Statistics -Intro

Definition of Statistics: Statistics has been defined differently by different authors from time to time. The reasons for a variety of definitions are primarily two. First, in modem times the field of utility of Statistics has widened considerably. In ancient times Statistics was confined only to the affairs of State but now it embraces almost every sphere of human activity. Hence a number of old definitions which were confined to a very narrow field of enquiry, were replaced by new definitions which are much more comprehensive and exhaustive. Secondly, Statistics has been defined in two ways. Some writers define it as' statistical data', i.e., numerical statement of facts, while others define it as 'statistical methods', i.e., complete body of the principles and techniques used in collecting and analyzing such data.

Statistics as 'Statistical Data':

Webster defines Statistics as "classified facts representing the conditions of the people in a State ... especially those facts which can be stated in numbers or in any other tabular or classified arrangement." This definition, since it confines Statistics only to the data pertaining to State', is inadequate as the domain of Statistics is much wider. Bowley defines Statistics as " numerical statements of facts in any department of enquiry placed in relation to each other." A more exhaustive definition is given by Prof. Horace Secrist as follows: " By Statistics we mean aggregates of facts affected to a marked extent by multiplicity of causes numerically expressed, enumerated or estimated according to reasonable standards of accuracy, collected in a systematic manner for a pre-determined purpose and placed in relation to each other."

Statistics as Statistical Methods:

Bowley himself defines Statistics in the following three different ways:

(i) Statistics may be called the science of counting.

(ii) Statistics may rightly be called the science of averages.

(iii) Statistics is the science of the measurement of social organism, regarded as a whole in all its manifestations.

But none of the above definitions is adequate. The first because Statistics is not merely confined to the collection of data as other aspects like presentation, analysis and interpretation, etc., are also covered by it. The second, because averages are only a part of the statistical tools used in the analysis of the data, others being dispersion, skewness, kurtosis, correlation, regression, etc. The third, because it restricts the application of Statistics to sociology alone while in modern days Statistics is used in almost all sciences - social as well as physical.

According to Boddington, " Statistics is the science of estimates and probabilities." This also is an inadequate definition since probabilities and estimates constitute only a part of the statistical methods.

Some other definitions are: "The science of Statistics is the method of judging collective, natural or social phenomenon from the results obtained from the analysis or enumeration or collection of estimates. "- King.

" Statistics is the science which deals with collection, classification and tabulation of numerical facts as the basis for explanation, description and comparison of phenomenon." -Lovitt.

Perhaps the best definition seems to be one given by Croxton and Cowden, according to whom Statistics may be defined as " the science which deals with the collection, analysis and interpretation of numerical data."

Importance and Scope of Statistics:

In modern times, Statistics is viewed not as a mere device for collecting numerical data but as a means of developing sound techniques for their handling and analysis and drawing valid inferences from them. As such it is not confined to the affairs of the State but is intruding constantly into various diversified spheres of life - social, economic and political. It is now finding wide applications in almost all sciences - social as well as physical-such as biology, psychology, education, economics, business management, etc. It is hardly possible to enumerate even a single department of human activity where statistics does not creep in. It has rather become indispensable in all phases of human endeavor.

Statistics and Planning: Statistics is indispensable to planning. In the modern age which is termed as 'the age of planning', almost all over the world, governments, particularly of the budding economies, are resorting to planning for the economic development. In order that planning is successful, it must be based soundly on the correct analysis of complex statistical data.

Statistics and Economics: Statistical data and technique of statistical analysis have proved immensely useful in solving a variety of economic problems, such as wages, prices, analysis of time series and demand analysis. It has also facilitated the development of economic theory. Wide applications of mathematics and statistics in the study of economics have led to the development of new disciplines called Economic Statistics and Econometrics.

Statistics and Business: Statistics is an indispensable tool of production control also. Business executives are relying more and more on statistical techniques for studying the needs and the desires of the consumers and for many other purposes. The success of a businessman more or less depends upon the accuracy and precision of his statistical forecasting. Wrong expectations, which may be the result of faulty and inaccurate analysis of various causes affecting a particular phenomenon, might lead to his disaster. Suppose a businessman wants to manufacture readymade garments. Before starting with the production process, he must have an overall idea as to 'how many garments are to be manufactured', 'how much raw material and labor is needed for that', and 'what is the quality, shape, color, size, etc., of the garments to be manufactured'. Thus, the formulation of a production plan in advance is a must which cannot be done without having quantitative facts about the details mentioned above. As such most of the large industrial and commercial enterprises are employing trained and efficient statisticians.

Statistics and Industry: In industry, Statistics is very widely used in 'Quality Control'. In production engineering, to find whether the product is conforming to specifications or not, statistical tools, viz., inspection plans, control charts, etc., are of extreme importance. In inspection plans we have to resort to some kind of sampling - a very important aspect of Statistics.

