WOODWORTH, R. S., Psychology (New York, Henry Holt & Co., 1921). YERKES, R. M., Introduction to Psychology (New York, Henry Holt & Co., 1911). Articles GILCHRIST, Olive, "A New View of Mental Development," Psychological Review (July, 1924), pp. 297-310. HUMPHREY, George, "The Psychology of the Gestalt," American Journal of Psychology (1924), Vol. 35, pp. 353 f. "The Psychology of the Gestalt," Journal of Educational Psychology (October, 1924), Vol. 15, pp. 401-402. KOFFKA, Kurt, "Introspection and the Method of Psychology," British Journal of Psychology (October, 1924), Vol. 15, pp. 149-161. "The Gestalt Theory," The Psychological Bulletin (1922), Vol. 19, pp. 531-585. OGDEN, R. M., "The Need of Some New Conceptions in Education," School and Society, Vol. 18, pp. 343–348. CHAPTER XXIV STATISTICAL METHODS FOR TEACHERS A proper understanding of educational psychology presupposes a working knowledge of statistical methods. Much of the data collected by students of education and teachers remain unanalyzed and not interpreted because of a lack of knowledge of statistical methods. The statistical terms that are used in this chapter are sufficiently elementary in nature to be understood and used by teachers anywhere. They were prepared for teachers by the Director of Reference, Research and Statistics, Board of Education, City of New York. 1. The A B C of Educational Statistics ["Educational Measurements for the Class Teacher." Courtesy of Board of Education, City of New York, Bureau of Reference, Research and Statistics, EUGENE A. NIFENECKER, Director, No. 6, September, 1922.] I-Why Is It Desirable for a Teacher to Understand Commonly Used Statistical Terms and to Be Able to Use the Simpler Statistical Methods? The teacher should have some familiarity with modern statistical terms and methods: 1. In order to enable her to handle properly the data resulting from any educational measurements which she may undertake; 2. In order to enable her to read understandingly the results presented in the reports of current educational measurements and investigations. II-What Are the Statistical Terms Most Frequently Used in Recent Educational Literature? Scale, unit, series, frequency, table, range, average, median, average deviation, quartile, middle 50 per cent, etc. 1. What is a scale? "A scale is a series of perfectly defined amounts, the differences between any two of them being also defined so that a series varying by steps of equal difference can readily be selected." "It is a linear distance or a difference in numerical magnitude which will represent or stand for the magnitude of the measures in question." For example the handwriting ability of a group of children may vary in magnitude from 30 to 70 as measured on the New York Penmanship Scale, which ranges from 20 to 90. The unit is a certain distance on the scale in terms of which quantities are expressed. In physical measurements the unit may be a foot, an inch, a pound, an hour. In educational measurements the unit may be a word as in spelling, a problem or example as in arithmetic tests, a question as in geography, a paragraph as in reading tests. In many educational tests and scales the unit used is a statistical unit, a measure of the variability of the group from its central tendency as a P. E., an S. D. or a "T" unit. 3. What is meant by a variable? A variable is a quantity which under the given conditions may assume different values. The spelling ability of eighth grade pupils is a "variable." The scores of the pupils would vary and each score would be a value of the "variable," i. e., the spelling ability of eighth grade pupils. The spelling ability of an individual pupil is a variable. If we test the pupil a number of successive times we find the results vary. The length of a given piece of copper wire, the weight of a given quantity of water are constants. Repeated measurements yield the same results. Any variation will be slight and is due to errors in measurement. III-What Are the First Steps in the Statistical Treatment of the Numerical Data Resulting from Any Given Class or School Tests? Assume that a spelling test of 50 words taken from the Ayres list was given to a 6B class of 50 pupils. The scores as taken from the individual papers are unorganized and no definite impression is obtained. From the individual scores we can gather only a very indistinct impression of the ability of the class. It is necessary to simplify the data in some way, and the first step is to arrange or group them into a series. 1. How shall we classify our original measures? We may classify the measures or scores resulting from our hypothetical spelling tests by arranging the scores as shown in Table I. The above arrangement constitutes a series, which, in statistics, is a grouping of measures of the variable by steps or classes 3. In Table I (a) What is the scale? The scale is the number of words correct from 0 to 50. (b) What is the unit? One word correctly spelled. (c) What is the size of one grouping or class? (d) What is the range of our measures? The range is the distance from the lowest measure to the highest. The lowest is 13 and the highest is 47, which gives a range of 34. 4. What further simplification or organization of our data can we obtain? In the above grouping our classes consisted of but one unit and as a result we obtained 35 classes. For greater ease in handling it is desirable to reduce the number of classes or groupings to not more than 20. We, therefore, may further condense our data of Table I by grouping our scores into classes having more than one unit. Let us group them in steps of five units as shown in Table II. TABLE II-DISTRIBUTION OF SPELLING SCORES IN A 6B (a) What is the class? 50 (N) Each group of measures, 46 to 50, 41 to 45, etc., is called a class. (b) What is the size of the class interval? 5 units (words correct). (c) How many classes have we? Ten. (d) What is the frequency column? It is the column which shows the frequency with which each score occurs, that is the number of scores tabulated in each class interval. It is designated by the letter ƒ in Table II. (e) How many scores have we? Fifty. The number of items or scores in this case (pupils) is designated by the capital letter N. |