APPLICATION OF STATISTICS IN EDUCATIONS PART SEVEN: STATISTICS, TESTS AND EXAMINATIONS

PART SEVEN: STATISTICS, TESTS AND EXAMINATIONS

v Application of Statistics in Education.

v Psychological Tests.

v Examinations and Scholastic Tests.

v  

Chapter 33

APPLICATION OF STATISTICS IN EDUCATIONS

The Chapter at a Glance

Introduction of precision.

Some basic statistical concepts.

Distribution of IQ.

The guiding role of statistics.

            As sciences progress they become more and more precise and quantitative. Says Walker:

"The more advanced the sciences have become the more they have tended to enter the domain of mathematics, which is a sort of centre towards which they converge. We can judge the perfection to which a science has come by the facility, more or less great, with which it may be approached by calculation."

Introduction of Precision

            Application of statistical methods to the problems of educa­tion has resulted in making the science of education more quantitative and more precise. In fact, the contemporary use of elaborate statistical procedures has made education more scientific than it used to be in earlier days.

            The presentation of the test results and other educational data in the forms of percentages, coefficients of correlations, tables, diagrams, curves, etc. has facilitated understanding, comparison, prediction and control in many fields of education.

Some Basic Statistical Concepts

            A teacher cannot be expected to have mastery over all the elaborate and complicated statistical procedures. Nevertheless, a working knowledge of some statistical concepts and techniques will certainly prove very helpful for a student of Educational Psychology and a prospective teacher.

            Some of the commonly used statistical terms which one frequently comes across in modern literature on education and psychology are explained in the following pages. A working familiarity with these simple statistical concepts is very desir­able.

The Central Tendency

            This is the tendency for judgments with regard to a quality or trait to gravitate towards the middle or the centre of the scale.

            The Three Types: The three averages or measures of central tendency that are frequently used are:

            (1) The Arithmetic Mean,

            (2) The Mode,

            (3) The Median.

(1) The Arithmetic Mean: This is popularly known as the average. In order to obtain the arithmetic mean, all the scores of a group of individuals are added and divided by the number of the score.

(2) The Mode: This is simply the score which is more often attained by a greater number of individuals in the group.

(3) The Median: It is the middle point of the group, i.e., the point which separates the upper half of the scores from the lower half.

            Value of the Central Tendency: The value of a measure of the central tendency is two-fold:

(a)      It is a single measure which represents all of the scores made by the group and as such gives a concise description of the whole of the group.

(b)      It enables one to make a comparison between two or more groups in terms of typical performance.

Frequency

            It literally means the number per second of periodic pheno­mena, such as vibrations or waves. In technical statistical language it refers to the number of cases with a certain value or score, or between certain values or scores, in tabulation for statistical purposes.

            The Frequency Distribution: The result of grouping of measures is called a frequency distribution. It is made up of two columns of figures as follows:—

(a)      A serial list of the "Class-Intervals", which are arranged preferably with the smaller measures at the lower end of the scale.

(b)      A column of Frequencies, which gives the number of measures tabulated in each class-interval.

            Graphic Representation: Frequency distributions are repre­sented graphically by the following:—

            (a)      Histograms or Column Diagrams or Block Diagrams.

            (b)      Frequency Polygons and frequency Curves.

             (c)      Cumulative Frequency Curves.

The Percentile

            If a frequency is divided into 100 equal parts, each part is called a percentile. A percentile is an indication of the position of a value or a score, in a series arranged in order of magnitude, by the percent­age of the value of scores falling at or below that position.

Achievement

            Achievement or accomplishment is performance in a stand­ardized series of tests, usually educational.

            Achievement Test: This is a test constructed and standar­dized to measure proficiency in school subjects.

            Achievement Age: This refers to the chronological age corresponding to any particular level on a scale of achievement tests.

            Achievement Quotient (AQ): This is the ratio of the achievement age to the chronological age of the individual test­ed. AQ is expressed in percentage.

Norms

    A norm is a representative or standard value or pattern, for a group or type.

