dtable and ranksum test

[LarsFolkestad]

Dear Listers

I havent work much with stat 18 yet, but have tried to make a dtable using median, and want to test between group differences using ranksum test.

dtable var1 var2 var3, continuous(var1 var2 var3, stat(p5 p50 p95)) by(group)

how do i include the ranksum test into that?

Thank you
Lars

[Jeff Pitblado (StataCorp)]

You will need to add option test in option by() and option
test(kwallis) within option continuous(). The
Kruskal-Wallis test is a multiple-sample generalization of the
two-sample (Wilcoxon / Mann-Whitney) rank-sum test.

Here is an example using the auto data.

sysuse auto

dtable mpg turn price, ///
    nformat(%9.1f p5 p50 p95) ///
    continuous(, stat(p5 p50 p95) test(kwallis)) ///
    by(foreign, test)

Here is the resulting output.

. sysuse auto
(1978 automobile data)

.
. dtable mpg turn price, ///
>         nformat(%9.1f p5 p50 p95) ///
>         continuous(, stat(p5 p50 p95) test(kwallis)) ///
>         by(foreign, test)
note: using test kwallis across levels of foreign for mpg, turn, and price.

------------------------------------------------------------------------------------------
                                                 Car origin
                         Domestic              Foreign                Total          Test
------------------------------------------------------------------------------------------
N                            52 (70.3%)            22 (29.7%)           74 (100.0%)
Mileage (mpg)            14.0 19.0 29.0        17.0 24.5 35.0        14.0 20.0 34.0  0.002
Turn circle (ft.)        34.0 42.0 48.0        33.0 36.0 38.0        33.0 40.0 46.0 <0.001
Price             3667.0 4782.5 13594.0 3798.0 5759.0 11995.0 3748.0 5006.5 13466.0  0.298
------------------------------------------------------------------------------------------

[Jack Lecester]

Hello everyone,
Thank you very much for this previous response, but I was wondering if it was possible in this similar case to use the Kruskal-Wallis test while taking into account ties. In the described case here, Stata does not take ties into account, and we end up with a p-value higher than the ranksum function, which, by default, considers ties.
Thanks in advance for the response.

[Leonardo Guizzetti]

Both the Kruksall-Wallis and Wicoxon-Mann-Whitney U-test allow for ties. How do you know ties are being excluded?

sysuse auto, clear

kwallis rep78, by(foreign)
di r(chi2_adj)
di chi2tail(r(df), r(chi2_adj))

ranksum rep78, by(foreign)
di (r(z))^2
di 2*(1 - normal(abs(r(z))))

Result, noting the square of a Z statistic is equivalent to a χ² statistic with 1 df; and the p-values are the same. There is perhaps an argument that the p-value display of -kwallis- is slightly misleading, but doesn't result in different conclusions.

. kwallis rep78, by(foreign)

Kruskal–Wallis equality-of-populations rank test

  +---------------------------+
  |  foreign | Obs | Rank sum |
  |----------+-----+----------|
  | Domestic |  48 |  1317.00 |
  |  Foreign |  21 |  1098.00 |
  +---------------------------+

  chi2(1) = 22.410
     Prob = 0.0001

  chi2(1) with ties = 25.050
               Prob = 0.0001

. di r(chi2_adj)
25.049655

. di chi2tail(r(df), r(chi2_adj))
5.587e-07

.
. ranksum rep78, by(foreign)

Two-sample Wilcoxon rank-sum (Mann–Whitney) test

     foreign |      Obs    Rank sum    Expected
-------------+---------------------------------
    Domestic |       48        1317        1680
     Foreign |       21        1098         735
-------------+---------------------------------
    Combined |       69        2415        2415

Unadjusted variance     5880.00
Adjustment for ties     -619.69
                     ----------
Adjusted variance       5260.31

H0: rep78(foreign==Domestic) = rep78(foreign==Foreign)
         z = -5.005
Prob > |z| = 0.0000
Exact prob = 0.0000

. di (r(z))^2
25.049655

. di 2*(1 - normal(abs(r(z))))
5.587e-07

[Jack Lecester]

I was referring to the "kwallis" option in the "dtable" function, which does not account for adjustments for ties.

sysuse auto

dtable headroom, ///
    continuous(, stat(p5 p50 p95) test(kwallis)) ///
    by(foreign, test)
    
ranksum headroom, by (foreign)
kwallis headroom, by (foreign)

. dtable headroom, ///
>     continuous(, stat(p5 p50 p95) test(kwallis)) ///
>     by(foreign, test)
note: using test kwallis across levels of foreign for headroom.

