We have collected data for a 3 x 3 within subjects experiment, with several dependent variables. Some of our 3x3 interactions are significant, and on an interaction plot we think it is easy to identify which data points are ‘causing’ the significant interaction? Is there something a bit more ‘scientific’ we can add? It just seems a bit incomplete as is.
It is regular ANOVA for comparison of parametric values with normal distribution, yes? I don't know, what statistical software are you using, but such identification should be indicated in the analysis report, along with values returned by the test. For me it is beginning of the next task - step by step analysis of indicated datasets with two-way ANOVA, and at next level next one-way ANOVA or t-test. This could give an accurate answer concerning sources of variability at all the levels.
It is important to tease apart the nature of the 3x3 interactions using two-way ANOVAs, one-way ANOVAS, and t-tests. Field (2013) provides an excellent step-by-step guide to follow-up analyses in complex ANOVAs.
Following up Karly Murphy's comment, above: Most stats programs include options to identify specific contrasts. Resulting test statistics are formed with variance estimates from the ANOVA sample. If you have an idea of where you think you need further attention this is a nice approach because it can minimize alpha-error risks by not running everything you can think of.
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