How to report two-way anova results?

Question

After finding a significant treatment in two-way anova, how do I report where the differences are? Every text I have read has left me at: Ah, the results are significant, so let's move on. In one-way anova I could use Tukey's HSD to find the means that differed, making my report much more effective. Right now I don't know how to do that with two-factor anova.

Here is an example from a text done in R:

Is there a difference in Friday tardy rates at different plants?

> mlate
        day  plant absences
1   march-4 plant1       19
2  march-11 plant1       22
3  march-18 plant1       20
4   march-4 plant2       18
5  march-11 plant2       20
6  march-18 plant2       16
7   march-4 plant3       27
8  march-11 plant3       32
9  march-18 plant3       28
10  march-4 plant4       22
11 march-11 plant4       27
12 march-18 plant4       26

> anova(lm(absences ~ plant+day, data=mlate))
Analysis of Variance Table

Response: absences
          Df  Sum Sq Mean Sq F value    Pr(>F)    
plant      3 216.250  72.083  41.191 0.0002134 ***
day        2  30.167  15.083   8.619 0.0172128 *  
Residuals  6  10.500   1.750                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

So I can see that both the plant and the day have an effect on worker's being late, but how do I compare the means like I would with a tukey's hsd in a one-way test?

Answer 1

The post hoc tests for 2 way ANOVA are conceptually no different than those for 1-way ANOVA. See this pdf, it gives examples of such post hoc tests for 2-way ANOVA.

In particular, the HSD test is also same.

http://ocw.mit.edu/courses/brain-and-cognitive-sciences/9-07-statistical-methods-in-brain-and-cognitive-science-spring-2004/lecture-notes/21_anova4.pdf