Statistical Analysis of Data in
Earl C. Chapin and Richard F. Burns Western N e w England College Springfield, Massachusetts
the General Chemistry Laboratory
In a recent paper, Musulin' has described the use of statistical analysis of data in the first year chemistry course as a means of judging student performance and as a guide for graduate assistants. We believe that additional benefits can he achieved if the students themselves are allowed to carry out this analysis on the data obtained by the class. Many of t,he experiments used in the freshman lahoratory are oversimplified versions of procedures used in analytical or physical chemistry and do not have the precision that is generally attributed to them. There may be considerable scattering of t,he data wit,h the result that certain students become discouraged with the experiment and with themselves. They do not realize t,hat they are the victims of a normal error distribution. We have chosen to test this approach using four standard experiments; i.e., Dumas molecular weight, equivalent weight of a metal, equivalent weight of an acid, and molecular weight by freezing point depression. Unknowns were handed out randomly to the students in several laboratory sections in such a way that 8-10 students received t,he same unknown. Each studeut was asked to make two or three determinations, thus giving a set of data containing 16-30 results for each unknown. The results were then listed in the proper groups and this listing returned to the student. They were then asked to find the mean, the standard deviation, and the 99% confidence level from the data on their unknown. Student reference for these calculations was Youden's "Experimentation and Mea~urement.~ At a follow-up session, the identity of each unknown was announced, a distribution curve or a histogram was made from a t least one set of data, and sources of error, precision and accuracy were discussed. A summary of some typical student data for the Dumas molecular 'MUBULIN, B., J. CHEM.EDUC.,41, 556 (1964). 2 Y o u ~ W. ~ ~ J., , "Experimentation and Measurement," National Science Teachers Association, Washington 6, D.C., 1962.
weight and the equivalent eight of an acid is shown in the table. The Dumas experiment was carried out early in the first semester according to the description given in Sienko and Plane, "Experimental Chemi~try."~ The student's lack of skill a t this time plus the inherent inaccuracies in the procedure lead to a high standard deviation for t,his experiment. The experiment on the equivalent weight of an acid was run later in the course using conventional analytical t,echniques. As a result, the precision obtained in this experiment was much better than that obtaiued on the Dumas. The range of values reported for both of these ewperiments was greater than anticipated. Prior t,o the experiment, the student was told that he should report all of his results unless he had made an obvious error in any of his runs. Undoubtedly, some of these decisions were made wisely and some were not. I t is interesting to note that none of the values actually report,ed could he discarded on the basis of the Q test described by Dean and Dixou.'l We would not expect this to be the case for larger samples of data. Several benefits have result,ed from this early use of statistics. I t encourages the student to do more careful laboratory work, and also adds a n element of interest not normally associated with freshman laboratory. There is a growing awareness on the part of the student that values reported in texts, handbooks, and other references are also subject to a certain probable error and the importance of significant figures is emphasized. Perhaps the most important result is t,he student's evaluation of himself. This approach gives t,he student a sense of reliance on his ability to get results that far transcends that normally achieved in freshman laboratory. The freshman student has begun to develop habits of thought and action t,hat should be of great benefit to him in his more advanced course. 3 SIENKO, M. J., AND PLANE,R. A,, "Experimental Chemistry," McGctw-Hill Book Company, New York, 1958, p. 79. 4 DEAN,R. B.,AND DIXON, W. J., Anal. Chem., 23, 636 (19.51).
Statistical Analysis of Student Data Compound
Theoretical value*
Number of determinations
Mean
Standard deviation
99% Confidence levelb
Range
9.78 7.46 4.71
&5.85 &4.05 12.82
36.7 :%.4 14.0
&0.85 +2.18 *1.97
7.4 13.2 13.0
Dumas Experiment Acetone Cyclohexane Chloroform
58.1 84.2 119.4
22 26 22
Succinir Acid Adipic Acid Salicylic Acid
59.0 73.1 138.1
21 21 24
54.2 80.9 116.5
Equivalent Weight Experiment 59.2 73.3 137.3
1.41 3.57 3.46
Molecular weight in the Dumas experiment and equivalent weight in the equivalent weight experiment. 'Using Stndent's 1.
564 / Journal o f Chemical Education
