Typical Misrepresentation of Statistical Facts - Essay Example

Chapter 12 is chosen as an instance of an implied connection misrepresentation and question 18, page 688, Chapter 12 is discussed to elaborate on the notion of a suspect sample error as well as to point out how to tread carefully while making decisions based on reported statistics.

Question 4, p 686
One of the most common misuses of statistics found regularly is that of an implied connection. Typically, this is found in advertisements for various kinds of weight loss, hair regeneration, etc products. How the error is made is that a success story of some person is cited, i.e., say Joe Smith lost 20 pounds of weight in 2 weeks by using product X. The claim is that or rather the implication is that if the product worked for Joe, it should be for every consumer. This is not true.

If the statement in the small print of the results not being typical accompanies a weight loss product advertisement, this implies that the advertised effect is not typical. That is, whatever remarkable weight loss story is portrayed as proof of the effectiveness of the product, is not the expected impact of the product on the average person based on statistical tests. The kind of misuse this statement reflects is one of implied connection. An advertisement that demonstrates some immediate weight loss as a result of using the product refers to a situation where the product had such an impact on one individual. But, the advertisement implies that whoever uses the product will benefit similarly. However, the small print refers to the truth obtained through statistical sampling. It was found that the extent to which the product had an effect was not as spectacular on most people tested. Thus, for the typical, or average person, the product had little or no effect compared to what was being depicted in the advertisement. This is only perceivable to the person who is careful enough to take note of the footnote.
Thus, this product is unlikely to have any significant impact on the average person. Because it had a spectacular effect on one individual as advertised, does not mean that it will have similar effects on all people. Further, the small print implies that the effect observed on most people was lower. Thus, although the advertisement implies a connection between the observed impacts and potential impacts on buyers, the small print reflects that such effects are unlikely.
Question 18, P - 688

The Norwegian study (under the assumption of a correct methodology) establishes the adverse effect on heavy coffee drinkers. But drawing the conclusion that we should give up our daily cup of coffee just based on the statistics presented in the newspaper report would be not justified.
We should not give up on our daily cup of coffee just based on the reported results of the Norwegian study. There are two fundamental reasons for this. First and foremost, the report could be an instance of misuse of statistics via the suspect sample error. In other words, unless we know whether the sample size was adequate or not or whether there were any selection biases in the sample, it is not an acceptable result. If the sample was not adequately large, in that case, it could be possible that the obtained results are entirely based on chance and not any causality or correlation. Again even if the sample was adequately large, it is unclear how externally valid these results are. That is to say, there is nothing in the statement to establish that these results can be extended to a non-Norwegian population as well. It could be that the adverse effects are only on Norwegian people because of certain geographical or climate conditions germane to the area. Additionally, it should also be noted that adverse effects are found in people who drink more than 9 cups of coffee each day. Thus if coffee is consumed in moderation (less than 9 cups) these adverse impacts would not be a cause for concern.
Thus, to conclude, for an average person who consumes only a cup or two of coffee there is nothing in the reports of the study to give up their daily cup(s) of coffee.

Here we showed how the “results not typical” mentioned in small print may reflect the opposite of what a weight loss campaign tries to promote. Also, we discussed the issue of external validity in the case of the Norwegian coffee drinkers example. We concluded in that case that the results applied only to people who drank as much coffee as 9 cups a day or more in Norway. How generalizable these results are for people from other climates and elevations is unclear. Additionally, the used sample may be non-representative. Thus, such results should always be taken with a grain of salt, and careful consideration is required before any decisions are taken based on such reports or advertisements.