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## Statistical Fallacies

Statistical are convincing. It is possible for the users of statistics to misinterpret them. It is also possible to present statistical information in a misleading way so as to mislead the users of such information. The misuses of statistics is as common as its uses. Therefore, it is important for users to know the pitfalls in statistics.

The correct interpretation of data is a difficult task and requires certain degree of skill, care, judgement and objectivity. If proper care is not taken, there is every liklihood that the data can be misused to prove things that are not true.

Statistical fallacies may arise in collection, presentation, analysis and interpretation of data. In general, wrong interpretation of data can occur due to:
1. Bias
2. Inconsistency in definitions
3. Faulty generalisations
4. Faulty deductions
5. Inappropriate comparisions
6. Misuse of various tools of analysis such as mean, median, mode, disperson, correlation, etc.
7. Faulty interpretation of trends, seasonal and cyclical variations, etc.
8. Technical errors
9. Failure to comprehend the total background of the data; and
10. Other reasons not listed above
The following paragraphs discuss some of these issues.

Bias
Bias, consciously or unconsciously, is very common in statistical work. It very often leads to false conclusions.

For example, if a training institute wants to showcase that its students are bright, it may reduce the difficulty of test papers, or may select only good students and exlude bad students from the sample. A mutual fund company trying to sell a mutual fund scheme may select its best performing fund to compare it with its competitors, and exlude other schemes in the comparison. A businessman trying to get capital from investors may highlight its profits while not fully disclosing other important financial and non-financial information.

Bias is very common. In fact, it is quite possible that all statistical data collected may contain some bias. The interpretation may also be biased as each person will interpret it based on its own experience and attitude towards the problem at hand.

Inconsistency in Definitions
Sometimes false conclusions are drawn because of failure to define properly the object being studied.

For example, while comparing the national income figures of India and China, it is absolutely essential that the definition of national income is taken to be the same in both the countries. Similarly, when comparing poverty levels in two countries, it is important to define poverty.

Defining certain things is not easy as it may seem. It requires proper understanding of the problem at hand and to come up with practical and workable solutions.

Faulty Generalisation
A basic error that is very often committed in statistical work is to jump to conclusions or generalisations on the basis of too small a sample or a sample that is not representative.

For example, by taking a sample of 5% to 10% of the population we can make a generalisation for the whole population. This could be a mistake and misleading. Even if the sample size is good enough, it may be still not possible to generalize in certain circumstances as the sample may not be representative of the whole population.

Faulty Deduction
If we apply a general rule errorneously to a specific case, it would lead to a faulty deduction.

Let's suppose that a firm's revenues has increased continously during the last 10 years except for the recent two years. This information may guide us to the conclusion that the firm is not doing good recently and may dissuade us from investing in the company's stock. It is quite possible that in the last two years, the firm faced lockdown, or it deliberately scaled down its operations, or there were temporary restrictions on exports due to which the revenues were less, or some other factors. Without understanding the real cause of the drop in the revenues, we cannot deduce just from the revenue numbers about the overall state of the company.

Inappropriate Comparisons
In order to draw conclusions from the data it is necessary to make comparisions. However, the comparisons between two things cannot be made unless they are really alike.

For example, if we were to compare the Consumer Price Index (CPI) data of the year 1999 with the year 2000, we must see to it that the number of commodities including, their qualities and method of constructing the index is the same for both the years, otherwise the two indices cannot be compared properly.

Summary
It is possible to misuse statistics due to lack of proper knowledge or it can be used deliberately to mislead the user.

One must remember that statistics can neither prove or disprove. It is only a tool which can help us if properly used. Think of a blind person who is walking with a stick. He can use the stick to find pit-holes in the road so that he can avoid them and reach his destination safely. It is also possible that the person uses them improperly and falls in the pit.

Statistics is like the stick to a blind person. It provides vital information but does not prove anything. it is up to the user to use his knowledge and wisdom to make the right inferences from statistical data for productive uses.

I shall conclude this article by pointing out a phrase of popular statistics Roberts and Wallis:

"He who accepts statistics indiscrimately will often be duped unnecessarily. But he who distrusts statistics indiscriminately will often be ignorant unnecessarily."

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Updation History
First updated on 12th August 2020.