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).
the Iowa norms and not from local norms for each "In its bare essentials, it consists of providing a situation where phenomena can be repeated and controlled, PUP. The paper as I originally submitted i t for publication and then varying one element in the situation to see did include a detailed statement of the method of con- what variation in the results is thereby produced. verting raw scores into percentiles, but the editor asked 'This means the isolation of a single variable and the me to condense it and I did so. In doing this, I do not determination of its results when the other variables or think that I affected the value of the paper in view of elements in the situation are constant." I certainly did not refer to the specific technic which I used, almy generous citation of other articles. I do not mind Peterson's comments on my use of though I do think that this particular technic of emchecks in certain portions of my study. No scientist ploying the experimental method might well be studied need ever apologize for checking on his work (even on more carefully by certain teachers. Again according his arithmetic). The fact is that he should be criticized to Crawforda the experimental method "is recognized as if he did not do so. probably the most essential instrument available in the When I cautioned the reader against "indiscrimi- quest for truth." The experimental method is certainly nately applying the above conclusions to other groups of well known to all scientists. students" I fully realized the import of my words, alI shall now leave it to the discriminating reader who thoughpeterson apparentlydoes notgive me credit for it. may have read my paper and the correspondence which My concluding remark, "It is hoped that this paper it has evoked to judge for himself whether I have may also serve to remind chemistry teachers of the truly used the experimental method and whether other applications of the well-known experimental method chemistry teachers should he encouraged to try to to problems of an educational nature," is apparently apply this general method to their own educational badly misconstrued by Peterson. I had in mind the problems. PAULE. CLARK universally known general method which is well described hv Crawfo~d.~
aC R A ~ R D "The , technique of research in education." The
University of Southern California, Los Angeles. Calif., 1928, p. 29.