--------------------------------------------------------------------------
                                        Car origin                        
                    Domestic          Foreign            Total        Test
--------------------------------------------------------------------------
N                     52 (70.3%)        22 (29.7%)       74 (100.0%)      
Headroom (in.) 1.500 3.500 4.500 2.000 2.500 3.500 1.500 3.000 4.500 0.012
--------------------------------------------------------------------------



. ranksum headroom, by (foreign)

Two-sample Wilcoxon rank-sum (Mann–Whitney) test

     foreign |      Obs    Rank sum    Expected
-------------+---------------------------------
    Domestic |       52      2162.5        1950
     Foreign |       22       612.5         825
-------------+---------------------------------
    Combined |       74        2775        2775

Unadjusted variance     7150.00
Adjustment for ties     -204.15
                     ----------
Adjusted variance       6945.85

H0: headroom(foreign==Domestic) = headroom(foreign==Foreign)
         z =  2.550
Prob > |z| = 0.0108
Exact prob = 0.0102

. kwallis headroom, by (foreign)

Kruskal–Wallis equality-of-populations rank test

  +---------------------------+
  |  foreign | Obs | Rank sum |
  |----------+-----+----------|
  | Domestic |  52 |  2162.50 |
  |  Foreign |  22 |   612.50 |
  +---------------------------+

  chi2(1) =  6.316
     Prob = 0.0120

  chi2(1) with ties =  6.501
               Prob = 0.0108

Sorry, I may have explained it incorrectly.

[Jeff Pitblado (StataCorp)]

Currently dtable computes the p-value using the r(chi2)
result after kwallis. In a future update we hope to add support
for using r(chi2_adj) instead.

In the mean time, you can override the kwallis test result with
your own p-value provided you tag it properly. Here is an example using
the auto data example. Note that I change the numeric format so we can
see 4 decimal places in the reported p-value.

sysuse auto

dtable headroom, ///
    continuous(, stat(p5 p50 p95) test(kwallis)) ///
    nformat(%9.4f _dtable_test) ///
    by(foreign, test)

* perform/collect alternate test -- will need to be done for each
* continuous variable
kwallis headroom, by(foreign)
collect get kwallis_ties=(chi2tail(r(df),r(chi2_adj))), ///
    tags(foreign[_dtable_test] var[headroom])

* remove kwallis_ties from autolevels
collect query autolevels result
collect style autolevels result _dtable_stats _dtable_test, clear

* redefine composite using custom test result
collect query composite _dtable_test
collect composite define _dtable_test = kwallis_ties, trim replace

* replay table with changes
collect layout

Here is the resulting table.

---------------------------------------------------------------------------
                                        Car origin
                    Domestic          Foreign            Total        Test
---------------------------------------------------------------------------
N                     52 (70.3%)        22 (29.7%)       74 (100.0%)
Headroom (in.) 1.500 3.500 4.500 2.000 2.500 3.500 1.500 3.000 4.500 0.0108
---------------------------------------------------------------------------

I recognize this kind of modification can be intimidating, given the
need to loop over the continuous variables and for changes to an undocumented
composite result, so I wrote a program that will perform the mod
provided you give it the by() variable.

program dtable_mod_kwallis_ties
    version 18
    syntax [varlist(numeric default=none)] , by(varname)

    if `:length local varlist' == 0 {
        * find all the continuous variables in the -var- dimension
        quietly collect levelsof var
        local varlist `"`s(levels)'"'
        unab alist : *
        local varlist : list varlist & alist
    }

    foreach var of local varlist {
        * perform kwallis, account for ties in p-value
        quietly kwallis `var', by(`by')
        collect get ///
            kwallis_ties=(chi2tail(r(df),r(chi2_adj))), ///
            tags(`by'[_dtable_test] var[`var'])
    }
    * remove new result kwallis_ties from it's autolevels
    quietly collect query autolevels result
    local levels = s(levels)
    local levels : subinstr local levels "kwallis_ties" ""
    collect style autolevels result `levels', clear

    * replace -kwallis- with -kwallis_ties- in _dtable_test
    quietly collect query composite _dtable_test
    local elements = s(elements)
    local elements : subinstr local ///
        elements "kwallis" "kwallis_ties", word
    collect composite define _dtable_test = `elements', trim replace

    * replay table
    collect preview
end

Using this program the above example shortens to:

. sysuse auto
(1978 automobile data)

.
. dtable headroom, ///
>         continuous(, stat(p5 p50 p95) test(kwallis)) ///
>         nformat(%9.4f _dtable_test) ///
>         by(foreign, test)
note: using test kwallis across levels of foreign for headroom.

