# post hoc test for 3 way anova

I am doing ANOVA using three fixed independent factors of which one is sex (two levels 'male' and 'female'), temperature (three levels: 1,2,3) and quality (two levels: good and bad) and I want to see the effect of these factors on dependent variable factors like life-span, weight and development. Now alongwith significant main effects I have significant interactions too. For eg. for weight I have significant three-way interaction of the above factors, and for development I have significant two way interaction of quality and temperature. the groups have unequal sample sizes. So what post-hoc tests can I use keeping in mind the unequal sample size and the three way interaction? I am interested in comparing between the good and bad quality effects for the three way interaction (as shown in the image below) Could anyone please guide me ? thanks .

Easiest may be to perform regression where you can choose whichever interactions you want:

lm(y ~ temperature + quality + gender, mydata)


or:

lm(y ~ temperature*quality + gender, mydata)


or:

lm(y ~ temperature*quality*gender, mydata)


or:

lm(y ~ temperature*quality*gender - quality*gender, mydata)

• But I have done anova, and want to do post-hoc test to see which levels/combinations are significant? – ps19 Jun 16 '15 at 13:06
• The interactions will be much clearer with regression. You can perform both if needed. Anova and regression are actually very similar. In anova also you can use terms as mentioned above. – rnso Jun 16 '15 at 14:15