A STATISTICAL COMPARISON OF THE GRAVIMETRIC, MOHR, AND FAJANS METHODS FOR CHLORIDE' BART PARK Michigan College of Mining & Technology, Houghton R w o m s from about 450 beginning quautitative analysis students, who analyzed unknown chloride samples by the gravimetric, Mohr, and Fajans methods have been subjected t o statistical analysis. The results are summarized in Table 1. Deviations were measured, not from the student averages, but from the established values of the 25 different unknowns. The variance, S2,the estimate of the standard deviation, S, and the standard error of the estimate, T,, were tabulated for each of the three methods. Results by the gravimetric method tended to be low rather than high in the ratio TABLE 1 Deviations and Precision of Chloride Methods Deviation in 70Cl, plus or mintis
Graoimetric High
0.0~.10 0.114.20 0.214.30 0.31-0.40 0.41-0.50 0.51-0.60 O.614.70 0.714.80 0.814.90 0.91-1.00
77 45 25 7 8 4 5 2 1 3
.frepuenc?,
Low 92 70 44 25 20 6 9 3 4 3
-
-
177
276
Total Report,fi
Mohv jrepurncy
High 76 64 44 34 16 13 5 2 0 0 254
Low 58 48 25 23 23 8 6 2 6
1 200
Fajans jiequenc!, High Low
72 65 4i 27 13 15 :1 2 1 2 247
57 53 25 28 22 II (i $1 3 1
225
larger by the smaller and comparing the value obtained, F, with tabulated values which depend upon the number of measurements used in calculating each variance and the probability of occurrei~ce.~The results are summarized in Table 2. TABLE 2 Variance Ratios Method
SP Variance
( I ) Gravimetric (2) Mohr (31 Faians
0.0901 0.0968
Tables of F a t N = 450, which is close enough to t,he number of reports in Table 2, give F = 1.167 and 1.128 at the 95y0 and 90% levels. Since the value 1.074 is considerably less than 1.128, the conclusion is that the gravimet,ric and Mohr methods are eouallv " precise. The value 1.153 lies between 1.167 and 1.128. The conclusion is that there is a statistical difference at the 90% level but not a t the 95% level.
.
TABLE 3 Basis for Grading Chloride Unknowns Number Grade receiving
T h e variance
=
S'
=
dev.% N - k'
Ta
N Rmmls 453 461 477
%
receivino
%
deszred
z0 s
Deuiatia in % Cl, plus or mznus
S = -
dm
N is the number of reports
& the compub,tions. - -
of three to two. The other methods gave a few more high than low results. There is little difference between the methods from the standpoint of precision. However, the application of Fisher's F test for significance of differences between calculated variances leads to the conclusion that a differenceas large as that between the variances found by the gravimetric and Fajans methods should be expected only about 8% of the time if the methods were equally precise. Comparison of two variances is made by dividing the
' Presented before the Division of Chemical Educlttlon a t tht. 132nd Meeting of the Amerirsn Chemicnl Sorietv, N e ~ vYovk Citv, September, 1957.
-
1168 100.0 100 " Values of 5 / 8 are taken from areas of the Normal Curve, Tables for Statisticians, ARKINAND COLTON,"College Outline Series," Barnes & Noble, Inc., New York, 1950.
The tventy-five chloride samples ranged from a low of 47 to a high of 60%. A grading scheme, designed t o give the distribution in Table 3, column 6, has been worked out from the tabulated values of the areas under the normal curve and the value of 0.3 for the standard deviation. Column 3 of Table 3 lists the grade distribution obtained. Column 4 gives the grade distribution desired; these values were arbitrarily See BENNETT AND FRANKLIN, "Statisticd Analysis in Chemistry and Chemical Industry," John Wiley & Sons, Inc., New York, 1954, p. 192, for an explanation of the F test.
JOURNAL OF CHEMICAL EDUCATION
chosen. The values in the fifth column are the areas of the normal curve corresponding to one-half of the per cent desired taken cumulatively. The maximum values given in column 6 mere obtained by multiplying
VOLUME 35, NO. 10, OCTOBER, 1958
values in column 5 by the standard deviation S. A penalty of ten grade points was imposed for a report which deviated by more than 0.59%, and a new uunknown was issued.