---------------------------------------------------------------------------
                                        Car origin
                    Domestic          Foreign            Total        Test
---------------------------------------------------------------------------
N                     52 (70.3%)        22 (29.7%)       74 (100.0%)
Headroom (in.) 1.500 3.500 4.500 2.000 2.500 3.500 1.500 3.000 4.500 0.0120
---------------------------------------------------------------------------

.
. dtable_mod_kwallis_ties, by(for)

---------------------------------------------------------------------------
                                        Car origin
                    Domestic          Foreign            Total        Test
---------------------------------------------------------------------------
N                     52 (70.3%)        22 (29.7%)       74 (100.0%)
Headroom (in.) 1.500 3.500 4.500 2.000 2.500 3.500 1.500 3.000 4.500 0.0108
---------------------------------------------------------------------------

[Jack Lecester]

Thank you very much Jef for your explanations and for the program.
It works perfectly

[Jack Lecester]

Sorry Jeff for bothering you again, but I don't understand why, when modifying the presentation by putting N under the variable name in your code, it removes the new p-value.

sysuse auto

dtable headroom, ///
    continuous(, stat(p5 p50 p95) test(kwallis)) ///
    sample(, place(seplabels)) ///
    nformat(%9.4f _dtable_test) ///
    by(foreign, test)

* perform/collect alternate test -- will need to be done for each
* continuous variable
kwallis headroom, by(foreign)
collect get kwallis_ties=(chi2tail(r(df),r(chi2_adj))), ///
    tags(foreign[_dtable_test] var[headroom])

* remove kwallis_ties from autolevels
collect query autolevels result
collect style autolevels result _dtable_stats _dtable_test, clear

* redefine composite using custom test result
collect query composite _dtable_test
collect composite define _dtable_test = kwallis_ties, trim replace

* replay table with changes
collect layout

                    
            Car origin                   
        Domestic    Foreign        Total      
        52 (70.3%)    22 (29.7%)    74    (100.0%)   
                    
Headroom    (in.)    1.500 3.500 4.500    2.000 2.500 3.500    1.500    3.000 4.500

Thanks in advance for the response.

[Jeff Pitblado (StataCorp)]

When you put the sample statistics in the column header with option place(seplabels), dtable adds dimension _dtable_sample_dim to the column specification. This dimension contains the sample statistics in the labels for its values. You need to add _dtable_sample_dim[_hide] to option tags() when you collect the value[s] for result kwallis_ties.

In the following modified example, look for EDIT in blue.

sysuse auto

dtable headroom, ///
    continuous(, stat(p5 p50 p95) test(kwallis)) ///
    sample(, place(seplabels)) ///
    nformat(%9.4f _dtable_test) ///
    by(foreign, test)

* perform/collect alternate test -- will need to be done for each
* continuous variable
kwallis headroom, by(foreign)
collect get kwallis_ties=(chi2tail(r(df),r(chi2_adj))), ///
    tags(foreign[_dtable_test] var[headroom] _dtable_sample_dim[_hide]) // <-- EDIT

* remove kwallis_ties from autolevels
collect query autolevels result
collect style autolevels result _dtable_stats _dtable_test, clear

* redefine composite using custom test result
collect query composite _dtable_test
collect composite define _dtable_test = kwallis_ties, trim replace

* replay table with changes
collect layout

Here is the resulting table.

---------------------------------------------------------------------------
                                        Car origin                         
                    Domestic          Foreign            Total        Test 
                   52 (70.3%)        22 (29.7%)       74 (100.0%)          
---------------------------------------------------------------------------
Headroom (in.) 1.500 3.500 4.500 2.000 2.500 3.500 1.500 3.000 4.500 0.0108
---------------------------------------------------------------------------

[Jack Lecester]

ok
Thank you for the explanations.

[Jeff Pitblado (StataCorp)]

FYI, continuous test kwallis_ties is now available in dtable -- it is part of today's update (14feb2024) to Stata 18.

3. dtable with option continuous(, test(ctest)) now supports continuous test (ctest)
kwallis_ties for reporting the p-value of the Kruskal-Wallis rank test adjusted
for ties.