Please consider the following dataset in SPSS:
v1 v2 weight 1 3 0,50 2 2 0,50 3 4 1,00 4 5 1,00 5 3 1,00 1 3 2,00 2 2 2,00 3 . 3,00 . 5 1,00 5 4 0,50
When I calculate correlations between v1 and v2 (pairwise missing deletion) with unweighted in SPSS, I get the following results:
Pearsons r: n=8; r=0.525
Kendalls tau: n=8, t=0,334
Suppose now, I'll apply case weights to the data, provided in the "weight" column. I now get the following results:
Pearsons r: n=8,5 (due to weighting); r=0.496
Kendalls tau: n=10 (weighted), t=0,274
My question/problem is that I don't understand why there are different weighted sample sizes for the two correlations. I understand SPSS weights as case weights, so for both correlations I was expecting a weighted sample size of 8,5, as it is indeed for Pearsons r.
Can anyone help me out here, why there is a different sample size for kendalls tau? If there is some scientific paper/website/whatsoever about that topic, I'm ready to read it on my own, but I didn't find anything useful on my own.
[Edit] Could it be that for Kendall's tau, SPSS is rounding the case weights to natural/whole numbers? In this case, we would indeed end up with n=10. But this then brings me to the question, why SPSS is doing so.
[Edit2] As suggested by Joel W., here's the SPSS syntax to reproduce what I'm doing.
Code for unweighted correlations:
CORRELATIONS /VARIABLES=v1 v2 /PRINT=TWOTAIL NOSIG /MISSING=PAIRWISE. NONPAR CORR /VARIABLES=v1 v2 /PRINT=KENDALL TWOTAIL NOSIG /MISSING=PAIRWISE.
Code for weighted correlations:
WEIGHT BY weight. CORRELATIONS /VARIABLES=v1 v2 /PRINT=TWOTAIL NOSIG /MISSING=PAIRWISE. NONPAR CORR /VARIABLES=v1 v2 /PRINT=KENDALL TWOTAIL NOSIG /MISSING=PAIRWISE.