NUMERALS AND WRITTEN NUMBERSThere is an interesting parallel between the relative standing of written numbers, and round numbers in paragraph form. The two tables in question are forms 7 and 8. The only difference in the two forms is that form 7 contains detailed numbers and form 8 round numbers. 1 The three paragraphs in question are forms 2, 3 and 4. The three forms are identical, except that form 2 contains round numerals (e.g., $5000), form 3 contains mixed numerals and written numbers (e.g., 5 thousand dollars) and form 4 contains entirely written numbers (e.g., five thousand dollars). The meaning and logical arrangement of the numbers is identical in the three paragraphs but the visual pattern is different.Considering the two statistical tables, forms 7 and 8, the round numbers produced scores* considerably higher than the scores produced by the detailed numbers in all questions dealing with specific amounts. In questions dealing with dynamic and static comparisons 1 Objection may be raised that detailed numbers do not differ from round numbers, in detail only, but that the total number is different: In an endeavor to offset this difference the children were told to answer in round numbers or approximate numbers only; and in scoring, greater range in approximation -was credited for the detailed than for the round numbers; e g., one detailed number (10,672,439) was intentionally nearer to the next higher round number (11,000,000) than to the number which appeared in the other forms (10,000,000); for children who had received the detailed number full credit was given for any answer between 10,000,000 and 11,500,000. It is interesting to note, however, that the children who received the detailed number did not give 11,000,000 as the approximation of what they had read any more frequently than the children who had read the round number. In both cases 10,000,000 was the most frequent answer although in the case of the detailed numbers 11,000,000 was actually the more correct approximation. This may indicate that the children responded more to the general appearance of the number than to its inherent meaning.' This phrase should be taken throughout to mean "the children who road the form made scores." 465 466
Writers are frequently confronted by the need of presenting numerical facts to their readers. Quantitative data concerning such matters as imports, earnings, products, population, historical statistics and the like, are not infrequent in their occurrence, and it is, therefore, important to know what form of tabular, textual or graphic arrangement is preferable under different circumstances. The present study reports the results of an objective measurement of the effect upon several thousand junior high school children of various arrangements of quantitative material. \~ The procedure was as follows: 2 A short account of the economic history of Florence was written. This unit was selected in order that the content might be equally unfamiliar to all the children. The narrative included one paragraph which contained specific quantitative facts. In each of the forms this paragraph was varied. The rest of the material was constant; and the paragraph in question varied only in'the form of presentation not in the data themselves.* In some of the
S, with no questions. T, with questions all at the beginning of the story. Y, with questions interspersed at the beginning of appropriate paragraphs.Z, with questions interspersed at the end of appropriate paragraphs. X, with the questions all at the end of the story. 1 Some of the questions dealt only with facts which were mentioned in the reading matter; some dealt with generalizations which were not made in the story but could be educed from the facts presented.II. The five forms of reading material were distributed among equivalent groups of junior high school children.III. Identical tests were given. The tests had five sections: 1. Factual questions not related to questions in the story. (In the discussion of results, scores in this part of the test are referred to as scores in "non-experimental facts.") 2. Factual questions directly connected with (in most cases, repeating) questions in the story. (Scores in this part of the test are referred to as scores in "experimental facts.") 3. Generalization questions not connected with questions in the story (referred to as "non-experimental generalizations").4. Generalization questions related to factual questions in the story. (The score in this part of the test is referred to as the score in '' semi-experimental generalizations.'') 5. Generalization questions directly connected with (in most cases, repeating) generalization questions in the story (referred to as "experimental generalizations").Thus the test was divided into "non-experimental facts," "experimental facts," "non-experimental generalizations," "semiexperimental generalizations," and "experimental generalizations." Examples of each of these five divisions will be given in the detailed account of the experimental procedure.1 This unalphabetical arrangement of the forms is followed throughout, and it may assist the reader in interpreting the tables and charts to note the pattern of the arrangement. The first is the control group form. In the two principal bar graphs this form is not represented by a bar, but constitutes the line from which the other bars rise or fall. The four experimental group forms are arranged according to the placement of the questions. The form in which the questions most precede the reading matter to which they refer, comes first; the form in which the questions only slightly precede the reading matter to which they refer, comes next; the form in which the questions follow closely the matter to which they refer, comes next; and the form in which the questions follow most remotely the matter to which they refer, comes last.
Since the great majority of children in this population were over 14.5 years of age, and since this was the assumed adult mental age used in deriving mental ages from chronological ages and I. Q. s, the M. A. s in this population are almost wholly functions of the I. Q. s.2 Self correlation obtained from population of college students retested after one semester.3 Spurious correlation has been deducted. In Musselman's formula ( 8 ) t/s = spurious r of a single test with a composite of which it is a part (t, being number of elements in a single test and s being number of elements in the composite), S was counted as 165 although it would be possible to earn 175 theoretically. Actually the maximum score in all elements except the wish element was frequently approached. Therefore, the obtained spurious r may be regarded as a little too low for all elements except the wish element, and for this it is a little too high.* Obtained from college students retested after one month. B Obtained by applying Brown's prophesy formula to a reliability of .90 ± .01 yielded by the sum of test elements exclusive of wishes. The N in the formula was counted as 1 2. However, by another population of college students the reliability of the whole OSPA score was the same (namely, .90 ± .02) as for the sum of the OSP elements alone.
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