# How do I produce nonparametric Spearman partial correlations using SPSS?

It is possible to produce partial nonparametric correlations. The SPSS syntax below further illustrates this approach using Spearman correlations which are equivalent to Pearson correlations on a pair of variables which have been rank transformed. Note: Spearman's partial rank-order correlation and Kendall's partial tau-b) may also be computed using PROC CORR in SAS.

The below example assumes that we wish to obtain partial correlations between literacy (litdif) and nonliteracy (nonlitdi) scores adjusted for attention deficit disorder (adhd) and occurrence of dyspraxia (dyspraxi).

A Spearman correlation can be regarded as a Pearson correlation between two ranked variables (see for example Howell, 1997, p.289). It follows from this equivalence that the Spearman partial correlation is simply equal to the Pearson correlation between the residuals of the linear regression of the ranks of the two variables on the ranks of the partialled variables. Note, however, the sampling distribution of this partial tau-b is unknown; therefore, the probability values are not available.

The SPSS syntax below works in any version of SPSS on this SPSS data set giving a partial correlation for litdif and nonlitdiff adjusted for adhd.

define !psp (!pos !tokens(1) /!pos !tokens(1) /!pos !cmdend). NONPAR CORR /VARIABLES=!1 !2 !3 /PRINT=SPEARMAN TWOTAIL NOSIG /MISSING=PAIRWISE /matrix=out(*) . RECODE ROWTYPE_ ('RHO'='CORR'). EXE. PARTIAL CORR /VARIABLES= !1 !2 BY !3 /SIGNIFICANCE=TWOTAIL /FORMAT=MATRIX /MISSING=LISTWISE /MATRIX=IN(*). !ENDDEFINE. !psp litdif nonlitdiff adhd.

A Youtube video illustrating the above approach in SPSS is shown here. An introductory discussion of nonparametric partial correlations is given in Sprent(1998, Section 9.6), and it is more fully discussed in Kendall and Gibbons (1990, Chapter 8) and by Siegel and Castellan (1988, Section 9.5).

References

de Winter JCF, Gosling SD and Potter J (2016) Comparing the Pearson and Spearman correlation coefficients across distributions and sample sizes: a tutorial using simulations and empirical data. *Psychological Methods* **21(3)** 273-290. Shows Spearman less biased than the Pearson for distributions which are peaked and/or heavy-tailed (e.g. having outliers).

Howell DC (1997) Statistical methods for psychology. Fourth edition. Duxbury Press:Belmont,CA.

Sprent P (1998) Data driven statistical methods. Chapman and Hall:London.

Kendall MG and Gibbons JD (1990) Rank correlation methods. 5th Edition. Edward Arnold:London.

Reynolds HT (1974) Nonparametric partial correlation and causal analysis. *Sociological Methods and Research* **2(3)** 376-392.

Siegel S and Castellan NJ (1988) Nonparametric statistics for the behavioral sciences. 2nd Edition. McGraw-Hill:new York.