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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?

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Mar 04, 2012
Misleading Claim - #1 - Mathematical Solution
by: Staff


Part I

Question:

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?


Answer:

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1. What is misleading about this claim?

This claim is extremely misleading.

“. . . it’s the #1 Dermatologist recommended brand” leads the reader to believe that dermatologists as a group (probably 10’s of thousands of licensed dermatologists) recommended the moisturizing lotion advertised as their top choice.

However, the reader cannot tell how many Dermatologists recommend the product because of the wording of the claim.

The statement uses the word Dermatologist instead of the plural Dermatologists. If the ad is read literally, only a single Dermatologist recommends the moisturizing lotion.

The ad does not state that every Dermatologist who evaluated the moisturizing lotion was selected on a random basis.

That ad does not state whether a Dermatologist who recommends this product is making an independent evaluation of the product based on the product’s merits alone.

A Dermatologist who is an employee of the manufacturer, or receives money from the advertiser (directly or indirectly), or has a financial interest in the product itself, has a conflict of interest. That Dermatologist is not impartial.

Next, the claim does not state what #1 actually means. #1 in comparison to what (#1 compared to not using any moisturizing cream at all, #1 in terms of the highest price, #1 in terms of the shape of the jar)? The comparison is not stated, and no scientific evidence is provided.

Finally, no statistical verification of the claim is provided.

The MARGIN OF ERROR and the CONFIDENCE INTERVAL are not given. These values could be anything.

IMPORTANT: the advertisement does not tell the reader HOW MANY separate STUDIES were CONDUCTED.

The number of studies is important.

For example, suppose a company wants to market a moisturizing lotion which is completely worthless (which I will call product ABC).

Suppose the company tests product ABC and found it was completely useless with a 1% margin of error and a 95% confidence interval.

Such a company can easily manufacture statistical evidence that “proves” that product ABC is highly effective.

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Mar 04, 2012
Misleading Claim - #1 - Mathematical Solution
by: Staff

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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


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