A number of robust absolute deviation (AD) statistics have been developed recently. Two such correlation coefficients are developed and discussed, one for ranked data and another for interval level data. The standard error and range of the coefficients are given. The algebraic relationship between the coefficients and three widely used correlation coefficients is given.
Get full access to this article
View all access options for this article.
References
1.
AcockA. C.StavigG. R.Measures of sampling error applied to statistical inference. Perceptual and Motor Skills, 1976, 43, 691–694.
2.
ArmstrongR. D.FromeE. L.A comparison of two algorithms for absolute deviation curve fitting. Journal of the American Statistical Association, 1976, 71, 328–330.
3.
CorteseC. F.FalkR. F.CohenJ. K.Further considerations on the methodological analysis of segregation indices. American Sociological Review, 1976, 41, 630–637.
4.
DaviesG. R.First moment correlation. Journal of the American Statistical Association, 1930, 25, 413–427.
5.
DevlinS. J.GnanadesikanR.KettenringJ. R.Robust estimation and outlier detection with correlation coefficients. Biometrika, 1975, 62, 531–545.
6.
DiaconisP.GrahamR. L.Spearman's footrule as a measure of disarray. Journal of the Royal Statistical Society B, 1977, 39, 262–268.
7.
GibbsJ. P.PostonD. L.The division of labor: Conceptualization and related measures. Social Forces, 1975, 53, 468–476.
8.
HoggR. V.Adaptive robust procedures. Journal of the American Statistical Association, 1974, 69, 909–923.
9.
KendallM. G.Rank correlation methods. New York: Hafner, 1970.
10.
LordF. M.NovickM. R.Statistical theories of mental test scores. Reading, MA: Addison-Wesley, 1968.
11.
O'BrienR. M.Partial regression coefficients, a ‘recomparison’ of Kendall's tau and Pearson'sr. Pacific Sociological Review, 1978, 21, 501–505.
12.
PearsonK.Draper company research memoirs. Biometrika, 1907, 3, 160.
13.
SmithC. F.DaviesG. R.Calculus for business and other related fields. Dubuque, IA: Wm. C. Brown, 1956.
14.
SpearmanC.‘Footrule’ for measuring correlation. British Journal of Psychology, 1906, 2, 89–108.
15.
SpearmanC.Correlation calculated from faulty data. British Journal of Psychology, 1910, 3, 271–289.
16.
StavigG. R.Measuring the magnitude of agreement between paired values for a single case. Sociology and Social Research, 1980, 64, 379–388.
17.
StuartA.Spearman-like computation of Kendall'stau. British Journal of Mathematical and Statistical Psychology, 1977, 30, 104–112.
18.
Student.An experimental determination of the probable error of Dr. Spearman's correlation coefficients. Biometrika, 1920, 13, 263–282.
19.
UryH. K.KleineckeD. C.Tables of the distribution of Spearman's footrule. Applied Statistics, 1979, 28, 271–275.
