In short, go for the Tukey HSD.

The detailed answer is that the Tukey HSD is a proper "post hoc" test whereas the Bonferroni test is for planned comparisons. The Bonferroni test also tends to be overly conservative, which reduces its statistical power.

That said, it is important to verify that your data meets critical assumptions to use the Tukey HSD. Each of the groups you're comparing should have approximately equal variance. You can verify equal variance using something like Levene's Test or the Brown-Forsyth test, which are available in most statistical software packages. If neither of these is available, then Hartley's Test might be used.

Should your data *not* have equal variance, then there are other post-hoc tests that might be used. The Games-Howell test is one good choice.

I hope this helps!

In short, go for the Tukey HSD.

The detailed answer is that the Tukey HSD is a proper "post hoc" test whereas the Bonferroni test is for planned comparisons. The Bonferroni test also tends to be overly conservative, which reduces its statistical power.

That said, it is important to verify that your data meets critical assumptions to use the Tukey HSD. Each of the groups you're comparing should have approximately equal variance. You can verify equal variance using something like Levene's Test or the Brown-Forsyth test, which are available in most statistical software packages. If neither of these is available, then Hartley's Test might be used.

Should your data *not* have equal variance, then there are other post-hoc tests that might be used. The Games-Howell test is one good choice.

I hope this helps!

Thanks Jay,

yes, i have checked the Tukey's assumption and my data is according to it.

Thanks for your valuable answer.