# How to interpret non-significant effect of a covariate in ANCOVA?

I need to use ANCOVA to analyse effect of executive functions (EF-covariate) on scores collected during a test. I want to compare this effect between a control and schizophrenics group (variable diagnoza).

I conducted an analysis of covariance and I have some questions. Here is SPSS output for my ANCOVA model:

Is it a problem that the effect of EF is not significant? Can I interpret this result as follows: There is a significant difference in MIE between groups when the effect of EF is controlled?

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You have included in your model Diagnosis and Diagnosis*EF, but no main effect for EF. Why? – boscovich Mar 30 '12 at 11:17
I run analysis one more time and add main effect of EF too. diagnoza has significat effect, EF and EF*diagnoza not. – Miso Hajduk Mar 30 '12 at 13:39
If the interaction term is not statistically significant, then it means that you don't have enough evidence to conclude that the effect of EF on your outcome is different between your two Diagnoza groups – boscovich Mar 30 '12 at 14:06

However, I would urge some caution here. First, it is not clear how much power you have to detect an effect, should one actually exist. I notice that you have an $N$ of 61. That simply may not be enough data to resolve what is nonetheless a real difference. Consider this, without meaning to be dismissive, an ANCOVA with 2 groups is essentially a glorified t-test. To use two arbitrary values that are often taken as standard, a 'medium' effect size & 80% power, a simple independent groups t-test requires an $N$ of 128, if I remember correctly. In this case, there are additional complexities due to this being an ANCOVA (i.e., you are burning extra degrees of freedom, but also have the opportunity to account for some of the residual variability). There are additional issues: power is maximal to detect a linear effect, but it's thinkable that a non-linear effect exists, you could have range restrictions that limit power, and my first guess would be that EF is not orthogonal to diagnosis (i.e., the distribution differs between the two groups, although I don't know). I would urge you to look at your data. For example, you could make a scatterplot of EF vs. MIE, with two different plotting symbols for the different diagnoses, and overlaid with a loess fit for each group. Check to see if the distributions and fits look sufficiently similar for your satisfaction before deciding what to conclude and what to do next.