ANALYTICAL CHEMISTRY
638 report as a 95% confidence interval, 40.14 * 0.072. If we calculate a confidence interval using the tables of ,f and the calculated value of s n e find t = 2.6 at the 95% level and ts-\/6 = 0.078. K e would report 40.14 * 0.078, a result substantially the same as t h a t obtained from the range of this particular sample. If the etandard deviation of a given population is known or ;issumetl from previous data, \+e can use the normal curve to calculate the confidence limits. This situation may arise when a given analysis has been used for fifty or so sets of analyses of m i i l a r samples. T h e standard deviation of the population may be estimated by averaging the variance, 5 2 , of the sets of observations or from K , times the average range of the sets of observawhere f is computed from a tions. T h e interval f * 1.96s/& new set of m observations, can be expected to include the population average 95% of the time.
If we had decided to reject a n cstrcnicb Ion. value if Q is as large or larger than would occur 90% of the time in sets of observations from a normal population, we would noiv reject t'he observation 40.02. I n ot,her words, a deviation this great or greater would occur by chance only 10% of the time a t one or the other end of a set of observations from a normally distributed population. By rejecting the firPt, value we increase the median from 40.17 t o 40.18 and thr, ave.l.:tgc' from 40.14 to 40.17 (see Figure 2). The standard deviation, 8 , falls from 0.067 t o 0.030 (it might be greater than 0.030 if we have erred in rejecting the value 40.02) and sra falls from 0.072 t o 0.034. The 95% confidence interval correspoiiding to the t test ir now 40.17 * 0.038 and from the median and range is 40.1s =t0.040, a reduction of about one half in the length of the interval. (Thv 95% is only approximate, as we have performrd a n intrrnwtiintt. $t;rtistical test.)
EXTRANEOUS VALUES
LlTERATURE CITED
Simplified statistics have been presented, which enable one to obtain estimates of a central value and to set confidence limits on the result. Let us consider the problem of ext,raneous values. T h e use of the median eliminates a large part of the effect of extraneous values on the estimatr of the central value, hut the range obviously gives unnecessary weight to a n estraneous value in a n est,imate of the dispewion. On the other hand, we may wish to eliminate extraneous valurs which fail to pass a screening test.
(1) Am. Sor. Test,ine: Mateikils, "Yianurtl on Pi,esentation of Data," 1945. (2) Dixon, \V..J.. A / I I I-1fritii. . ,Stat., 21, -188 (1950). (3) I b i d . , in press (4) Dixon. IT. .J.. ant1 llasjey, F. ,J., "Iutroduction to Statistical .halysis," 1). 2 % S , Xew York, McGraw-Hill Book T o . . 1951. (5) Ibid., p. 239. (6) Ihid.. p. 242. (7) Ibid.. p. 319. (8) Fisher. H . .I..:ind l a t e s , Frank, "Statistical Tables for Biological, dgricultural, and Medical Research," Edinburgh, Olivei and Boyd. 1943. (9) Grant, E. L.. "Statistical Quality Coiitrol," p. 538, S e w Tork. hIcGi,aw-Hili Book Co., 1946. (10) Kendall. M. G., ".Idvanced Theory of Statistics," T'ol. 11, p. 6, London, C'harles Griffin & Co., 1946. ndell, E. B., "Textbook of Quantitative p. " 0 , New York, hlacmillan C o . . 1948. (12) Lord, E.. Biomttri'kri, 34, 11 (1947). (13) Ihitl., 37, 64 (1950). (14) hleri,ingtoii, l l a x i n e , I M . , 32, 300 (1942). (15) Pearson, E . P..I!,Ld., 37, 88 (1950). (16) Pierce, IT. C.. and Haenisch, E. L., "Quantitative dnalyais," p. 48, Sew Tork, *JohnITiley & Sons, 1948. (17) Tippett, L. H. C., Biomctdxz, 17, 364 (1925). (18) Youden, K., iinpuhlished data.
One very simple test, the Q test, is as follows: Calculate the distance of a doubtful observation from its nearest neighbor, then divide this distance by the range. The ratio is Q \There
Q
= (.r?- . r i ) / i 0
01'
Q
= (.r,z
-
~ n - i ) / ~
If Q exceeds the tabulated values, t,he questionable observao ( 2 , 3 ,7 ) . I n the example tion may be rejected with O O ~ confidence cited 40.02 is the questionable value and
Q
=
(40.12 - 40.02)/(40.20 - 40.02)
0.56
This just equals the tabulated value. of 0.56 for 90% confidence, so n-e may wish to rrject the, value.
