep enhancement,”the article states.“The use of an estrogen patch or gel for three months did not improve any objective measure of sleep architecture.” The research team studied 51 women who participated in an overnight sleep challenge at U-M Hospitals.Women underwent a 24-hour blood sampling protocol to examine their hormone levels and wore electrodes for sleep monitoring from 11 p.m.to 7 a.m.Researchers studied sleep stages, REM sleep and sleep disruption. The researchers noted that because this study involved an in-hospital,one-night sleep observation,further research examining women’s natural sleep patterns in their own homes over multiple nights could give more insight into why women sleep poorly at midlife. They added that in the future,researchers could build on their study and look for such variants as oxygen saturation to look for sleep apnea, leg muscle movement during sleep, and patterns associated with hot flashes,determined by monitoring skin temperature.Hormone replacement therapy might diminish muscle movement during sleep and calm hot flashes,Lukacs said, which could account for some of the beliefs about estrogen improving sleep.
(a) Is this an observational study or an experiment?
(b) What are the explanatory and response variables?Hint:The article states the researcher “tested the connection between the hormone estrogen and women’s sleep quality.”This gives the general variables being linked.However,the article does go on to state some of the specific response variables that were compared. List some of these response variables.
(c) Consider the following hypotheses,tested using a 5% significance level. The use of an estrogen patch or gel for three months does not improve the total sleep time on average. The use of an estrogen patch or gel for three months does improve the total sleep time on average. Basedontheresultsstatedinthearticle,givetwopossiblevaluesforthep-valueofthistest.
(d) Consider the following sentence from the article:“For example,she examined a 47-yearold woman still having regular menstrual cycles and compared her data to a 47-year-old woman who had not had regular cycles for 12 months.”What is this design technique called and why was it done?
(e) What were some of the other possible confounding variables that the researchers suggested might be incorporated into future studies
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(a)
As the researcher is simply observing the women under study, without attempting to influence/manipulate their sleep patterns in any way, this is an observational study.
(b)
Response variables: The main response variable is the quality of sleep received by the women measured by the total sleep time, as it is at the focus of the study.
Some other explanatory variables, which can potentially measure the sleep quality are time spent awake at night, and efficiency of sleep time of the women.
Explanatory variables: The main explanatory variable of interest is levels of estrogen in blood, as its effect on the sleep quality is of vital importance here.
Some other explanatory variables, which can potentially affect the sleep quality are: age of the women, whether the women were using estrogen therapy, whether the women were having hot flashes, etc.
(c)
The null hypothesis is, H0: “The use of an estrogen patch or gel for three months does not improve the total sleep time on average”; the alternative hypothesis is, Ha: “The use of an estrogen patch or gel for three months does improve the total sleep time on average”.
The study concludes that there was no evidence to support the popular claim made in the alternative hypothesis. In other words, there was no evidence found to suggest that the use of an estrogen patch or gel for three months does improve the total sleep time on average.
Now, if the null hypothesis is not rejected, it must imply that the p-value was greater than the level of significance, which is 5% or 0.05 in this case.
Hence, two possible values for the p-value of the test, based ion the stated results are: 0.06, 0.27. (Taken off the top of our head; these can be any value greater than 0.054 and at most 1).
(d)
Note that, the researchers did not determine whether the women took estrogen supplements or had hot flashes. They simply made an observational study, considering two comparable populations of women of each age group- those who had regular menstrual cycles, and those who did not. Then, they observed the sleep-quality of each woman, and attempted to identify whether the two populations varied with respect to the sleep qualities (Disease: suffers from poor sleep quality, which are the cases, and No Disease: does not suffer from poor sleep quality, which are the controls).
Hence, the given is a matched-pairs case-control study, where the matching is done based on the ages.