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False Generalizations in Statistics (with Examples)

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Interpretation of data is an extremely important and useful branch of the science of statistics because it makes possible the use of collected data. Statistical facts have
by themselves no utility and interpretation makes it possible for us to utilize the collected data in various fields of activity. The usefulness and utility of collected information lie in its proper interpretation.

A statistician should be very careful when interpreting the data to avoid some of the most common fallacies in statistical interpretation. One of the fallacies that must be avoided is the fallacy of false generalizations.

The Fallacy of False Generalization:

The reason for such types of mistakes generally lies in the fact that people draw conclusions about the whole by only studying a part. It is not always necessary that whatever is true of the part must be true of the whole also. Sometimes it may be that the changes recorded in part are very similar to changes in the whole of the data but it is not so invariably. Moreover, to draw generalizations about the whole it is necessary to know the movements recorded in various parts. It is likely that in one part the movement is in one direction while in the other it is in the reverse direction. Under such circumstances, conclusions drawn on the basis of the study of a part would not be applicable to the whole.

Such generalizations are mostly done by propagandists and advertisers. They magnify the conclusions drawn from parts and it appears as if the statements made are true of the whole; actually, they are not. Thus if a manufacturer of a medicine advertises that 90% of the patients who used a particular medicine manufactured by his company are cured of a particular disease, it appears from the statement that the medicine is
really a very good one. But it may be that the percentage of cured amongst those who used some other medicine is 99 or even 100. It may also be a fact that 99% of those persons who do not take any medicine for that particular disease are automatically cured. Yet another possible snag in the statement may be that the patients on whom
that medicine is tried are those who have just contracted the disease and are thus in the very early stages of it. Thus it is obvious that if conclusions are drawn from parts they may not be true about the whole. Let us look at some more examples of the fallacy of hasty generalization.

Example 1:

Suppose it is said that since the per capita income of our country has increased, therefore, there is economic progress in the country, and we are financially better off from previous years when the per capita income was at a lower figure. The argument appears to be all right but if we go a little deep into the matter we shall realize that inferences drawn from the fact that the per capita income of the country has gone up
may not be correct. Thus if the per capita income has increased on account of the fact that the price level has gone up there may not be any progress and financially people may be worse off. If the per capita income of a country is doubled and if the prices increase fourfold then in terms of goods and services the income per capita has gone down. Again it is also likely that rich people might have become richer and the poor poorer so that only a small section of the people are better off while a large majority of people are actually worse off from the previous period. It is also possible that the calculation of per capita income in two different periods may have been done by two different methods and this may be responsible for the increase in the figure of the national income in the latter period. It is also likely that the increase in per capita income may be of a very temporary nature due to special circumstances. Thus in times of war when the production is at its peak point and the prices also go up the figure of the per capita income generally increases but it hardly indicates any solid type of economic progress.

Example 2:

Suppose it is argued that since the im· ports in the country are increasing year after year, therefore, people are consuming more goods and it is an indication that the economic condition of the people is improving. This statement also appears to be logical at first thought but if we think about it carefully we may find many pitfalls in it. Thus it is possible that along with an increase in the imports the number of re-exports may also have gom up in which case there is little increase in the per capita consumption of the goods. Even if the quantity of the re-exports has not increased there may have been a decline in the consumption of homemade goods and there may not have been an increase in the per capita consumption. It is also likely that the population of the country has increased and the additional imports are accounted for by the increase in population. If none of these factors have changed and the per capita consumption of goods has really gone up it is no proof that the economic condition of the people has improved. It may be that the additional imports are mostly luxury goods consumed by a handful of rich persons who may have become richer whereas the vast majority of the people may be consuming the same quantity of goods as formerly or even less. It is very obvious that the conclusion which appears all right at the beginning may not at all be accurate.

References:

Fundamentals of Statistics – D.N. Elhance

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