The geology of the deposit was covered by him in an article entitled "An Unusual Fluorspar Deposit" published in the Engineering and Mining Journal, for September, 1928. LENHERSCHWERIN VIcronv FLUORSPAR MININGCOMPANY EL~AEETRTOWN, ILLINOIS
OBJECTIVE TESTS IN ORGANIC CHEMISTRY The 1940-1941 Series of the Cooperative Objective Tests in Organic Chemistry are now in the process of preparation. It is believed that the present series will meet the need of the average instructor of organic chemistry somewhat better than any of the tests of this series thus far prepared. It is hoped, furthermore, that those who elect to use these tests during the coming school year will cooperate with us to the extent that this series may be standardized and the validity of each item determined. One page is devoted t o each of twenty-six topic examinations in organic chemistry, and three pages each to the final examinations for the t i r t and second semesters, making a total of thirty-two mimeographed pages to a set. These sets are available to instkctors and graduate students or research workers in lots of five or more a t twenty cents each. Single sets are thirty-five cents. Those using these tests in their classes will be provided with a key for convenience in grading. Anyone who is interested in examining or using the 1940-1941 Series of Cooperative Objective Tests in Organic Chemistry may place his order with Ed. F. Degering, Chairman, Cooperative Objective Tests in Organic Chemistry, Purdue University, Lafayette, Indiana. Ep. F. DEGERING P ~ U UNIVERSITY E LAFAYETTE. INDIANA
"THE EFFECT OF THE NATURE OF THE COURSE ON ACHIEVEMENT IN FIRST-YEAR COLLEGE CHEMISTRY" To the Editor DEARSIR: Clark might be able to philosophize upon the socalled "conclusion-inevitable" that he makes in the article entitled, "The Effect of *Nature of the Course on Achievement in First-Year College Chemistry,"' but no statistician or scientist would allow him to base his conclusions upon the numerical gymnastics that he
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C-, "The effect of the nature of the course on achievement in first-year college chemistry," J. C m . EDUC.,16,510-11 (Nov.. 1939).
describes. Of course, it is possible that the experimenter may have made many other computations without bothering to record them in his paper. Certain additional data could certainly prove useful, but this critic will naturally have to assume that all of Clark's work is described in the report. Little does Clark apparently realize how correct he actually is when he says, "Perhaps the reader should be cautioned against indiscriminately applying the above conclusions to other groups of students." (1) Clark attempts to compare the gains made by students in the elementary group and the advanced group by determinimg their "average gain". He obtains this gain by "end-test percentile minus pre-test percentile." By chance, the particular groups with which he was dealing (those having had high-school chemistry credit) actually increased their percentile ranks, thereby allowing him to ohtain positive numbers rather than negative ones. Percentile ranks are similar to rank order in which i t is easy to understand that a class of seventy-five must have seventy-five rank orders represented hoth in the pretest and in the end-test. The various changes both plus and minus that occur must always become equal to zero algebraically. A person holding his own must actually be gaining in true score and achievement if the class as a whole is learning anything. If a group, as was the case here, actually gains in rank order or percentile, it merely means that they are somewhat more select in their rate of increase than the others in that same group. Clark compares these rates of gains with the rates of gains of another group that apparently has not been equated in any way. These figures are meaningless arid misleading. (2) Clark'finds a correlation of 0.88 between the pre-test and end-test percentiles for the control group (elementary chemistry). In the 6rst place, percentiles represent a rectilinear distribution rather than a frequency distribution which might,be more similar to the normal curve. Equations for computing correlation are not designed for rectilinear distributions and therefore the data are less meaningful than might be supposed. (3) However, after finding this correlation of 0.88, Clark sets up a regression (for this elementary group) and gives i t as
XI
=
0.98 Xs f 17.12
With this, he can predict the end-test ranks from those on the pre-test. Accordingly, "end-test percentiles were then predicted for all members of the control group and a correlation of 0.88 was actually found between the predicted and the earned values." All Clark seems to have proved by this useless manipulation is that his arithmetic has apparently been correct both times and that the old truth, things equal to the same thing are equal to each other, is still as true as ever. (4) "By means of this same regression equation," for the clark then predicted the end-test students in the advanced group. The real meaning of
