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The authors' purpose was to examine the degree to which low achievement is related to ontogenetic factors (i.e., personal psychological traits expressed as attention and depression) or microsystemic factors (i.e., socioeconomic status, parenting, relationship with peers and teachers), using a total of 721 middle school students in South Korea. Based on the percentile rank, low-achieving students (bottom 15%; n = 323) and high-achieving students (top 15%; n = 398) were grouped, and a multigroup structural equation modeling was employed to determine which ecological factor(s) contribute to predict low achievement of middle school students. Results from multigroup structural equation modeling showed that 3 of the 6 ecological and ontological factors had significant direct or indirect effect on low achievement: socioeconomic status (direct effect), attention (direct effect), parenting (indirect effect). The findings are discussed in terms of the intertwined influences of ecological factors on low achi...

Using data collected in 1972 on a national random sample of 16,685 high school seniors, ten different grade average reporting systems were analyzed by means of a nonlinear least squares procedure. A grade conversion table was created by relating reported grade averages in all of the systems to common percentile ranks in class. It is suggested that the ten systems are probably reducible to only four fundamentally different systems.

Fifty-one experienced classroom teachers participated in an experiment designed to investigate the effects of test score reporting format (grade equivalents vs. percentile ranks vs. deviation IQs) on educational decisions. Although the scores were equated in terms of the case study student’s position in the distribution of scores, teachers were more likely to recommend special education placements when they were asked to evaluate percentile ranks rather than grade equivalents or deviation IQs. There was also a trend for the teachers to be more likely to diagnose the case study child as learning disabled and predict future academic problems when percentile ranks were used in contrast to grade equivalents or standard scores. The implications of these findings for the use of test scores in diagnostic decision-making practices are discussed.

1. The passing grade?commonly 75 percent. 2. The norm?usually an average on a standardized test secured from a fairly wide testing program. 3. The percentile rank. 4. The grade attainment. This is not a complete list. It does not, e.g., include the well-known McCall T Score, so mystifying to the average teacher. The passing grade doubtless occupies three-fourths to seven-eighths of the field the country over today. The other indexes listed above are a result of the application of statistics to the field of examining, grading, and promotion. In general, these various indexes are interchangeable ; that is, any one can be trans lated into any of the others. Types of Subject-Matter, Types of Teaching, Types of Testing? It is appropriate to ask what should determine the incidence of learning in any particular case. Are there types among which there may be different standards? Obviously there are, and this would easily be conceded in this group if applied to different subjects. Doubtless, anyone here would agree that any attempt to check or measure in the field of history would be very different from what it is if one were measuring handwriting or spelling or the fundamentals of Arithmetic. If it is conceded that there are different types of subject matter as among different subjects, then doubtless there are some who would con cede that there are different types of subject matter in almost any field and therefore in the field of arithmetic. Specifically, it is probable that everyone here would insist that a sixthor eighth-grade pupil should know XA paper read before the American Education Research Association at their annual meeting in Cleveland, February 25, 1939. 425

The purpose of this study was to determine how well semester grades in a course in college algebra (Mathematics 1 at the University of Wis consin) could be predicted from records available after the first week of instruction, using a minimum of statistics. This experiment was preliminary to a statistical study involving the same data.1 The complete statistical methods of prediction as carried out in that study will always give more exact results than any simpli fied procedure. Many persons wishing to use predictions have not the technical knowledge required, or lack time to carry out the extensive computation. The writer maintains that such people could?and no doubt some do?use available records to great advantage in making predictions involving very little statistical work. The subjects of this study were 361 students, nearly all freshmen, enrolled in Mathematics 1 for the semester ending in February, 1934. The predictive records available for all were the number of semesters of high school algebra and the numerical marks on the placement examina tion, which was given at the end of one week of class work. For nearly three-fourths of the group there.were also available, as part of entrance records, percentile ranks based on the rank in class in high school, and percentile ranks on a psychological test. For the few upperclassmen, grade point averages for college work already completed were available. At the end of the semester, grades were assigned by each instructor sep arately to the students in his own sections, as follows: A, B, C, D, E (condition), or F. The fact that grades were used as a criterion has no bearing on the methods involved. Grades, however bad, are the scale by which college success or failure is measured. Any more reliable criterion would merely be easier to predict. To obtain the information necessary for predicting the grades of the 1934 group, records for the corresponding 1932 and 1933 groups were compiled. For the predictive measures (i. e., placement ex amination marks, and high school and psychological test percentile ranks) class intervals of ten points were used, 0 ? 9, 10 ?19, etc. Scatter diagrams were prepared showing the grades obtained by students scoring in each class interval of each of the predictive meas

