Statistics are convincing and this has led many people to think that they can be accepted without question. However, this belief is mistaken since there are many misuses of statistics. The figures only provide raw material; the data needs interpretation. The interpretation of data requires a high degree of skill, care, judgment, and objectivity. Statistical fallacies may arise at the stages of collection, presentation, analysis, and interpretation of data. The following are some of the specific examples illustrating how statistics can be misinterpreted or how fallacies arise in using statistical data.
Bias is very common in statistical work and often leads to false conclusions. For example, if a researcher wants to show that the wages at a particular company are very low he may select the sample in such as manner as to exclude high paid workers. Similarly, businessmen may use statistics to prove the superiority of their own business over others. For example, a business owner may present data from a quarter in which his business performed relatively better compared to the competition. Of course, the conclusion would only be valid if the data included a representative number of quarterly revenue.
Unconscious bias is also a problem. Perhaps all statistical reports contain some unconscious bias, since the result of statistical work is interpreted by human beings each of whom can judge only in terms of his experience and his understanding of the problem at hand. If biased data must be used in the absence of better information, the nature and probable amount of the bias must be considered in interpreting the results.
2. Inconsistency in Definitions
Sometimes false conclusions are made because of failure to define things in a consistent manner. For example, when comparing the national incomes of two countries it is important to make sure that the same definition for national income is being used for both countries. For comparison purposes, it would be incorrect to use the GDP (Gross Domestic Product) as an indicator of national income for one country while using the GNI (Gross National Income) for the other country.
3. Faulty Generalization
It is incorrect to rush to conclusions on the basis of a sample that is too or small or not representative of the entire population. For example, by taking a sample of three students it would be incorrect to generalize about the academic ability of students attending a particular college. Even if a large sample of students is taken but only from a single section, the conclusions would still be invalid. This is because a sample taken from a single section of the college is not representative. We can choose a representative sample by choosing a random sample of some students from each section. This method of selecting a sample is known as stratified sampling.
4. Faulty Deductions
If we apply a general rule erroneously to a specific case, it would be a faulty deduction. For example, if the profits of a firm have declined in a particular year it would be wrong to conclude that the firm is declining. This is because it might be the case that if we consider data of profits over 10 years, the firm shows an improved performance nine out of ten times with the particular year with the decline being an exceptional case.
5. Inappropriate Comparison
This is a statistical fallacy where a comparison between two things is made even though they are not alike. Comparison between dissimilar things leads to fallacious conclusions. For example, if the per capita income of a country is twice of what it was a decade ago we cannot conclude that the people are twice as better off compared to a decade ago. We must also study the behaviour of prices during this period. the conclusion would be valid only if the prices remain unchanged throughout this entire period.
6. Misuse of Statistical Tools such as Mean
This is one of the most common statistical fallacies. The various tools of statistical analysis are misused to deceive the public. For example, a public company having 1005 shareholders may declare that the average holding of shares of their shareholders is 100. But an analysis of individual shareholders might reveal that the five persons controlling the company have 98500 shares with the remaining 1000 shareholders having only 1500 shares. Thus, the average holding of the remaining shareholders is only 1.5.
A measure of dispersion must always accompany the average for a proper interpretation of the average. In the above example calculating the coefficient of variation will give us some idea of how the shares are spread apart among the various individuals.
7. Technical Errors
Many kinds of technical errors are possible in statistical works which would have the effect of arriving at wrong conclusions from the data. For example, A person might calculate the arithmetic mean in a situation where the harmonic mean is more appropriate. For instance, the harmonic mean is used in situations where we wish to calculate the average speed.
A comparison of percentages without knowledge of the base to which they refer would lead to error and confusion. For example, suppose that two cities have an unemployment rate of 1% each. It would be inappropriate to conclude that the two cities are similar in terms of employment without knowing the absolute population of each of the two cities. It may happen that the first city has a population of 10000 and the other a population of 10 million in which case the economic situation in the two cities would be entirely different.