Interpreting Output KS test

[Laurens Helsen]

Dear all,

I am Laurens Helsen, currently writing a masterthesis on the topic of firm size distributions. I would like to check if a given variable (log(employment)) has a power law distribution (I am using the cumulative distribution as the theoretical one).
So the expression I am executing in stata is the following:

ksmirnov logempl42=thdist42
where logempl42 is the variable of which I would like to check the cdf and thdist is the theoretical CDF of that variable (that I am assuming)
this leads to the following output:

Now my question is: what is this output telling me? Since I am using a cumulative, should I look at the cumulative line and use that p-value as the p-value of the nullhypothesis or what are the other lines telling me?
I have been searching on this topic yet but didn't found a convenient explanation on the output.

Thank you in advance

Laurens Helsen

[Carlo Lazzaro]

Laurens:
I would just take a step aside, first.
Please, see the warnings about using this test in -ksmirnov- entry,Example 2, Stata .pdf manual.

[Laurens Helsen]

Dear mr Lazzaro

Thanks for your answer, I am aware of the problems of using the ksmirnov test.
I am actually using this test because another paper has been using it and I would like to use the same procedure.

kind regards
Laurens

[Carlo Lazzaro]

Laurens (Carlo is enough; mr Lazzaro is very polite, but makes me feel older than I'm).
due to the abovementioned warnings for small samples, like yours, I would consider the p-value from the cumulative line (P=0.729).
For a good explanation of the output from -ksmirnov- I would take a look at the Example 1 in the same entry (even though it refers to a two-sample test).

[Laurens Helsen]

Carlo,

Thank you very much for your answer!

kind regards
Laurens

[Isabel Marc]

Hi!

I have a similar question, but the previous answers have not helped me yet.
I want to test whether a discrete variable taking the values 1, 2, 3 or 4 follows a uniform distribution. But I don't know how to interpret the output. What are the three values of c_answer, cumulative, combined K-S? Which one should I use?

I've read the manual and understood the explanation for the two-sample test. However, the output for the one-sample test looks different.


So the expression I am executing in stata is the following:

ksmirnov c_answer = round(runiform(1,4))

This leads to the following output:


One-sample Kolmogorov-Smirnov test against theoretical distribution
round(runiform(1,4))

Smaller group D P-value
-----------------------------------
c_answer: -0.0600 0.698
Cumulative: -3.9600 0.000
Combined K-S: 3.9600 0.000

Thank you very much in advance for your help!