(1922). The Calculation and Interpretation of Percentile Ranks. The Journal of Educational Research: Vol. 6, No. 3, pp. 225-235.

IN THE STUDY of college academic success, one sees students whose level of achievement far exceeds that which might be expected from them according to some measurement of their scholastic aptitude. Likewise, some students fall considerably below their academic expect ancy. Therefore, the question of the non-intellectual characteristics up on achievement is raised. The present study is an attempt to develop a scale for the Minnesota Multiphasic Personality Inventory (MMPI)(1) which might select out underand over-achievers. The first step was to obtain a group of college students who could be called over-achievers and another group who could be called under achievers. These two groups were determined on the basis of an individ ual's percentile rank on the American Council on Education Psychological Examination (ACE) administered to freshmen and his first semester grade point average at the University of Wisconsin. Assuming that the student with the average ACE percentile for his class theoretically should earn the mean first semester grade point average for his class, these two values were equated and the ACE percentile ranks and grade point averages were converted to standard scores. A student who earned a grade point average which was one-half a standard deviation above the grade point average corresponding to his ACE total score was called an over-achiever. The student who earned a grade point average one-half a standard deviation below the grade point average corresponding to his ACE total score was called an under-achiever. If his grade point average fell within these limits, i. e. (+. 5a) he was declared to be achieving up to expectancy. Since the expectancy range was probably exaggerated there seemed to be little doubt that the persons really belonged to the group to which they wer? assigned. The case records of all the first semester freshmen males at the University of Wisconsin who sought out the services of the Student Coun seling Center in their first semester of the 1947-48 school year were examined in order to obtain two extreme groups. Fifty male students fell into the under-achiever group and twenty-seven in the over -achiever group. An item analysis of the MMPI statements (card form) was completed for these groups. Twenty-one items were obtained which distinguished between the two groups with critical ratios of 2. 33 or greater. Since Altus (2) has reported a similar study on a college achiever and non achiever scale, his items were examined. Three additional items were added to this scale which were on the Altus scale and had critical ratios

Three alignment charts for use in selective admissions were presented: (1) a chart for computing Y - R (SAT-V) + Ba (SAT-M) -f- B' (CHSR) ? C for various values of ft, B? and C and various scores on the Scho lastic Aptitude Test (SAT-V and SAT-M) and transformed rank in high school graduating class (CHSR); (2) a chart for computing the probability that an applicant with a given predicted grade-point average (?) will obtain a grade average of Y or greater; (3) a chart for computing either the percentile rank (P) at which the cutoff score should be set on a selection variable, or the number of entrants (X) forecasted when the cutoff is set at P. The first two charts represent a generalization and extension of a nomograph described in an earlier paper (1), and the third chart is a graphical representation of a procedure described by Hills and Klock (2).