            The number of points made by a subject on a test or the number of test items answered correctly by him constitutes his raw score. By itself a raw score does not signify anything. In order to be meaningful it must be interpreted with reference to some standard, e.g., an age norm.

            An age norm is the average score of the majority of indivi­duals of a particular age. Thus, for instance, the average score of the 10 years old children is the 10 year norm and so on.

Mental Age (MA)

            An individual's raw score on a test can be converted into his mental age if the norms are available. Thus a child or an adult has a mental age of 10 years if his raw score just equals the 10-year norm. If his score falls exactly half way between the 10-year and the 11-year norms his mental age is 10.5 years.

            A Measure of Intellectual Achievement: Thus the MA conveys definite meanings regarding the ability of an individual. When we say that a child of 10 has reached the MA of 10 year olds we definitely imply that he falls in the average of his group. Similarly, when it is said that a child of 10 has reached the age of 11 years, we imply that he is above the average of his group. If the MA of the same child is 9, it signifies that he is below the average.

MA thus is a measure of the level of one's intellectual achievement.

Intelligence Quotient (IQ)

            IQ is the ratio of the mental age (MA) to chronological age (CA, i.e., the life age counted from birth). It is expressed in percentage.

            Intellectual Achievement with Reference to Others: MA as we have already seen indicates the intellectual achievement as such. The IQ, on the other hand, gives an index of the intellec­tual achievement with reference to other individuals of the same age.

            Thus, for instance, a 4-year old child with an MA of 6 years is a very bright child. But if he is 10 years old and has the same MA, he is definitely dull. The IQ is a very convenient way of calculating an individual's brightness or dullness in mathe­matical terms.

            Formula for IQ: If we divide mental age by chronological age and multiply the sum by 100 we get the IQ. In statistical terms the formula for obtaining IQ is as follows: —

Given a child of 4 with an MA of 6, the IQ would work out thus:

            This indicates that the child is very much above the average of the children of his own chronological age. The exact average IQ for any age is 100.

Similarly, the IQ of 10-year old child with an MA of 8 years would be:

Such a child is definitely below the average.

IQ Distribution among Children: The following table shows the usual distribution of IQ among various categories of children and the percentage of their distribution in the total population.

Distribution of IQ

IQ Range	% of Population	Category of Children
Over 140	1	Genius
130-139	2	Very Superior
120-129	8	Very Superior
110-119	16	Superior
100-109	23	Average
90-99	23	Average
80-89	16	Dull Average
70-79	8	Dull Average
60-69	2	Mentally Deficient
Below 60	1	Mentally Deficient

The Guiding Role of Statistics

            As already stated, statistics plays a significant role in modem social sciences. Its applied role in education cannot be exag­gerated. A mastery of the theory and technique of statistics is very helpful for a student conducting research in the field of education. For a teacher or a school administrator, however, a practical knowledge of the basic statistical concepts would be quite sufficient.

The Exact Significance of Statistical Data

            It should, however, be remembered by research workers and teachers alike, that statistical figures and correlations are not to be assigned undue significance. The science of statistics is only a guide. It is not an end in itself. If, for instance, the statistical figures establish a high correlation between poor educational achievement and poverty of a group of students, it does not necessarily establish a causal relation between the two, i.e., it does not prove that poverty is the cause of poor educa­tional achievement. All that is suggested by a positive statistical correlation between the two factors is that they have usually been found together in a group of students studied by the observer.

Suggestive of Further Research

            Yet we cannot ignore the great significance of such a sta­tistical correlation. It is a significant indicator which points to the necessity of conducting further research in a particular field. All statistical data, percentages, coefficients, curves, figures, tables, graphs, etc. are mostly helpful and suggestive of the need for conducting further investigation in a particular field.

            Thus when a statistical correlation is established between two phenomena further evidence may too reveal the causes which are responsible for their happening together. Knowledge of these causes proves very helpful in taking appropriate steps for understanding, improvement, treatment, etc., in a given situation.