How to calculate effect size for Kruskal-Wallis test?

[Faruque Sunny]

Dear all, I am struggling to estimate the effect size for the Kruskal-Wallis test in Stata. I will be grateful if anyone guides me through the procedures. Thank you very much.

[Carlo Lazzaro]

Faruque:
-kwaliis- gives back chi2 and p-value.
To investigate the effect size, you should better switch to -qreg-:

. use https://www.stata-press.com/data/r16/census
(1980 Census data by state)

. qreg medage i.region
Iteration  1:  WLS sum of weighted deviations =  24.856174

Iteration  1: sum of abs. weighted deviations =  24.899998
Iteration  2: sum of abs. weighted deviations =  24.599998
Iteration  3: sum of abs. weighted deviations =  24.499998

. qreg medage i.region
Iteration  1:  WLS sum of weighted deviations =  24.856174

Iteration  1: sum of abs. weighted deviations =  24.899998
Iteration  2: sum of abs. weighted deviations =  24.599998
Iteration  3: sum of abs. weighted deviations =  24.499998

Median regression                                   Number of obs =         50
  Raw sum of deviations     29.9 (about 29.700001)
  Min sum of deviations     24.5                    Pseudo R2     =     0.1806

------------------------------------------------------------------------------
      medage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      region |
    N Cntrl  |       -2.4   .7724916    -3.11   0.003    -3.954945   -.8450546
      South  |  -2.199999    .729936    -3.01   0.004    -3.669284   -.7307139
       West  |  -3.199999   .7596516    -4.21   0.000    -4.729098     -1.6709
             |
       _cons |       31.8   .5839488    54.46   0.000     30.62457    32.97543
------------------------------------------------------------------------------

.

[Nick Cox]

I'd say Kruskal-Wallis was nearer ordinal regression in spirit than quantile regression. What information does it use? The ranks! Mind you, it seems to me that most uses I see of Kruskal-Wallis and similar tests are unduly pessimistic and arise out of a flawed logic still to be found in texts and courses "My data are not normally distributed so I should use non-parametric tests". That is what some of my non-statistician teachers seemed to think in the early 1970s and they were out of touch with best practice even at the time.

[Faruque Sunny]

Dear Carlo, thank you very much for your kind response and I really appreciate your help in resolving the problem. Thanks a lot again.

[Bruce Weaver]

In 2019, someone posted to ResearchGate asking what effect size measure to use in conjunction with the Kruskal-Wallis test. See Savatore Mangiafico's reply posted on 22-Jan-2019. It does not have Stata-specific advice, but may still be helpful to you.

• https://www.researchgate.net/post/Do...al-Wallis_test

[Faruque Sunny]

Thank you nick and bruce for your suggestions.

[Faruque Sunny]

Dear Carlo, to interpret the effect size we have to report the coefficient value, right?

[Carlo Lazzaro]

Faruque:
the best way (for me, at least) to investigate (and self-learning) what you're after is to invoke -predict- after -qreg-, recalculate the fitted values by hand and compare the results of your calculation with -predict-:

. use https://www.stata-press.com/data/r16/census
(1980 Census data by state)

. qreg medage i.region
Iteration  1:  WLS sum of weighted deviations =  24.856174

Iteration  1: sum of abs. weighted deviations =  24.899998
Iteration  2: sum of abs. weighted deviations =  24.599998
Iteration  3: sum of abs. weighted deviations =  24.499998

Median regression                                   Number of obs =         50
  Raw sum of deviations     29.9 (about 29.700001)
  Min sum of deviations     24.5                    Pseudo R2     =     0.1806

------------------------------------------------------------------------------
      medage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      region |
    N Cntrl  |       -2.4   .7724916    -3.11   0.003    -3.954945   -.8450546
      South  |  -2.199999    .729936    -3.01   0.004    -3.669284   -.7307139
       West  |  -3.199999   .7596516    -4.21   0.000    -4.729098     -1.6709
             |
       _cons |       31.8   .5839488    54.46   0.000     30.62457    32.97543
------------------------------------------------------------------------------

. predict fitted, xb

. list state region medage fitted in 1

     +------------------------------------+
     | state     region   medage   fitted |
     |------------------------------------|
  1. | Alabama   South     29.30     29.6 |
     +------------------------------------+

. di 31.8 -2.199999
29.600001

*the median age (medage) is lower (and statistically significantly so) in South vs. NE (the reference category) -region-*

. list state region medage fitted in 2

     +-----------------------------------+
     | state    region   medage   fitted |
     |-----------------------------------|
  2. | Alaska   West      26.10     28.6 |
     +-----------------------------------+

. di 31.8 -3.199999
28.600001

*the median age (medage) is lower (and statistically significantly so) in West vs. NE -region-*
. list state region medage fitted in 13

     +--------------------------------------+
     | state      region    medage   fitted |
     |--------------------------------------|
 13. | Illinois   N Cntrl    29.90     29.4 |
     +--------------------------------------+

. di 31.8 -2.4
29.4
*the median age (medage) is lower (and statistically significantly so) in N Cntrl vs. NE -region-*
.

[Faruque Sunny]

Dear Carlo, thank you very much for your guidance. Due to a lack of knowledge, I cannot understand how to perform the test and interpret the results. But I am eager to learn and due to people like you, nick and bruce – we can learn a lot. Thank you so much again.

[Carlo Lazzaro]

Faruque:
it's easier done than said.
It's just a matter of practising !