IN ADDITION TO the use of standardized test data in determining pupil status by use of norms and his needs and difficulties by. item analysis and diagnosis of difficulties, it is a common practice in con ducting educational surveys to compute the central tendency of distri butions of test data for class or grade groups. These medians or means provide a method of appraising the status of such class or grade in relation to norms. The object of this paper is to present a summarization of data which appear in the manuals for the California Achievement Tests and the California Test of Mental Maturity, various levels, which make possible the adjustment of achievement norms to the mental ability of class or grade groups. Numerous studies have shown the positive correlations of the achieve ment of individuals in the basic skills with mental ability. These cor relations, when corrected for normal range, are ordinarily in the vi cinity of . 70 which is properly interpreted to mean that about 50 per cent (r^ = . 49) of the variance, or common elements, is accounted for. It is a common and desirable practice for counselors and teach ers to consider the achievement of individuals in relation to their men tal ability, frequently expressed as intelligence grade placement, men tal age grade placement, expectancy, or their percentile or standard deviation rank in mental ability as related to their rank in achievement. The data presented in this report are designed to provide a similar basis for comparison of median achievement to be expected of class groups or grades with varying levels of mental ability expressed as intelligence quotients. The various distributions in the accompanying pages of tabulations show the median achievement above or below the norm for grades 1 to 14, inclusive. They are presented by percentile rank of I. Q. groups for reading vocabulary, reading comprehension, total reading; arith metic reasoning, arithmetic fundamentals, total arithmetic; and me

It is a well known fact that a variety of methods are now available for representing a pupil's attainment on a group of tests by means of a single composite score. The relationships which exist among various types of scores, however, are not always clearly understood. It is the purpose of this article to consider the nature of three types of scores, all of which are based upon the same test and involve the same group of students. The individuals concerned in this study consist of six hundred stu dents to whom was administered the 1924 edition of the Psychological Examination which is edited by the National Research Council. This Examination consists of nine separate tests, each of which yields its own score. The examination provides that a composite score be determined in the following manner. Percentile ranks are computed for each test so that each of the nine raw scores earned by a student may be con verted into its corresponding percentile rank. The median of the nine percentile ranks is then found, this median being used as a single index of attainment in the entire examination. A second method of computing a composite score is to find the total of the raw scores earned by an individual on the nine tests. Under this procedure the various tests have equal weights in determining the com posite score only when the variabilities of the tests are equal or approxi mately equal. The tests under consideration do not have equal varia bilities, however, since their standard deviations for the group studied range all the way from 3.34 to 18.65, this large range being due chiefly to the fact that "perfect" scores on these tests range from 15 to 150. A totaling of the raw scores on these tests does not, therefore, result in giving them all equal weights. A composite score which does give equal weights to all of the tests may be obtained by converting the raw or original score on each test into the corresponding standard score, and then finding the sum of the standard scores earned by an individual on the nine tests, the resulting total being used as a single index of attainment in the entire examination. 224

