Kruskal Wallis test

[Maria Ribeiro]

Dear Statalist users,

I'm using Kruskal Wallis test as a non-parametric test for comparing three groups of analysis (P, A and B). My dependent variable is a measure of efficiency, with values that range from 0 to 1.
However I am not quite understanding the obtained output in what concerns the "rank sum" column, which is as follows.
Further, is it correct to say that the results indicate that there is a statistically significant difference among the three type of firms?

. kwallis theta if Y==2014, by(type)

Kruskal-Wallis equality-of-populations    rank test

+-------------------------+
type  Obs   Rank Sum
-------+-----+-----------
P     411  109374.50
A     223  111253.50
B     190  119272.00
+-------------------------+

chi-squared =   340.233 with 2 d.f.
probability =     0.0001

chi-squared with ties =   340.234 with    2 d.f.
probability =     0.0001

Thanks,
Maria

[Nick Cox]

That's significant. To get a better idea of how Kruskal-Wallis sees your data, calculate the ranks and plot their distributions, e.g. with -dotplot- or -stripplot- (SSC).

[Maria Ribeiro]

I'm not quite sure if the following codes are what you meant, and the correct way to understand the relationship!?

egen rank_theta=rank( -theta ), by(Y) track

The obtained graphs are as follows by using stripplot:

stripplot rank_theta if Y==2014, by(type) xlabel(, format(%9.2f))

or dotplot:

dotplot rank_theta , over(type) center median bar

Thanks,
Maria

[Marcos Almeida]

Hello Maria,

Your output, as Nick remarked, presents statistical significance. In short, there is "some sort of difference" between groups. If the groups have a simillar pattern of distribution of the dependent variable, I gather we can underline there is a difference related to the median. Otherwise, the difference is fundamentally related to the sum of the ranks. To spot which group is different from the others, you may want to perform post hoc comparisons, taking into account the issue of familywise error.
Best,
Marcos

[Nick Cox]

Presumably you should apply the same condition to all graphs:

stripplot rank_theta if Y==2014, over(type) vertical box center cumul 

dotplot rank_theta if Y==2014, over(type) center median bar

[Maria Ribeiro]

I appreciate both insights.

Following Marcos' suggestion I runned Dunn's test after a Kruskal–Wallis test.

According to Nick's suggestion the previous code within -stripplot- gives a more clear picture of the outcomes.

[Siluleko Mkhize]

I am confused about the Kruskal-Wallis test. I have an ordinal outcome variable for food security which has three levels (food secure, At risk of hunger, food insecure). My independent variable is sex where male (1) and female (2). I have already found the prevalence of food security in the two different sexes. Now how do I compare the prevalence among males only and again compare the prevalence among females only? and is a Kruskal-Wallis appropriate in this case?
Here is the code and output:
kwallis Sex if AGE_VQ_P>=20 & Sex==1, by(Hunger_cat)

Kruskal-Wallis equality-of-populations rank test

+------------------------------------------------+
| Hunger_cat | Obs | Rank Sum |
|-----------------------+---------+--------------|
| Food secure | 1,840 | 3.61e+06 |
| At risk of hunger | 960 | 1.88e+06 |
| Experience hunger | 1,119 | 2.19e+06 |
+------------------------------------------------+

chi-squared = -0.000 with 2 d.f.
probability = 1.0000

chi-squared with ties = . with 2 d.f.
probability = 0.0001

[Nick Cox]

If interested in #7 please follow thread at https://www.statalist.org/forums/for...ing-prevalence