the regression equation implies that for that group, and To the Editor for that particular course, there is a certain relationship DEAR SIR: between pre-test percentiles and end-test percentiles. I am writing this letter concerning the criticisms of Using that same regression equation on the data from Peterson of my paper entitled, "The Effect of the another class, one should certainly not expect to pre- Nature of the Course on Achievement in First-Year dict their final-test scores. The only thing that Clark College Chemistry."' might have presumed, but apparently didn't, is that His major criticisms seem to arise from a lack of this would indicate the ranks that the students in the understanding as to how I calculated the percentiles advanced class might have attained if they had, in- which my students made on the pre-test and on the stead, been in the elementary class. end-test. He apparently assumes that the raw scores

(5) Comct use of the regression equation technic earned by the students were transmuted into percentiles for comparing data makes i t entirely unnecessary to by using norms established for each local group of pair the stndents from the two groups. However, students and for each of the two times the tests were Clark has paired thirty-two students in the elementary given. This assumption is incorrect and seems uu- group with thirty-two in the advanced group. He ap- justifiable in view of the fact that I cited a previous parently paired them on the predicted end-test score publication2 of mine in which the source of the norms for he says "both members of a given pair had the same used was explained. However, I shall repeat it here. predicted end-test percentile." It will be remembered For a given student, the pre-test and the end-test from the previous paragraph that the same regression forms were exactly the same. However, not all stu- equation was nsed for both groups and hence if the dents included in the study took the same form. They predicted scores were the basis for pairing, he might were all either "Iowa Placement Examination," New just as well have nsed the pre-test percentiles of which Series, Form X or "Iowa Placement Examination," they were directly a function. Again, Clark labori- Series C TI, Revised A. The norms used were those ously tests his own arithmetic by discovering that the developed by the Bureau of Educational Research and "mean predicted end-test percentiles were exactly the Service of the Extension Division of the University of same for the two groups, i. e., 58.9 . . . ." He chose Iowa, and the same norms were used in transmuting those which were equal, so i t is little wonder that they end-test scores as were nsed in transmuting pre-test actually are equal. scores. Hence the end-test and pre-test scores of all

(6) After his job of pairing the individuals, he states stndents were equated on the basis of Iowa percentile that "within the limits of error of the experimental norms. method employed, the membersof Group Cshould have Due to the fact that not all of the students took the earned the same mean percentile on the end-test as same form, raw scores could not be used. Since it the members of Group B except for the influencing seemed desirable to include more students in the study factor of the course taken in college chemistry." He than reports on either form would permit, transmuta- finds that the mean earned end-test percentile for the tion into percentiles and a combining of the groups were elementary group was 59.9 and that for the advanced decided upon. This was done only after receiving the group was 65.3. Again, let it be emphasized that one favorable advice of a representative of the psychology cannot compute the difference to be 5.4 percentile and department of the State University of Iowa. attribute that this "diierence is in favor of those stn- Using the gain which a student showed, then, in his dents who took . . . . the course designed especially percentile (end-test percentile minus pre-test percentile) for them." The individuals were paired without any would be equivalent, but not mathematically equal, to concept of the meaning of percentile ranking in the using the gain which he would have made on his raw first place, for the actual achievement medians of the scores. Certainly in this case Peterson's comment two groups had not been equated. Then, even though that "the various changes both plus and minus that they had been equated and assuming that they had been occur must always become-equal to zero algebraically" matched correctly a t the beginning of the experiment, would be absolutely untrue. As a matter of fact, in the actual end-test percentile has no meaning unless reviewing my data, I find that the percentile of only these medians are equated again. about ten per cent. of all of the students (not just those

Clark concludes his article hoping "that this paper paired) was less for the end-test than for the pre-test. may also serve to remind chemistry teachers of the This would be expected when the method which I applications of the well-known experimental method to used was employed. Peterson has just missed the problems of an educational nature." This critic would point. like to conclude this paper with the hope that all those Peterson's comment about the application of the re- who are familiar with the same "well-known experi- gression equation to the advanced group does not hold, mental method" refrain from using i t in problems of in view of the fact that the equation was derived from this sort. -

SHAILER A. PETERSON CLARK, "The effect of the nature of the course on achievement in first-year college chemistry," J. CHEM. EDUC., 16, 510-11,

IJNIVERSITY HIGH SCAOOL (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 P U P .

The paper as I originally submitted i t for publication did include a detailed statement of the method of con- verting raw scores into percentiles, but the editor asked me to condense it and I did so. In doing this, I do not think that I affected the value of the paper in view of my generous citation of other articles.

I do not mind Peterson's comments on my use of checks in certain portions of my study. No scientist need ever apologize for checking on his work (even on his arithmetic). The fact is that he should be criticized if he did not do so.

When I cautioned the reader against "indiscrimi- nately applying the above conclusions to other groups of students" I fully realized the import of my words, al- thoughpeterson apparentlydoes notgive me credit for it.

My concluding remark, "It is hoped 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," is apparently badly misconstrued by Peterson. I had in mind the universally known general method which is well de- scribed hv Crawfo~d.~ -

a C R A ~ R D , "The technique of research in education." The University of Southern California, Los Angeles. Calif., 1928, p. 29.

"In its bare essentials, it consists of providing a situa- tion where phenomena can be repeated and controlled, and then varying one element in the situation to see what variation in the results is thereby produced. 'This means the isolation of a single variable and the determination of its results when the other variables or elements in the situation are constant." I certainly did not refer to the specific technic which I used, al- though I do think that this particular technic of em- ploying the experimental method might well be studied more carefully by certain teachers. Again according to Crawforda the experimental method "is recognized as probably the most essential instrument available in the quest for truth." The experimental method is certainly well known to all scientists.

I shall now leave it to the discriminating reader who may have read my paper and the correspondence which it has evoked to judge for himself whether I have truly used the experimental method and whether other chemistry teachers should he encouraged to try to apply this general method to their own educational problems.

PAUL E. CLARK