This chapter is concerned with measures of correlation for bivariate data. The usual multivariate measures of correlation and covariance for continuous random variables are produced by routine CORVC. For data grouped by some auxiliary variable, routine COVPL can be used to compute the pooled covariance matrix along with the means for each group. Partial correlations or covariances, given the correlation or covariance matrix computed from CORVC or COVPL, are computed by PCORR. Routine RBCOV computes robust estimates of the covariance matrix and mean vector. If data are grouped by some auxiliary variable, routine RBCOV can also be used to estimate the pooled covariance matrix and means for each group. The remaining routines are concerned with rank and/or discrete data. General references for these routines are Conover (1980) or Gibbons (1971).
CTRHO and TETCC produce measures of correlation for contingency tables. In CTRHO, the inverse normal scores obtained from the row and column marginal distributions are assumed known, and the correlation coefficient is estimated by assuming bivariate normality. In TETCC, a 2 × 2 table is produced from continuous input data using estimates for the sample medians. The correlation coefficient is estimated from the resulting 2 × 2 table.
If one of the variables is dichotomous while the second variable can be ranked, the routines BSPBS or BSCAT can be used. The difference between these routines is in whether the class values for the ranked variable are given by the user (BSPBS) or are estimated as inverse normal scores from the marginal cumulative distribution (BSCAT). Routine CNCRD computes Kendall’s coefficient of concordance, and routine KENDL computes Kendall’s rank correlation coefficient . Probabilities for are computed by routine KENDP.
Other Routines
Other IMSL routines compute measures of correlation or association and may be of interest. Routine CTTWO described in Chapter 5, “Categorical and Discrete Data Analysis,” computes measures of association for the 2 × 2 contingency table. Routine CTCHI in the same chapter computes measures of association for the general r×c contingency table. Routine CDIST in Chapter 11, “Cluster Analysis,” computes measures of similarity and dissimilarity, including the correlation coefficient. Measures of multivariate association or correlation are computed in Chapter 2, “Regression,” and in “Independence of Sets of Variables and Canonical Correlation Analysis.”
