# Thread: Cramer's V effect size based on df

1. ## Cramer's V effect size based on df

I saw a presentation about chi-square testing and correlations. Specifically calculating effect size for Cramer's V results. The puzzling thing was the according to the degrees of freedom. Basically higher df produces smaller values for the effect size to be large or medium.

You can see what i mean in the presentation here:
http://www.slideshare.net/edithosb/chi-square-in-spss

Can anyone tell me why is that and how can i calculate what is the effect size(small,medium,high) for cramer's V when the df = 6?

2. ## Re: Cramer's V effect size based on df

The relationship between w and Cramers V is: w = V * SquareRoot(r-1)
where "r" is the smaller of the number of rows and number of columns
(mind that in this context "df" does not mean degrees of freedom of
the Chi square statistic). As you already know (from the presentation
with r=2), w=0.1 may be assumed as "small", 0.3 as "medium", 0.5 as
"large".

Reference:
Martin A Volker (2006): Reporting effect size estimates in school psychology research.
Psychology in the Schools, Vol. 43(6), 653-672.
http://www.ed.utah.edu/users/daniel....%282006%29.pdf

Regards

K.

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micdhack (10-12-2011)

4. ## Re: Cramer's V effect size based on df

Karabiner thank you very much for the detailed response. I have two more questions based on what you wrote.

Based on the above if i have a result such as V = 0.274, p = 0.007 with number of columns 3 and rows 4 then my r is going to be 3. Based on that my w will be 0.38 which translates into a medium effect size. Am i correct so far? Can i conclude that i have a correlation where one variable has a medium effect over an other variable?

A second thing that i would like to ask is that i tried to test the correlation with Spearman's rho(ρ). The result was ρ = 0.288 and p < 0.01. How do i know what is the effect size for this? 0.288 is closer to 0 than above 0.5 but does this mean that i have to conclude that there is assosiation between the two variables?

Regards,
m.

5. ## Re: Cramer's V effect size based on df

Mind that sample "effect sizes" are not effect sizes. Effect sizes refer to populations.
Measures such as V or rho (or d or whatever), if they are calculated from sample data,
are not real effect sizes, because they are composed of real effects and of chance variation.
That's why we perform statistical tests -- sample "effects" could
possibly be completely due to chance.

Regarding your first question, I guess your result corresponds to what is described
in the cited reference.

Regarding your second question, I am not sure what you mean to ask. Whether there
is an association between two variables is judged by the p-value, not by the size of
the sample statistic (here: rho).

Regards

K.

6. ## Re: Cramer's V effect size based on df

I thought that effect sizes could be applied to samples as well. Now i understand that this is not the case :S

About the rho that's what i thought too! The p value if it is significant it means that there is a significant correlation at hand. But then i see websites such as this one (http://www.wikihow.com/Calculate-Spe...on-Coefficient) which basically say that the p tells you the chances of something occurring by chance (significance) but how strong is the correlation should be determined by the rho.

And so in my example ρ = 0.288 and p < 0.01, the p tells me that i have a significant result but the rho is only 1/3 as strong as the ultimate correlation which would have been 1. Which poses the question, can i claim that i have a statistically significant correlation or not?

7. ## Re: Cramer's V effect size based on df

Hi,
you have to pay attention to what any statistic is actually saying, and to what the p value is saying as well.
They tell a different story.
To keep with the correlation example, r informs us about the strenght of the correlation between the two variables at hand. You can have no correlation, a moderate or a strong or a perfect one.
On the other hand, the p value is informing us about how likely is that the correlation you have found exists in the parent population. So, you can have a strong correlation BUT a non significant p value; or you can have a moderate or even weak correlation that turns up to be significant. This depends on the sample size: other things being equal, the bigger your sample, the more likely is that your correlation (even weak) truly exist in the population. If you have few data (i.e. smal sample) you simply do not have enough data to say if the correlation (even strong) truly exist in the population.

Hope this helps
Regards
Gm

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micdhack (10-14-2011)

9. ## Re: Cramer's V effect size based on df

And so in my example ρ = 0.288 and p < 0.01, the p tells me that i have a significant result but the rho is only 1/3 as strong as the ultimate correlation which would have been 1.
A correlation r=0,3 is not so bad. Medium size. In those research areas which deal with living, non-technical systems you rarely will
find correlations > 0.6 or so. Mind again, the size of rho in the population will be different (smaller or larger) from your sample rho.
The p-value at least tells you that you can assume that in the population rho is NOT = 0.000000.

Regards

K.

10. ## The Following User Says Thank You to Karabiner For This Useful Post:

micdhack (10-14-2011)

11. ## Re: Cramer's V effect size based on df

Supplementing Karabiner's reply,
I would add that, for both r or rho, it could be useful to provide the confidence interval, in order to get the idea of the variability of those statistics in the population.
I believe that any statpack should routinely provide confidence interval for r or rho.
A confidence interval could be "attached" with bootstrap procedures as well....But this is another story....

Regards,
Gm

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micdhack (10-14-2011)

13. ## Re: Cramer's V effect size based on df

Awesome! Thanks to both of you! Btw, is there any easy way to calculate confidence intervals? SPSS doesn't have this feature for spearman or pearson

14. ## Re: Cramer's V effect size based on df

I do not recall if JMP provides this (I guess it does).
You could try my Excel Template, where I implemented CI for Pearson'r. You find info in the "Other Software" section of this Forum.
If you want a free tool for stat, you could consider to use the PAST program.

If I recall in what program I saw CI for Spearman, I will let you know.

Regards,
Gm

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micdhack (10-15-2011)

16. ## Re: Cramer's V effect size based on df

I have to say that i tried SAS, SPSS, Deducer for R and none of these programs had post hoc analysis for tests such as Friedman. The program that you suggested, PAST, it has right out of the box post hoc analysis for tests such as Friedman. In addition i tried spearman tests and its really easy. Basically as program is really practical.

And btw it run on linux with wine.

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