THE INVESTIGATION here reported seeks an swers to two questions: To what extent can the pre dictive qualities of selected college entrance exam inations serve counselors and advisors in guiding education majors who are required to take co u r s e work in mathematics as a part of their curriculum? Assuming the validity and reliability of the scores from the selected tests, to what extent do such var iables as motivation and interest intervene to re duce the predictability value of these instruments (4)? The first question can be answered by testing the relationship between the entrance test scores of students majoring in education and the letter grades they received in mathematics course work.x* The oretically, a measure of high relationship indicates a high degree of predictability for the test and vice versa. Counselors and advisors could deter m ine the relative risk in assigning mathematics course work on the basis of entrance test score rank. A "high" rank score would suggest high probabil ity of success while a "low" rank score would suggest some need for preliminary work in a prepar ato ry course or special tutoring in the foundation of gen eral mathematics. 2 This, however, is a simplified theoretical ex planation in the prediction of performance. As for what occurs in the empirical setting, a corollary to this theoretical framework must be entertained. This is related the problem of answering the second question. Theoretically, motivational and interest factors intervene to a greater or lesser degree to produce performance levels not totally congruent with entrance test score rank (1). Obviously, theory serves to explain the disparity between entrance test score rank and actual perfor mance but it cannot fully answer the question as to the degree to which intervening m o t i v a tional and interest variables are operative for individual cases. Herein lies the problem of performance prediction,, The sample tested in this study is primarily composed of students majoring in elementary edu cation although mathematics education and indus trial education majors are well rep resented. The sample is segmental in nature and is composed of students whose entrance dates range from 1950 through 1955. The testing program was virtually unchanged during this period of time. The cases were recorded without reference to age, sex, or marital status. An attempt was made to minimize the inclusion of transfer students from other col leges within the University and to exclude transfer cases from schools outside of the University., The total number of cases employed in the sample is 100. However, since most students enr o lied in more than one mathematics course, the N value is greater than 100 for most of the cross-tabulationSo Tables I, II, and HI show percentage distributions of mathematics course grades and percentile scores for selected entrance examinations. The over all pattern appears to be absence of a gradient for per centage values consistent with the gradient for per centile rank scores. Rank Correlations (3). Several rank correlation values were computed to test the relationship be tween the observed performance and the exp e c t e d performance in mathematics on the basis of en trance tests. The disparity between the actual and the theoretical conditions is demonstrated schemat ically with corresponding correlation values. The greater the disparity, the greater the support for the theory of intervening variables. The reverse is true when the disparity is slight. It is interest i n g to note that the modal or most popular grade achiev ed in mathematics is "C" for most of the entrance tests regardless of percentile score range. This is in spite of the fact that Tables I, II, and III show higher percentages of "A" and "B" grades for the upper ranges of test scores. The Performance Profile. A d e m ons trat ion of the relationship between performance in specific mathematics courses most frequently taken by ed

Intelligence tests were until recently used primarily to deter mine the mental age of children by the comparison of the chron ological age with the mental age. When mental tests are given to adults, this type of analysis is no longer suitable since the intelligence of adults does not increase noticeably with age. The intelligence tests are used with adults in order to place a given person's intelligence with reference to the distribution of general adult intelligence. The scores are, therefore, more suit ably expressed in terms of ranks or percentile ranks or of the standard deviation of the distribution of adult intelligence. An intelligence test should be so adapted as to its difficulty that it will differentiate into significant and distinguishable groups the population for which it is intended. This cannot well be done if the test is either too difficult or too easy. In general, however, a fairly symmetrical distribution of test scores will be obtained for any given population with tests of considerable variation in difficulty. The test for which I am here submitting some norms was arranged in difficulty as nearly as possible to suit college freshmen. During the last five years I have been experimenting with over fifty different varieties of mental tests with college freshmen at Carnegie Institute of Technology in its various departments. My procedure was the general one of giving the tests as early as possible in the freshman year, filing the scores until scholarship records and instructors' estimates could be obtained, and then determining the predictive value of each test by the correlations between its scores and the objective criteria of the students' abilities. I have found that instructors' estimates, on account of their unreliability, are, in general, unsuitable as a criterion by which to judge the predictive value of a mental test. The several instructors' estimates for the same student vary considerably more than the corresponding scholarship grades. Lately I have used scholarship records almost exclusively as the general criterion to determine the predictive value of a mental test. The procedure is quite different, however, in work 265

