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PAGE EIGHT by Jonathan Dolhenty, Ph.D.
Evaluating Statistical Information Statistical techniques are valuable tools in gathering, organizing, and analyzing data. The negative attitude that some people unfortunately have toward statistics is unwarranted. It is true there have been abuses in statistical gathering and reporting and probably there will continue to be abuses, but we all have an obligation to be aware of proper statistical interpretation. It does not mean we all have to become statisticians. We simply need to know the general concepts involved in statistics and be aware of the statistical fallacies that may be lurking out there to deceive us and trip us up. Statistical fallacies involve a misuse of the statistical method. Many people, unfortunately, think that "you can make statistics prove anything." But this is true only if statistical methodology is misused. The proper and correct use of the statistical method has been extremely valuable for the accumulation of scientific knowledge, most of which has been beneficial to mankind. The use of statistics in advertising commercials needs to be carefully evaluated by any consumer. For example:
The most misleading cases of statistical misuse we are seeing lately have to do with scientific reports on health matters appearing in the popular press. Most scientific studies, properly performed and presented, contain specific limitations as to the overall efficacy of their conclusions. Actually, most scientific studies are quite conservative and tentative. But this is not the impression one necessarily gets from the media. All too often, the media selects a tentative conclusion and offers it to us as if it was already a "truth" or fact of science. New scientific studies are particularly tentative and the conclusions should be treated accordingly. One example of this is when it is reported, for instance, that eating eggs is bad for you, only to report later that, well, eating eggs now may not be so bad after all. Another danger in the use of statistics that has arisen is the selective and misleading use of statistics to garner support for some specific political or social action. Remember, statistical data have to be interpreted and interpreted properly. We must be aware constantly of the possible misuse of statistics in the heat of social and political debate. Many errors are made in passing from generalizations, based on group behavior, to the individual case. Equally frequent errors are made in passing in the opposite direction from the individual case to a statistical generalization. Reasoning From a Generalization to a Particular Case A statistical average is a stable value which describes one important characteristic of a population. The average if often erroneously interpreted as referring to every individual item in the group from which the average is computed. It has to be stressed that a statistical study yields generalizations which apply to the group as a whole rather than to the individual cases which compose the population. Common errors of deduction can be avoided if this distinction is remembered. Reasoning From a Particular Case to a Statistical Generalization It is quite as easy to make errors of the opposite kind, that is, to pass from the individual case to a generalization which is not justified. It must be stressed that the data must be adequate. Since statistical results to be meaningful must related to "mass" data, it is dangerous to pass from only a few cases to a generalization concerning variations. Defective induction is probably the most common error in statistical and other types of reasoning. Sweeping generalizations are often made on the basis of inadequate and individualized data because of ignorance or wishful thinking. Errors in the Assignment of Causation Another error in logic against which all must be on guard may be called the post hoc, ergo propter hoc fallacy in reasoning. This means in effect "after this, therefore on account of it." Great care must be exercised in assuming that cause and effect relationships are present merely because variables move together. Two apparently related events may move together because a third influence bears on both alike. Or, relationships may so change with the passage of time that the nature of the relationship will be quite different at different dates. Moreover, in considering such statistical computations as these we should know how large the sample is and how it was selected. We must be constantly on guard in assigning cause and effect relations to events. Correlation does not indicate cause. Causal relationships cannot be proved by quoting statistics or making extended calculations. Errors of Definition and Comparison Another pitfall is the comparison of things which are not really comparable. Definitions change from time to time and comparing two items at different times, especially if many years have lapsed, may not yield meaningful results. For instance, the definition of "family" as used by the U.S. Census Bureau has changed over time. To compare the family today with the family of 1890 without taking the change in definition into account is risky business. The object being measured must be defined carefully and the definition must be held constant in making comparisons. The types of error we've just discussed do not, unfortunately, exhaust the list of common mistakes. Errors are frequently made in sampling and in the interpretation of results secured in correlation analysis and these potential errors have been discussed. But a discussion of all potential errors in statistical method would fill a couple of volumes. The knowledgeable and wise critical thinker will not just accept statistical data at face value. The critical thinker will always be on guard, ready to challenge any statistical information presented. The key is to Question, Question, and Question. Two Philosophers Put the Statistical Method to the Test! Two philosophers decided to find out why they kep becoming intoxicated. So they decided to apply the statistical or scientific method to discover the cause. They proceeded to their favorite tavern, where they had dinner and during the process comsumed several drinks composed of scotch and water. They became intoxicated and had to be taken home. The next night they repeated the process. They had exactly the same food, but this time, as a beverage, they drank Irish whisky and water. Again they became intoxicated and had to be carried from the premises. The third night they repeated the same steps, varying only the drink. This time they drank rye whisky and water, again becoming drunk. They concluded, in accordance with the statistical method, that since water was the only constant factor in all their drinks, it must be the water which was making them intoxicated!
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