the regression equation implies that for that group, and for that particular course, there is a certain relationship between pre-test percentiles and end-test percentiles. Using that same regression equation on the data from another class, one should certainly not expect to predict their final-test scores. The only thing that Clark might have presumed, but apparently didn't, is that this would indicate the ranks that the students in the advanced class might have attained if they had, instead, been in the elementary class. (5) Comct use of the regression equation technic for comparing data makes i t entirely unnecessary to pair the stndents from the two groups. However, Clark has paired thirty-two students in the elementary group with thirty-two in the advanced group. He apparently paired them on the predicted end-test score for he says "both members of a given pair had the same predicted end-test percentile." It will be remembered from the previous paragraph that the same regression equation was nsed for both groups and hence if the predicted scores were the basis for pairing, he might just as well have nsed the pre-test percentiles of which they were directly a function. Again, Clark laboriously tests his own arithmetic by discovering that the "mean predicted end-test percentiles were exactly the same for the two groups, i. e., 58.9 . . . ." He chose those which were equal, so i t is little wonder that they actually are equal. (6) After his job of pairing the individuals, he states that "within the limits of error of the experimental method employed, the membersof Group Cshould have earned the same mean percentile on the end-test as the members of Group B except for the influencing factor of the course taken in college chemistry." He finds that the mean earned end-test percentile for the elementary group was 59.9 and that for the advanced group was 65.3. Again, let it be emphasized that one cannot compute the differenceto be 5.4 percentile and attribute that this "diierence is in favor of those stndents who took . . . . the course designed especially for them." The individuals were paired without any concept of the meaning of percentile ranking in the first place, for the actual achievement medians of the two groups had not been equated. Then, even though they had been equated and assuming that they had been matched correctly a t the beginning of the experiment, the actual end-test percentile has no meaning unless these medians are equated again. Clark concludes his article hoping "that this paper may also serve to remind chemistry teachers of the applications of the well-known experimental method to problems of an educational nature." This critic would like to conclude this paper with the hope that all those who are familiar with the same "well-known experimental method" refrain from using i t in problems of this sort. SHAILER A. PETERSON IJNIVERSITY HIGHSCAOOL
To the Editor DEARSIR: I am writing this letter concerning the criticisms of Peterson of my paper entitled, "The Effect of the Nature of the Course on Achievement in First-Year College Chemistry."' His major criticisms seem to arise from a lack of understanding as to how I calculated the percentiles which my students made on the pre-test and on the end-test. He apparently assumes that the raw scores earned by the students were transmuted into percentiles by using norms established for each local group of students and for each of the two times the tests were given. This assumption is incorrect and seems uujustifiable in view of the fact that I cited a previous publication2 of mine in which the source of the norms used was explained. However, I shall repeat it here. For a given student, the pre-test and the end-test forms were exactly the same. However, not all students included in the study took the same form. They were all either "Iowa Placement Examination," New Series, Form X or "Iowa Placement Examination," Series C TI, Revised A. The norms used were those developed by the Bureau of Educational Research and Service of the Extension Division of the University of Iowa, and the same norms were used in transmuting end-test scores as were nsed in transmuting pre-test scores. Hence the end-test and pre-test scores of all stndents were equated on the basis of Iowa percentile norms. Due to the fact that not all of the students took the same form, raw scores could not be used. Since it seemed desirable to include more students in the study than reports on either form would permit, transmutation into percentiles and a combining of the groups were decided upon. This was done only after receiving the favorable advice of a representative of the psychology department of the State University of Iowa. Using the gain which a student showed, then, in his percentile (end-test percentile minus pre-test percentile) would be equivalent, but not mathematically equal, t o using the gain which he would have made on his raw scores. Certainly in this case Peterson's comment that "the various changes both plus and minus that occur must always become-equal to zero algebraically" would be absolutely untrue. As a matter of fact, in reviewing my data, I find that the percentile of only about ten per cent. of all of the students (not just those paired) was less for the end-test than for the pre-test. This would be expected when the method which I used was employed. Peterson has just missed the point. Peterson's comment about the application of the regression equation to the advanced group does not hold, in view of the fact that the equation was derived from
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CLARK, "The effect of the nature of the course on achievement in first-year college chemistry," J. CHEM.EDUC.,16, 510-11, (Nov.. 19391. C ~ A R K . he effect of high-school chemistry on achievement in beginning college chemistry," ibid., 15, 285-9 (June,1938).
