Here’s the basic layout that I recommend for writing about ANOVA results:
1. Provide the ANOVA table. (This may be optional.)
2. Provide a graphical or tabular summary of the data, or both.
3. Give the results of general tests of significance.
4. Give specific quantitative or qualitative results.
By general tests of significance, I really mean the so-called “omnibus” tests of significance that are shown in the ANOVA table. These are generally tests that try to answer questions like “Does Factor X have any effect on growth?” In some cases, you may need to report such things as overall model significance, which answers the really general question of “Is there any explanatory value of any of these factors compared to just taking the mean of all the data?”
These omnibus tests include test of main effects and tests of interaction effects. Without going into detail just yet, main effects are probably what most people think of when they wonder if some experimental factor has any effect. However, interaction effects can be very interesting results themselves, so don’t be upset if you find statistically significant interactions!
An interaction effect means that the effect of one factor depends somehow on the effect of another factor. Or, more correctly, the effect of one factor is associated to a different effect depending upon the level of some other factor.
By specific quantitative results, I mean such items as estimates of differences or other specific quantities, perhaps along with confidence limits. By qualitative results, I generally mean breakout analysis such as pairwise comparisons or specific contrasts created from the model. These are sort of the “drill-down” of the model.
So, the general model for a unit of ANOVA would be something like this, assuming an imaginary study of IQ in response to Factor X:
4.3 Factor X Effect on IQ
Figure 1: (The raw data or the data in summary form)
Table 1: (The ANOVA table)
Figure 1 displays IQ scores by levels of Factor X. Table 1 gives the results of ANOVA. Factor X seems to have affected IQ (p=0.0498). Specifically, low levels of Factor X were associated with an IQ drop of about 10 points with a 95% CI of (0.9, 21.1) when compared to the average of medium and high levels. Medium and high levels of Factor X were associated with very similar levels of IQ, 100 and 102 points respectively.
If there was more than one factor in the analysis, then things start to get more complicated. However, you can use the same basic structure, either folding the other factor(s) into the mix or giving each factor its own little paragraph. I tend to start with them separated, and after all analyses have been completed it may be that some general organizational scheme will present itself.