Bonferroni adjustment in SPSS - what does it do? I'm probably being a bit simplistic here, but from what I understand the Bonferroni post hoc test is simply when we adjust the alpha to account for inflated error when several post hoc tests are conducted. You divide the alpha by number of tests. So what exactly does SPSS do when we click the button for Bonferroni? 
Shouldn't the dividing of alpha be done by us in interpreting the result, e.g. if we do 10 post hoc tests our alpha criterion should be .005 so if the p value is .012 then it is not significant, but SPSS hasn't done anything there, we have just changed our interpretation. So what exactly is it adjusting?
 A: SPSS multiplies the p-value of the least significant differences (LSD) by the number of tests, and produce a new p-value.
Here is an example using the Employee data.sav file:

There are three categories, totally 3 possible pair-wise comparisons. In LSD (no adjustment), the p-value is $.126$ for Clerical vs. Custodial. In Bonferroni, you can see that the p-value is now $.126 \times 3 = .378$. (It's .379 due to rounding). This means when checking the SPSS output, you can safely stick to the $p < 0.05$ criterion.
A: According to IBM, they compute the confidence intervals for the difference between two means $\bar{x}_{i}$ and $\bar{x}_{j}$ out of $k$ total levels to be compared with Bonferroni correction as:
$\bar{x}_{i}-\bar{x}_{j} \gt s_{pp} \sqrt{\frac{1}{2} \left( \frac{1}{n_i} + \frac{1}{n_j}\right)} \sqrt{2F_{1-\alpha^{\prime},1,n-1}}$
where the term $\alpha^{\prime}=\frac{2\alpha}{k \left( k-1 \right)}$ is the adjusted false positive rate based on $\alpha$ as an overall false positive rate, group sample sizes $n_i$ and $n_j$, and the square root of the mean square error $s_{pp}$. 
So basically solve for $\alpha$ and you get a new $p$ value. In the case of 4 groups with pairwise comparisons, the new $p$ values would be the unadjusted ones multiplied by $\frac{4\times3}{2}=6$
