Protein Shakes and Weight Loss Correlation
A gym surveyed 200 members who joined one year ago. Of 120 members who regularly drank protein shakes, 80 lost more than 5 pounds. Of the 80 members who did not drink shakes, 40 lost more than 5 pounds. The gym owner concludes that drinking protein shakes causes greater weight loss. However, the survey also found that shake drinkers attended an average of 4.5 exercise classes per week, while non-shake drinkers attended an average of 2.0 classes per week. Additionally, shake drinkers were more likely to have personal trainers. The survey relied on self-reported weight loss and shake consumption.
1. Identify the most serious problem with the gym owner's causal conclusion.
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The conclusion rests on a correlation with a likely confounder. The raw rates are: shake drinkers 80/120 = 66.7% lost >5 lbs; non-drinkers 40/80 = 50%. That is a 16.7-point difference. But shake drinkers also attended 4.5 exercise classes per week versus 2.0 for non-drinkers, and were more likely to have personal trainers. Either factor could independently cause greater weight loss. Because the groups differ systematically in exercise and coaching, the survey cannot isolate the effect of shakes. Self-reported weight and shake consumption add further measurement error.
2. What would be the most useful follow-up study to test the causal claim?
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A randomized controlled trial: assign members to a protein shake or a placebo drink with identical taste and calories, hold exercise classes and trainer access constant across groups, and measure weight loss objectively. Alternatively, a stratified observational study could compare shake and non-shake members within the same exercise-class level. The key is to break the link between shake drinking and exercise/trainer access, so the only systematic difference is the shake.
3. If the gym owner argues that the 16.7 percentage point difference is too large to be explained by exercise alone, how would you evaluate that claim?
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The claim is unsupported without a quantitative model. A 16.7-point difference could be explained by exercise if class attendance has a strong dose-response effect, and the groups differ by 2.5 classes per week. The owner would need to show that exercise and trainer access together account for less than 16.7 points, e.g., by regression or stratification. Since the data are observational and self-reported, the size of the raw difference does not establish that shakes are the cause.