In: Statistics and Probability
You wonder whether green tea lowers cholesterol.
(a) To research the claim that green tea lowers LDL (so-called bad)
cholesterol, you ask a random sample of individuals to divulge
whether they are regular green tea users or not. You also obtain
their LDL cholesterol levels. Finally, you compare the LDL
cholesterol levels of the green tea drinkers to those of the
non-green tea drinkers. Explain why this is an observational
study.
(b) Name some lurking variables that might exist in the
study.
(c) Suppose, instead of surveying individuals regarding their
tea-drinking habits, you decide to conduct a designed experiment.
You identify 120 volunteers to participate in the study and decided
on three levels of the treatment: a placebo, one cup of green tea
daily, two cups of green tea daily. The experiment is to run for
one year. The response variable will be the change in LDL
cholesterol for each subject from the beginning of the study to the
end. What type of experimental design is this?
(d) Explain how you would use blinding in this experiment.
(e) What is the factor? Is it qualitative or quantitative?
(f) What factors might you attempt to control in this
experiment.
(g) Explain how to use randomization in this experiment. How does
randomization neutralize those variables that are not
controlled?
(h) Suppose you assigned 40 subjects to each of the three treatment
groups. In addition, you decided to control the variable exercise
by having each subject perform 150 minutes of cardiovascular
exercise each week by walking on a treadmill. However, the 40
subjects in the placebo group decided they did not want to walk on
the treadmill and skipped the weekly exercise. Explain how exercise
is now a confounding variable.
a. Here in this case study, we observe the sample of individuals if they are regular green tea drinkers or not. And then measure the LDL cholesterol levels of the green tea drinkers and non-green tea drinkers. With the measured levels of LDL cholesterol levels, we compare the mean levels of the green tea and non-green tea drinkers. So we just observe the two different types of individuals and measure the LDL cholesterol levels, and we do not try to modify or influence the individuals to drink a particular type of tea. That is why this type of studies are called observational studies.
b. Drinking green or not as a categorical response from the individuals is the independent variable, and level of LDL cholesterol is the dependent variable. The hidden or lurking variables are the brand of the green tea, number of cups of green tea, and green tea with or without sugar or milk, and origin or production site of the green tea etc,
c. Factor is the change in LDL cholesterol level and at three different influencing factors such as number of cups of green daily, and an additional experimental unit, placebo. There is one factor and three different groups as the levels of interest of the factor, so this type of experimental design is called as completely randomised design.
d. Experimental units or individuals as placebo should be informed about the purpose of measurement of the LDL cholesterol for studying the impact or effect of the treatment with the green tea drinks.
e. The Level of cholesterol is the qualitative data, levels of LDL cholesterol is the label relative to the severity of its impact on the health of the heart, they do not represent numbers that come from counts or measurements.
f. Age group, Gender category are the other two main groups that I will be interested to add us factors to have a better results to control in this experiment.
g. From the placebo group, a random sample is taken say for 10 individuals and measured the LDL cholesterol levels. Similarly for the green tea drinkers of two levels with one cup daily and two cups daily. Then those 10 samples LDL cholesterol level from each of the three groups, mean values are compared to study if green tea drinking lowers the LDL cholestrol level or not using single factor analysis of variance method.
h. Sometimes the regular cardiovascular exercises lowers the LDL cholesterol level, but the placebo group did not participate in the exercises, and do not drink green tea will produce a clear or wider difference in the LDL cholesterol levels compared to the individuals who take weekly cardiovascular exercises and the green tea. Exercise is the confounding variable, because it is one of the clear alternative explanatory variable of the green tea drinking to explain the variations in the LDL cholesterol levels of the individuals under different treatment levels.