Statistics and Mathematics: Statistics and mathematics are very intimately related. Recent advancements in statistical techniques are the outcome of wide applications of advanced mathematics. Main contributors to statistics, namely, Bernouli, Pascal, Laplace, De-Moivre, Gauss, R. A. Fisher, to mention only a few, were primarily talented and skilled mathematicians. Statistics may be regarded as that branch of mathematics which provided us with systematic methods of analyzing a large number of related numerical facts. According to Connor, " Statistics is a branch of Applied Mathematics which specializes in data." Increasing role of mathematics in statistical analysis has resulted in a new branch of Statistics called Mathematical Statistics.

Statistics and Biology, Astronomy and Medical Science: The association between statistical methods and biological theories was first studied by Francis Galton in his work in 'Regression'. According to Prof. Karl Pearson, the whole 'theory of heredity' rests on statistical basis. He says, " The whole problem of evolution is a problem of vital statistics, a problem of longevity, of fertility, of health, of disease and it is impossible for the Registrar General to discuss the national mortality without an enumeration of the population, a classification of deaths and knowledge of statistical theory."

In astronomy, the theory of Gaussian 'Normal Law of Errors' for the study of the movement of stars and planets is developed by using the 'Principle of Least Squares'.

In medical science also, the statistical tools for the collection, presentation and analysis of observed facts relating to the causes and incidence of diseases and the results obtained from the use of various drugs and medicines, are of great importance. Moreover, the efficacy of a manufactured drug or injection or medicine is tested by using the 'tests of significance' - (t-test).

Statistics and Psychology and Education: In education and psychology, too, Statistics has found wide applications, e.g., to determine the reliability and validity of a test, 'Factor Analysis', etc., so much so that a new subject called 'Psychometry' has come into existence.

Statistics and War: In war, the theory of 'Decision Functions' can be of great assistance to military and technical personnel to plan 'maximum destruction with minimum effort'.

Thus, we see that the science of Statistics is associated with almost all the sciences - social as well as physical. Bowley has rightly said, " A knowledge of Statistics is like a knowledge of foreign language or of algebra; it may prove of use at any time under any circumstance."

Limitations of Statistics: Statistics, with its wide applications in almost every sphere of human activity; is not without limitations. The following are some of its important limitations:

(i) Statistics is not suited to the study of qualitative phenomenon. Statistics, being a science dealing with a set of numerical data, is applicable to the study of only those subjects of enquiry which are capable of quantitative measurement. As such, qualitative phenomena like honesty, poverty, culture, etc., which cannot be expressed numerically, are not capable of direct statistical analysis. However, statistical techniques may be applied indirectly by first reducing the qualitative expressions to precise quantitative terms. For example, the intelligence of a group of candidates can be studied on the basis of their scores in a certain test.

(ii) Statistics does not study individuals. Statistics deals with an aggregate of objects and does not give any specific recognition to the individual items of a series. Individual items, taken separately, do not constitute statistical data and are meaningless for any statistical enquiry. For example, the individual figures of agricultural production, industrial output or national income of any country for a particular year are meaningless unless, to facilitate comparison, similar figures of other countries or of the same country for different years are given. Hence, statistical analysis is suited to only those problems where group characteristics are to be studied.

(iii) Statistical laws are not exact. Unlike the laws of physical and natural sciences, statistical laws are only approximations and not exact. On the basis of statistical analysis, we can talk only in terms of probability and chance and not in terms of certainty. Statistical conclusions are not universally true - they are true only on an average. For example, let us consider the statement:" It has been found that 20 % of a certain surgical operation by a particular doctor are successful." The statement does not imply that if the doctor is to operate on 5 persons on any day and four of the operations have proved fatal, the fifth must be a success. It may happen that fifth man also dies of the operation, or it may also happen that of the five operations on any day, 2 or 3 or even more may be successful. By the statement we mean that as number of operations becomes larger and larger we should expect, on the average, 20 % operations to be successful.

(iv) Statistics is liable to be misused. Perhaps the most important limitation of Statistics is that it must be used by experts. As the saying goes, " Statistical methods are the most dangerous tools in the hands of the inexperts. Statistics is one of those sciences whose adepts must exercise the self-restraint of an artist." The use of statistical tools by inexperienced and untrained persons might lead to very fallacious conclusions. One of the greatest shortcomings of Statistics is that they do not bear on their face the label of their quality and as such can be moulded and manipulated in any manner to support one's way of argument and reasoning. As King says, " Statistics are like clay of which one can make a god or devil as one pleases." The requirement of experience and skill for judicious use of statistical methods restricts their use to experts only and limits the chances of the mass popularity of this useful and important science.