RECEIVEDM a y 27, 1950. Presented before the Division of Analytical CHEMICAL SOCIETY. HousChemistry a t the 117th Meeting of the AMERICAS ton, Tex.
Determination of Intrinsic Low Stress Properties of Rubber Compounds USE OF INCLINED PLANE TESTER W. B. DUNLAP, JR., C. J. GLASER, JR., AND A. H. NELLEN Lee Rubber & Tire Corp., Conshohocken, Pa.
P
H I M C A L test methods for vulcanized natural and synthetic rubber compounds as comnionly employed today do not provide an accurate basiq tor evaluating service performance. especially in the case of tire compounds. Poor correlation between ordinary laboratory physical tests and observed performance in tire service on the road is the rule rather than the exception. Substantial improvement is needed in developing tests which are less subject to the human variable, tests in which the criteria examined are more in line with the actual service conditions, and tests which are mechanirally simple and easy to perform. One
significant advance has been made in this direction by the development of the Sational Bureau of Standards' comparatively new strain test ( 3 ) . This paper reports progress made by the Lee laboratories in developing one phase of an evaluation system which more accurately predicts compound performance than will the methods previously employed. As a starting point for this work, it was decided first to determine the important physical characteristics of a tire compound and, secondly, t o devise a new test or alter an existing test t o give the desired information. It is assumed that an accurate appraisal of the physical characteristics listed in Table I is required.
V O L U M E 2 3 , N O . 4, A P R I L 1 9 5 1
639
The test described in this paper was developed as part of a laboratory evaluation system designed to give better correlation between laboratory results and tire performance than is possible with conventional methods of testing. This test, which is made on an inclined plane tester under eonstant conditions of temperature and humidity, measures initial load and load on recovery accurately at low stress. It is rapid and reproducible. Autographic recording of data practical1)- eliminates the human variable.
HYSTERESIS LOOP
w:sr
r .
1 he hysteresis Ioq) t t x p t was oiie of tlie eiirliwt tests to be used f o i , nicwuring the 1iystc.resi.; chnr:ictc-ri~tiwot vulcanized rubber ($''I. I t is not g(~rier:illy coiisitlrwtl ( 1 i :in accurate indes of li!~stc~wi.iiloss.
Table I .
Phj-sical Characteristics of Tire Compounds Carcass State oi cure Llynamic energg- loas Dynaniic cord adhehion T ~ a r i n presistance I q i n g resistance
l.r?ad
State of cure Dynamic energy lor;. Hate oi wear Crack initiation a n d growth Static a n d dynamic ozone resistance Aging resistance Ikgree oi reinforrpinent ____.~~___
~
.
fIowever, the hystcswsis loop measured accurately at, low stress over a series of' cures docs provide a reinarkably accurate measure of rate and stat,(, of cure. Furthermore, relationship between initial load and load 0 1 1 recovery at low stress correlates esceptionally well with o1)served heat generation in actual tire service. .% 2-inch T-50 specimen is molded with a cross section of 0.1 X 0.1 inch in the testing area. T h e end tabs of the specinieii are 0.5 inch square and 0.1 inch thick. A series of samples is cured, for instance, for lo-, 20-, 40-, 60-, 80-, and 100 minutes at 280" F. The saniples are conditioned for i: minimum of 16 hours at 75' F. and 5iyorelative humidity and corictitions. Tests are rarried out on an IP-4 plarw constant, rate of load tester. T h e clamps used are T-50 type clamps set for :I 2-inch jaw opening. A 5-pound carriage is used for tread-type compounds and a 2-pound carriage for carcays and gum-t>ye compounds. T h e criteria observed are initial load, pounds per square inch a t 50% elongation (LI 50), loatl on recovery, p( ids per square inch a t 50% elongation (LR 501. and hysterc loss, L I 50 f L E 50 or I/R 50. Loop curvw are drawn automatically on a recorder chart. During the test,, one end of the p h i e is depressed by means of a screiv which travels a t the rate oi 22.8 inches per minute. The complete cycle for oiie tcast requires 41 second
