How to analyze rater's rank data and generate Kendall's coefficient of concordance?

[SAS-questioner]

Hi, I have a data like below:

person      i1 i2 i3 i4
    1       1  2  3  4
    2       3  2  4  1
    3       2  1  3  4
    4       4  1  2  3

Each person needs to rank the four things (i1, i2, i3, i4), for example, if the person thinks i4 is the best, then put 1 for i4; if the person thinks i3 is the second best, the put 2 for i3;  if the person think i1 is the third best, the put 3 for i1; if the person think i2 is the worst, then put 4 for i2. So the rank of four things (i1-i4) for this person is 3 4 2 1.

I want to compute Kendall's W for the data like this, do you know the code for SAS? I checked online, PROC FREQ and PROC CORR can be used, but the data seems different from mine. Does anyone know how to do it? Thank you!

[StatDave]

As always with questions of statistic availability, check the link to the list of Frequently Asked-for Statistics (FASTats) at the top of the Statistical Procedures Community page. You will find Kendall's coefficient of concordance there pointing to a macro that can be used to compute it.

[FreelanceReinh · Accepted solution]

Hi @SAS-questioner,

Here's the code you can use once you have compiled the %MAGREE macro recommended by StatDave:

data have;
input person i1 i2 i3 i4;
cards;
1 1 2 3 4
2 3 2 4 1
3 2 1 3 4
4 4 1 2 3
;

proc transpose data=have name=item out=want(rename=(col1=rank));
by person;
var i1-i4;
run;

%magree(data=want,
        items=item, raters=person, response=rank,
        stat=kendall, options=wcl)

Main part of the output:

Kendall's Coefficient of Concordance for ordinal response

Coefficient                                                    Lower         Upper
     of                 Num    Den              Standard    Confidence    Confidence
Concordance      F       DF     DF    Prob>F      Error        Limit         Limit

    0.3        1.286    2.5    7.5    0.3406     0.34233         0          0.97095

[Ksharp]

Check   @Rick_SAS   blogs:

On computing Kendall's tau statistic in SAS - The DO Loop

Weak or strong? How to interpret a Spearman or Kendall correlation - The DO Loop (sas.com)

data have;
input person i1 i2 i3 i4;
cards;
1 1 2 3 4
2 3 2 4 1
3 2 1 3 4
4 4 1 2 3
;

proc transpose data=have name=item out=temp(rename=(col1=rank));
by person;
var i1-i4;
run;
proc freq data=temp noprint;
table item*rank/out=want sparse;
run;




proc freq data=want;
   weight count;
   tables item*rank / measures CL norow nocol nopercent;
run;

[Ksharp]

As Freelance said, If you are looking for Kendall's W. Check %magree macro.