# Calculating Bonferroni correction

#### ctobola

##### New Member
I have a correlation matrix with an extremely large number of statistically significant correlations.

One of my advisers said I should apply the Bonferroni correction to address this issue. (I understand the limitations of Bonferroni.)

The question is this: In calculating the Bonferroni-adjusted significance level, do I count the A-A correlations, or just the A-B/C/D correlations?

For example, in a 4x4 matrix would I use .05/6 or .05/10 as a significance level?

Thanks!

#### SE_Lazic

##### New Member
Definitely 6. There this no point in reporting or discussing something correlated with itself.

A side issue is that many prefer to adjust the p-value instead of the alpha (significance) level. So instead of 0.05/6 = 0.0083 being your new cut off level, multiply each p-value by 6, and call significant any p-value still under 0.05.

A further side issue is that you might want to consider using Holm's method rather than Bonferroni's (http://en.wikipedia.org/wiki/Holm–Bonferroni_method).

#### ctobola

##### New Member
Thanks for the reply. Can you tell me a little more about your second point - multiplying the p value by 6? Is there an easy way to do that in SPSS?

Thanks!

-Cloy

#### SE_Lazic

##### New Member
One can either use a more stringent alpha level, or keep alpha=0.05 but make the p-values bigger...the effect is the same. I'm not sure how to do this in SPSS, but there might be an option to do some type of correction for multiple tests from a correlation matrix.

Here is an example using R. Suppose we have three p-values: 0.001, 0.01, 0.04. A Bonferroni adjusted alpha level would be 0.05/3 = 0.016777, and so the first two p-values would be considered significant, but the third one would not.

If we use the p.adjust function in R we get

Code:
p.adjust(c(0.001, 0.01, 0.04), method="bonferroni")
[1] 0.003 0.030 0.120
and so we would come to the same conclusion (first two p-values are significant (<0.05), but the third one not). The documentation for this function states "The adjustment methods include the Bonferroni correction (‘bonferroni’) in which the p-values are multiplied by the number of comparisons."

I hope this helps.

#### elmer

##### New Member
Definitely 6. There this no point in reporting or discussing something correlated with itself.

A side issue is that many prefer to adjust the p-value instead of the alpha (significance) level. So instead of 0.05/6 = 0.0083 being your new cut off level, multiply each p-value by 6, and call significant any p-value still under 0.05.

A further side issue is that you might want to consider using Holm's method rather than Bonferroni's (http://en.wikipedia.org/wiki/Holm–Bonferroni_method).
I am working on an article for publication and one of the reviewer's suggestion is to use Bonferroni correction for correlations. I also have a 4 x 4 correlation matrix so i would use .oo83 as cut off level. If I am asked to cite my reference for this method, what would I write. thanks...

#### hlsmith

##### Omega Contributor
There are plenty of resources that can be cited, but if you describe the method briefly in the methods section you should be fine, in that its application is fairly common.