# How to present several ANCOVA findings

I have six scatterplots (such as the one below) that show an insignificant interaction of the factor (X2) (e.g. gender, age, education etc.) with the predictor (X1) on Y. (X1 is significant.)

The simplest interpretation is that as X1 increases, Y increases for both levels of the factor (in this case, males and females). In other words, gender does not affect the relationship between X1 and Y and the difference in slope is due to sampling error.

These two statements apply to all other factors (e.g. age, which has three categories; education, which has three levels etc.).

One option is to present the six scatterplots and repeat the above statements as explanation. However, this seems tedious.

Is there a better (and succint way) of presenting these findings?

(I guess this is not a statistical question but it certainly relates to data analysis and interpretation!)

-
The question has ANCOVA in the title... is this in any way related to the problem? –  John Jan 18 '12 at 13:20
Yes, the regression lines for the factor were tested using the GLM function in SPSS. It involves a covariate (continuous), a factor (categorical) and a continuous dependent variable. ANCOVA captures continuous and categorical IVs to test for main effects and interaction. –  Adhesh Josh Jan 18 '12 at 20:25

If all the interactions are as small as this one, you need not present them at all, you can just say they were small and not statistically significant.

If you still want them all, then, like @john said, you can drop the raw data and have 12 lines (two for each pair of covariates), using different linestyles and colors to differentiate them. Perhaps 6 colors and 2 line styles would work well. This might be possible on one graph.

On the other hand, if you present 6 graphs (one for each covariate) you could put in a lot more info, like ellipses and density plots. THis can be done in R or SAS, I don't know if can be done in SPSS. If you want to do it in SAS, I wrote a paper for NESUG

For R, I like what John Fox has to say (but there are lots of good regression/graphics packages in R)

-