# Misleading Claim - #1 - Mathematical Solution - four out of five

In an ad for moisturizing lotion, the following claim is made:”…it’s the #1 dermatologist recommended brand. What is misleading about this claim and what would be the mathematical solution to make this claim true?

### Comments for Misleading Claim - #1 - Mathematical Solution - four out of five

 Mar 04, 2012 Misleading Claim - #1 - Mathematical Solution by: Staff --------------------------------------------------- Part II This is how. Statistically, 5% of the results that lie outside the 95% confidence interval. There is a 5% chance that the 95% result is false. That means 2 ½ % of the time (5% ÷ 2) a statistical result will show product ABC is effective to some extent. A small fraction of the studies will actually show the product to be highly effective. To promote a completely useless product, all the seller needs to do is conduct one study after another UNTIL one study shows the product is superior. The seller (or distributor) can then selectively report that particular study without telling the reader about all the other studies which show the opposite result. 2. What would be the mathematical solution to make this claim true? This is really a question about methodology. The survey must be designed so that the results are strong enough (mathematically) that they are not due to chance. A) At least 1000 INDEPENDENT dermatologists should take part in the study Note: Since the margin of error is proportional to 1/√N, N must be a high enough to minimize the margin of error. If 1000 dermatologists who take part in the survey, the margin or error should be in the ±3% range with a 95% confidence level. (You are probability aware that many political polls use an approximate value of 1000 for their sample size to control the margin of error.) B) Every dermatologist should be selected randomly. The dermatologist is the independent variable. Selection of which dermatologists take part in the survey can be manipulated. True random selection will minimize possible manipulation. C) The survey result is the dependent variable. Reported results must include the margin of error and confidence interval to mathematically establish the reliability (“truthfulness”) of the survey. D) The survey must define what #1 means (#1 in comparison to what). Thanks for writing. Staff www.solving-math-problems.com