Re: Bonferroni correction and number of comparisons

Posted by Bruce Weaver on Jan 19, 2011; 9:47pm
URL: http://spssx-discussion.165.s1.nabble.com/Bonferroni-correction-and-number-of-comparisons-tp3348337p3348646.html

Ryan, multiplying the observed (uncorrected) p-values by the number of contrasts can give you results that make no sense.  E.g., if the uncorrected p-value = .25 and the number of contrasts is 6, you'll get a corrected p-value = 1.5.  But p-values are conditional probabilities, and must fall within the range 0-1.  

Here's an example using oneway ANOVA.  Notice that the Bonferroni-corrected p-values (or Sig. values as SPSS labels them) are  not simply 3 x the uncorrected (LSD) p-values.

MATRIX DATA VARIABLES=Group ROWTYPE_ Score /FACTORS=Group.
BEGIN DATA
1 N 96
2 N 96
3 N 96
1 MEAN 22.98
2 MEAN 25.78
3 MEAN 26.56
1 STDDEV 8.79
2 STDDEV 9.08
3 STDDEV 8.50
END DATA.

ONEWAY Score BY group /
 matrix = in(*) /
 POSTHOC=LSD BONFERRONI ALPHA(0.05)
.

Jan, given that figuring out how to compute corrected p-values may be quite time-consuming, I would see if I could persuade the person who asked that the usual approach (i.e., comparing p to a corrected alpha level) is sufficient.  

HTH.

R B wrote

You asked about  applying a Bonferroni correction in post hoc tests-->
"Is the Bonferroni adjustment for 6 comparisons and the corrected
p-value (.05/6=.008333)"

Answer. No. You have presumably adjusted the alpha level, not the
p-values. Multiply the each p-value by the number of post hoc tests
performed (6 in the example you provided). Then compare the adjusted
p-values to the alpha level you set (e.g., .05).

Ryan

On Wed, Jan 19, 2011 at 1:56 PM, J McClure <[e-mail]> wrote:
> Hi,
> I am doing a post hoc analysis comparing column proportions and
> adjusting (Bonferroni) for multiple comparisons (CTables, test
> statistics option).
> I've been asked to provide the corrected p-value.
> I'd like to know if I am correct in reporting the corrected value as .008.
> The row variable has two levels (yes and no) and the column variable has
> 4 levels, so I am making 6 comparisons for 'no' and 6 for 'yes'.  n*(n-1)/2
> The output shows the comparison for the 'no'  and for the yes level of
> the row variable. Is the Bonferroni adjustment for 6 comparisons and the
> corrected p-value (.05/6=.008333)
> Also, I have 19 row variables for which I am running column proportion
> comparisons. I think that the comparisons for each of the 19 variables
> are considered independent from each other so no further adjustment is
> made by SPSS.  Is this the way reviewers look at the question?
> Thanks for any help,
> Jan
>
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