SCENARIO TWO: In 1970, Linus Pauling, a well-known chemist and Nobel Prize-winning scientist, published "Vitamin C and the Common Cold" (1970), creating a great deal of public and scientific interest. In short, Pauling argued that taking Vitamin C would reduce one's risk of the common cold. This book almost singlehandedly made Vitamin C one of the most widely used dietary supplements, a status it retains to this day (Nutritional Supplement Review, 2009). Subsequent to the publishing of his book, Pauling wrote a paper that appeared in the Proceedings of the National Academy of Sciences in 1971.
In this paper, he describes a study conducted by a physician in Basel, Switzerland, in the early 1960s. Here is an excerpt from the paper explaining the study design:
The study was carried out in a ski resort with 279 skiers during two periods of 5-7 days. The conditions were such that the incidence of colds during these short periods was large enough (about 20%) to permit results with statistical significance to be obtained. The subjects were roughly of the same age and had similar nutrition during the period of study. The investigation was double-blind, with neither the participants nor the physicians having any knowledge about the distribution of the ascorbic-acid tablets (1000 mg) and the placebo tablets. The tablets were distributed every morning and taken by the subjects under observation, so that the possibility of interchange of tablets was eliminated. The subjects were examined daily for symptoms of colds and other infections. The records were largely based on subjective symptoms, partially supported by objective observations (measurement of body temperature, inspection of the respiratory organs, auscultation of the lungs, and so on). Persons who showed cold symptoms on the first day were excluded from the investigation. After the completion of the investigation, a completely independent group of professional people was provided with the identification numbers for the ascorbic-acid tablets and placebo tablets, and this group performed the statistical evaluation of the observations.
Although not stated explicitly in the paragraph above, the participants were randomly assigned to take ascorbic-acid tablets or the placebo.
Research Question: Are you less likely to get a cold when taking vitamin C?
Describe the observational/experimental units.
Identify the explanatory and response variables, categorical or quantitative?
Explanatory: Whether the participant took Vitamin C or the placebo (categorical)
Response: Whether the participant developed a cold or not (categorical)
Is this study an experiment or an observational study? How did you decide?
This study is an experiment because the participants were randomly assigned to take either Vitamin C or the placebo.
Describe the parameter (Vitamin C - Placebo) of interest in words. What symbol would you use?
The parameter of interest is the difference in the proportion of participants who developed a cold between the Vitamin C group and the placebo group. The symbol used would be p1 - p2.
Set up the hypothesis in symbols (Vitamin C - Placebo).
H0: p1 = p2 (There is no difference in the proportion of participants who develop a cold between the Vitamin C group and the placebo group)
Ha: p1 ≠p2 (There is a difference in the proportion of participants who develop a cold between the Vitamin C group and the placebo group)
Of the 139 skiers assigned to take Vitamin C, 17 developed a cold. Of the 140 skiers assigned to take a placebo, 31 developed a cold.
Fill out the 2x2 chart.
Cold No Cold Total
Vitamin C 17 122 139
Placebo 31 109 140
Total 48 231 279
Calculate the conditional proportions for each group. Assign a symbol to each.
p1 = 17/139 (proportion of participants who developed a cold in the Vitamin C group)
p2 = 31/140 (proportion of participants who developed a cold in the placebo group)
Calculate the relative risk.
Relative Risk = p1/p2
Calculate the difference in proportions (Vitamin C - Placebo).
Difference in Proportions = p1 - p2
Using the Two Proportions Applet, simulate a null distribution and identify the following:
Simulated SD:
P-value (R or FTR?):
Calculate the standardized statistic using the simulated standard deviation. (R or FTR)
Using the Theory Based Inference Applet, identify the following:
Confidence Interval Given from Applet (R or FTR?):
Show how the confidence interval above was calculated.
Use a standard error of 0.0447 (rounding error may cause it to not be the exact answer but it should be pretty close).
Interpret the confidence interval in context.
Identify the population of interest.
Can we generalize our results to the population of interest? Explain.
Can we determine a cause and effect relationship? Explain.
Draw a conclusion in context.