Limitations of Statistics

Despite the usefulness of statistics in many fields, the impression should not be carried out that statistics are like magical devices which always provide the correct solution to problems. Unless the data are properly collected and critically interpreted there is every likelihood of drawing wrong conclusions. Therefore, it is also necessary to know the limitations and the possible misuse of statistics. The following are the important limitations of the science of statistics:

1. Statistics do not deal with isolated measurement: Not all quantitative data are statistical. Isolated measurements are not statistical. Data are statistical when they relate to the measurement of masses not statistical when they relate to an individual item or event as a separate entity. For example, the wage earned by an individual worker at any one time taken by itself is not a statistical datum but taken as a part of a mass of information, it may be a statistical data. It should be noted that the wage of one worker over a period of time, being a series of wages, can be used statistically.
2. Statistics deals only with quantitative characteristics: Statistics are numerical statements of facts. Such characteristics as cannot be expressed in numbers are incapable of statistical analysis. Thus, qualitative characteristics like honesty, efficiency, intelligence, blindness, and deafness cannot be studied directly. However, it may be possible to analyze such problems statistically by expressing them numerically. For example, we may study the intelligence of boys on the basis of the marks obtained by them in an examination.
3. Statistical results are true only on an average: The conclusions obtained statistically are not universally true; they are true only under certain conditions. This is because statistics as a science is less exact as compared to natural sciences.
4. Statistics is only a means: Statistical methods furnish only one method of studying a problem. They may not provide the best solution under all circumstances. Very often may be necessary to supplement the conclusions arrived at by the help of statistics with the other methods that may be used to study a problem. It should be carefully noted that statistics is only a means and not an end. It analyses the facts and throws light on the real situation. In deciding a course of action it may be necessary to take into account the country’s culture, religions, philosophy, personal, political, or other non-quantitative considerations. Exclusive dependence on statistics may lead to fallacious conclusions in many situations.
5. Statistics can be misused: The greatest limitation of statistics is that it is liable to be misused. The misuse of statistics may arise because of several reasons. For example, if statistical conclusions are based on incomplete information, one may arrive at fallacious conclusions. Thus the argument that drinking beer is bad for longevity since 99% of the persons who take beer die before the age of 100 years is statistically defective since we are not told what percentage of persons who do not drink beer and die before reaching that age. Statistics are like clay and they can be molded in any manner so as to establish right and wrong conclusions. Moreover, Tom, Dick, and Harry cannot deal with statistics. It requires experience and skill to draw sensible conclusions from the data; otherwise, there is every likelihood of wrong interpretations. Also, statistics cannot be used to full advantage in the absence of a proper understanding of the subject to which it is applied.

Distrust of Statistics

By distrust of statistics, I mean a lack of confidence in statistical statements and statistical methods. It is often believed that “Statistics can prove anything.” The following three main reason accounts for such notions being held by people about statistics: ----------

1. Figures are convincing and, therefore, people are easily led to believe them.
2. They can be manipulated in such a manner as to establish conclusions.
3. Even if correct figures are used, these may be presented in such a manner that the reader is misled. For example, note the following statement. “The profits of firm A are 4 lakhs for the year 2011-2012 and that of Firm B 5 lakhs for the same period.” On the basis of this information, only one would form the opinion that firm B is better than firm A. However, if we examine the amount of capital invested in the firms, the quality of work done, etc., we might reach a different conclusion.

It should be noted that statistics neither prove anything nor disproves anything. It is only a tool. If properly used, tools can do wonders and, if misused, can be disastrous. The same is true of statistical tools. If used properly, they help in taking wise decisions and if misused they can do more harm than good. But the fault does not lie with the science of statistics as such.

Sources: S.P. Gupta and M.P. Gupta, 2004. Business Statistics