The geology of the deposit was covered by him in an article entitled "An Unusual Fluorspar Deposit" pub- lished in the Engineering and Mining Journal, for September, 1928.

LENHER SCHWERIN VIcronv FLUORSPAR MINING COMPANY 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 com- ing 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 E UNIVERSITY LAFAYETTE. INDIANA

"THE EFFECT OF THE NATURE OF THE COURSE ON ACHIEVEMENT IN FIRST-YEAR COLLEGE CHEMISTRY"

To the Editor DEAR SIR:

Clark might be able to philosophize upon the so- called "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

describes. Of course, it is possible that the experi- menter may have made many other computations with- out 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 ap- parently 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 ob- tains 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 fre- quency distribution which might,be more similar to the normal curve. Equations for computing correlation are not designed for rectilinear distributions and there- fore the data are less meaningful than might be sup- posed.

(3) However, after finding this correlation of 0.88, Clark sets up a regression (for this elementary group) and gives i t as

X I = 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 be- tween the predicted and the earned values." All Clark seems to have proved by this useless manipula- tion 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," C-, "The effect of the nature of the course on achieve- clark then predicted the end-test for the ment in first-year college chemistry," J. C m . EDUC., 16,510-11

(Nov.. 1939). students in the advanced group. The real meaning of

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).