A short time before this investigation was undertaken, the writer had found that the correlation between scores earned in the Meier-Seashore Art Judgment Test and scores earned in the McAdory Art Test was but .27 ? .06, a barely reliable relationship. Evidently the two tests do not measure the same kind of art ability. It was thought that some light might be thrown upon the question as to precisely what each did measure by comparing results with instruc tors' judgments. Following up this possibility, the writer asked the seven members of the staff of the art education department of the Col lege of Education, University of Minnesota, to arrange in rank order the 103 students who were majoring in art. These instructors were directed to base their ratings on the comparative creative abilities of the students. Since each instructor was not thoroughly familiar with the abilities of the one hundred or so art majors, it became necessary to make some classification of the basis on wThich the opinions were given. The follow ing was finally decided upon : (1) comparatively certain ; (2) doubtful ; and (3) guess. From the scores given, composite ranks were arrived at for those who received comparatively certain and doubtful ratings, and for those who were represented in all three columns. A table was then drawn up showing the percentile ranks of each student according to his instructors' judgment, his success with the McAdory test, and his suc cess with the Meier-Seashore test. (See Table I). Instructors' judg ments in this table include only those which were classified as compara tively certain. The twenty students whose records are presented were chosen at random from the total of 103, the only limitation being that each must have been well enough known to have received a "compara tively certain" rating by at least four of his instructors. Since the in structors numbered seven, four constituted a majority. An examination of the comparative percentile ranks reveals immedi ately the marked disagreement among the three measures. For example

USERS OF school achievement tests are becom ing increasingly desirous of making an interpreta tion of the results, both individual and group, in re lation to what has come to be known as "expectan cy. " As this term is now generally used, the ex pected level of a pupil's achievement is determined from one characteristic only, i. e. , his level of in telligence. In their efforts to develop the full po tential of all youth, schools are feeling the need for some standard by which they may evaluate achieve ment in relation to the capacity to achieve: Is this pupil doing as well as can be expected for his abili ty? Is the school's average achievement level com mensurate with the average intellectual capacity of its pupils? This need has been felt in some degree since the recognition of the extent of individual diff e r e ne e s among school children, and the development of tests to measure both their achievement and their intelli gence. Various schemes and formulas have been offered to give numerical expression to this achieve ment-intelligence relationship, beginning with the Accomplishment Quotient of the early 1930's. Most of these proposals have failed to meet all of the re quirements for a satisfactory means of making the desired evaluation. One source of error has been in the lack of com parability of the paired achieve ment and intelligence measures. An educational age derived from the age norms of an achievement battery may not be com parable with the mental age from an intelligence test that has been standardized on an entirely differ ent population. And the use of other types of rela tive measures, such as percentile ranks and stanine levels, does not afford proper comparisons unless the ranks for achievement and for intelligence are based upon the same reference population. A requirement often ignored is the need to take account of the varying part intelligence plays in the several specific areas of achievement. C?rrela tions of intelligence with reading or science, for ex ample, are generally found to be higher than those with spelling or arithmetic computation. The school that "expects" identical achievement in all sub jects for a given level of ability is failing to take account of these differentiated relationships. The achievement expected predicted for a given lev el of IQ must be established separately for each sub ject-test in the achievement battery. A related point, also often ignored, concerns the matter of regression. Since the setting of ex pected achievement levels is essentially a predic tive process, and the correlation between the pre dictor (intelligence) and the predicted achievement is something less than 1. 00, the expected achieve ment percentile rank (or stanine) will be identical with the percentile rank (or stanine) for intelli gence only at the mean. Above and below the mean, the predicted achievement will tend to be nearer to the mean than is the predictor, the pupil's intelli gence. Pupils whose stanine level in intelligence is nine may average only eight, or even seven on certain achievement subtests. Schools "expecting" a one-to-one correspondence between achievement and intelligence percentile ranks or stanines may make quite unwarranted conclusions, particularly at the extremes, by failure to take this regression effect into account, since they may appear to be do ing a very poor job with their highly successful pupils but being quite successful with those of rath er low intelligence, when the result is entirely in line with the regressed achievement levels expec ted.

The study compares scores from the WISC and PPVT given in individual administration to 406 children ages 6 to 13. Means and percentile scores on both tests were computed for each age level. The PPVT appeared to yield slightly higher IQ scores although the differences were significant only at ages eight and nine. All possible inter-correlations of the WISC subscales and the PPVT were computed. The PPVT appeared to correlate about as highly with the Performance and Verbal scales as these two scales correlate with each other. Except for averaging one to three points higher at some age levels, the PPVT appears to be quite comparable to the WISC.