Spearman's footrule measure of the relationship between two sets of ranks is shown to be a chance-corrected measure of agreement. The footrule is generalized to include tied ranks and a comparison with Spearman's rank-order correlation coefficient is provided. Procedures to determine the nonasymptotic probability of the footrule with tied ranks are presented.
Get full access to this article
View all access options for this article.
References
1.
BartkoJ. J. (1976) On various intraclass correlation reliability coefficients. Psychological Bulletin, 83, 762–765.
2.
BlandJ. M.AltmanD. G. (1986) Statistical methods for assessing agreement between two methods of clinical measurement. Lancet, 1(8476), 307–310.
3.
Burry-StockJ. A.ShawD. G.LaurieC.ChissomB. S. (1996) Rater agreement indexes for performance assessment. Educational and Psychological Measurement, 56, 251–262.
4.
CohenJ. (1960) A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20, 37–46.
5.
DiaconisP.GrahamR. L. (1977) Spearman's footrule as a measure of disarray, Journal of the Royal Statistical Society, Series B, 39, 262–268.
6.
DinneenL. C.BlakesleyB. C. (1982) Letter to the editors: definition of Spearman's footrule. Applied Statistics, 31, 66.
7.
FranklinL. A. (1988) Exact tables of Spearman's footrule for N=11(1)18 with estimate of convergence and errors for the normal approximation. Statistics & Probability Letters, 6, 399–406.
8.
HarterH. L. (1969) A new table of percentage points of the Pearson type III distribution. Technometrics, 11, 177–187.
9.
KendallM. G. (1962) Rank correlation methods. (3rd ed.) London: Griffin.
10.
KrippendorffK. (1970) Bivariate agreement coefficients for reliability of data. In BorgattaE. G. (Ed.), Sociological methodology. San Francisco, CA: Jossey-Bass. Pp. 139–150.
11.
LinnR. L.BakerE. L.DunbarS. B. (1991) Complex, performance-based assessment: expectations and validation criterion. Educational Researcher, 20, 15–21.
12.
LovieA. D. (1995) Who discovered Spearman's rank correlation?British Journal of Mathematical and Statistical Psychology, 48, 255–269.
13.
MielkeP. W. (1984) Meteorological applications of permutation techniques based on distance functions. In KrishnaiahP. R.SenP. K. (Eds.), Handbook of statistics. Vol. 4. Amsterdam: North-Holland. Pp. 813–830.
14.
MielkeP. W. (1991) The application of multivariate permutation methods based on distance functions in the earth sciences. Earth-Science Reviews, 31, 55–71.
15.
PearsonK. (1907) Mathematical contributions to the theory of evolution: XVI. On further methods of determining correlation. (Drapers' Company Research Memoirs Biometric Series IV). London: Dulau.
16.
SalamaI. A.QuadeD. (1990) A note on Spearman's footrule. Communications in Statistics—Simulation and Computation, 19, 591–601.
17.
ScottW. A. (1955) Reliability of content analysis: the case of nominal scale coding. Public Opinion Quarterly, 19, 321–325.
18.
SpearmanC. (1904) The proof and measurement of association between two things. American Journal of Psychology, 15, 72–101.
19.
SpearmanC. (1906) ‘Footrule’ for measuring correlation. British Journal of Psychology, 2, 89–108
20.
StuartA. (1977) Spearman-like computation of Kendall's tau. British Journal of Mathematical and Statistical Psychology, 30, 104–112.
21.
UryH. K.KleineckeD. C. (1979) Tables of the distribution of Spearman's footrule. Applied Statistics, 28, 271–275.
22.
WhitehurstG. J. (1984) Interrater agreement for journal manuscript reviews. American Psychologist, 39, 22–28.