comparing shapes of distributions to determine appropriate alternate hypothesis for Kruskal Wallis

[MaryA_Marion]

I am using SAS Studio 3.8 Enterprise Edition

SAS release: 9.04.01M6P11072018
SAS platform: Linux LIN X64 3.10.0-1062.9.1.el7.x86_64
Site name: SAS ONDEMAND FOR ACADEMICS

This question has to do with determining the alternate hypothesis of a Kruskal Wallis test. I can't talk about medians if shapes of distributions are not the same. How do I determine that? 

I want to compare the medians of three brands of bulbs. Before doing so using a K_W test, I want to see whether the shapes of the distributions of the three brands are the same. I can do histogram plots or compare cdf plots (edf option in proc npar1way). Which would be better?  Which formal test should I use? Also in case of three groups p-value for KS test is not output. Do I treat SAS output as quantiles and go to hardcopy tables?  Thank you.

DATA bulbs
INPUT brand $ lifetime;
subject=_n_;
DATALINES;
A  73
A  64
A  67 
A  62
A  70
B  84
B  80
B  81 
B  77
C  82
C  79 
C  71
C  75
;

proc npar1way data=bulbs;
class brand;
var lifetime;
run; quit; title

[StatDave · Accepted solution]

The K-W test is a general test of location and is distribution free. So you can use it regardless of the distribution(s) in the data. However, if you particularly want to test for differences in distribution shape, you can use the empirical distribution function tests available with the EDF option. These are described in the NPAR1WAY documentation.