Do a full six-step evaluation

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Appraising Scientific Reasoning [PHI031] Department of Philosophy University of California, Davis (UCD) Fall 2017

ANSWER KEY: Homework 5 Exercise 8.2 Vitamin C and the common cold: the Salisbury study Giere et al., 2006: 249

The following report on a study done at the Common Cold Research Unit in Salisbury, England; is adapted from Linus Pauling’s book Vitamin C and the Common Cold. These investigators reported observations on human volunteers and concluded that “there is no evidence that the administration of ascorbic acid has any value in the prevention or treatment of colds produced by five known viruses.” Of the 91 human volunteers, 47 received 3 g of ascorbic acid per day for 9 days and 44 received a placebo. They were all inoculated with cold viruses on the third day. In each of the two groups, 18 developed colds. The incidence of colds observed in the subjects receiving ascorbic acid (18/47) was 6 percent less than that in the control group (18/44). This difference is not statistically significant. The number of subjects, 91 in the two groups, was not great enough to permit a statistically significant test of a difference as large as 30 percent in the incidence of colds in the two groups to be made, although a difference of 40 percent, if it had been observed, would have been reported as statistically significant (probability of observation in a uniform population equal to 5 percent).

1. Real-world population

Population of interest: Humans. Population actually sampled: Human volunteers in Salisbury, England. Variables: Exposure to ascorbic acid (+, -) and getting a cold (+, -). Causal hypothesis: Ascorbic acid (vitamin C) is a negative causal factor (NCF) for colds. (or a PCF for reduced incidence of cold)

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2. The Sample data

n: 91 x group: 47 received ascorbic acid, 18/47 developed cold (0.38 or 38%) k group: 44 received a placebo; 18/44 developed cold (0.41 or 41%)

The frequency difference is: 0.38 - 0.41 = -0.03 (ascorbic acid, vitamin C, is a negative causal factor for colds) 0.41 - 0.38 = 0.03 (ascorbic acid, vitamin C, is a positive causal factor for colds) It is OK to calculate the frequency difference as 0.03 for either a negative or a positive

causal factor, since our interest is in the absolute difference between the frequencies. 3. Design of the experiment

The study is a Randomized Experimental Design (RED) because the volunteers “sampled” from the population at large were split into two groups and one subjected to treatment while the other was given a placebo (controls).

4. Random sampling

The sampling process was done through volunteers. (a) All members of the population who might exhibit a property of interest have an equal chance of being selected? No (b) Is there any correlation between the outcome of one selection and any other? No My best pick is: Somewhat well met. The assumptions of random sampling are probably only somewhat well met. Although randomization was probably good in the second phase (assignment to treatment or control group), the fact that sample subjects volunteered makes us suspect that they might not be a good random selection of the population of interest.

5. Evaluating the hypothesis

The margin of error for sample sizes near 50 (Table 6.1) is about 0.14. So, the interval estimate of the proportion getting colds in the treatment groups is 0.38 ± 0.14, i.e. (0.24,