Are you asking how the Bonferroni method works or if there are other approaches to correct for multiple testing?

Bonferroni would simply be alpha-level divided by the amoint of comparisons, e.g. with an alpha of 0.05 and 12 comparisons, the corrected alpha value would be 0.05/12=0,00417.

There are other methods like Bonferroni-Holm or False Discovery Rate, which are not as conservative as Bonferroni.

Bonferroni controls the family-wise error-rate, this is the expected rate of "at least one false rejection among a family of k tests".

The probability of...

... a false rejection in a single test is alpha.

... not making a false rejection in a single test is 1-alpha.

... not making (even) a (single) false rejection in k (independent) tests is (1-alpha)^k.

Thus, the probability of...

... making at least one false rejection in k tests is 1 - (1-alpha)^k.

Bonferroni showed that 1 - (1-alpha*)^k < alpha when alpha* = alpha/k.

.

Example for alpha = 0.05 and k = 12: alpha* = 0.05/12 = 0.00417

   1-(1-0.00417)^12 =0.0489

so the expected family-wise error rate is close to the desired 0.05 if an individual null hypothesis from a family of 12 hypotheses is rejected only if p < 0.00417.

Alternatively, instead of dividing the alpha by k and the comparing it to p, one can likewise multiply the p-value by k and compare it to alpha.

http://en.wikipedia.org/wiki/Boole%27s_inequality#Bonferroni_inequalities

@ Jochen: multiplying p-value with k, isn't that what SPSS actually does?

@Rainer,

If "Bonferroni-corrected p-values" are presented it means that the raw p-values are simply multiplied with k. So if SPSS reports this (I don't have SPSS to look it up) then I am quite sure that this is correct, yes.