where to find z score and df in multiple comparison ?

Dear

I would like to get z value and degree of freedom in the multiple comparison.

For example,

[p,table,stats] = kruskalwallis(data,groups);

Then, I used multicompare function.

[c,m,h,nms] = multcompare(stats,'alpha',.05,'ctype','dunn-sidak');

1 2 107.358736884486 149.713883016209 192.069029147931 0

1 3 120.836759163490 153.690374387319 186.543989611148 0

2 3 -32.2920513577527 3.97649137111020 40.2450340999731 0.991192034848183

here is the result for c, and 6th column would be p value.

For each comparison, where to get z value?

(z value for 1-2 / 1-3 and 2-3)

I really appreciate it if someone could help.

Answer 1

[Scott MacKenzie]

The degrees of freedom is n -1, when n is the number of columns in the data set:

[p,table,stats] = kruskalwallis(data,groups);
df = size(data,1) - 1 ;

Above, it is calculated from the data. You can also use n from the stats structure:

df = stats.n - 1;

[Sang Hoon Kim]

Thanks for your comments~!

BTW, do you know how to get z value from each comparison pair?

For example, let's say I have 3 groups. (group1, group2 and group3).

[p,table,stats] = kruskalwallis(data,groups);

From here, I could get z value in total.

Then, I used multicompare function.

[c,m,h,nms] = multcompare(stats,'alpha',.05,'ctype','dunn-sidak');

I could get p value for each comparison (pair 1-2, pair 1-3, and pair 2-3).

In addtion to p value, I would like to get z value from each pairs.

Thanks for your help~!

[Scott MacKenzie]

What is z? In your question, you equate z to degrees of freedom.

[Sang Hoon Kim]

Sorry. There was confusion.

Z is not the degrees of freedom.

z score is standard score

'z = (x – μ(mean value)) / σ(standard deviaiton)'

[Scott MacKenzie]

My guess is that you should just calculate z from the original data:

meanData = mean(data); % one mean per column
sdDAta = std(data); % one SD per column
z = (data - meanData) ./ sdData; 

z and data are the same size. Each z-score is standardized according to the distribution of the data in that column.

If you want to lump all the data together, then...

meanData = mean(data(:)); % one mean for all the data
sdDAta = std(data(:)); % one SD for all the data
z = (data - meanData) ./ sdData;

[Sang Hoon Kim]

I was wondering if function itself provides z values.

Thanks for your comments~!

[Scott MacKenzie]

I'd say no. The Kruskal Wallis test is a non-parametric test: It downgrades the data to ranks. Any of the stats emerging from the kruskalwallis function have nothing to do with standardized z-scores. That's why I suggested calculating z from the original data.

[Sang Hoon Kim]

Yes. I just wanted to know if we could get z score from the MATLAB function. When I run the 'R' program, I could automatically get z score as well as p value. However, in MATLAB, it seems to calculate manually.

ex) from 'R' program, I could get output like this:

Kruskal-Wallis chi-squared = 131.7343, df = 2, p-value = 0

Comparison of x by g

(Šidák)

Col Mean-|

Row Mean | 1 2

---------+----------------------

2 | 8.440001

| 0.0000*

|

3 | 11.16992 0.261792

| 0.0000* 0.9912

List of pairwise comparisons: Z statistic (adjusted p-value)

---------------------------

1 - 2 : 8.440001 (0.0000)*

1 - 3 : 11.16992 (0.0000)*

2 - 3 : 0.261792 (0.9912)

This R function provides z score for each comparison. I wonder if I could do same thing from MATLAB.

I really appreciate your comments~!

[Scott MacKenzie]

Sorry, but I don't know about this. You might consider posting another question, specifically asking about standardized z-scores from a Kruskal Wallis test. If you do, don't mention degrees of freedom. :)

[Sang Hoon Kim]

Thanks~!