Weird ANCOVA result

[jiupui]

Hello,

Would someone please help me to understand the strange ANCOVA result below?  This is from an anaylsis in which I'm using ANCOVA to look at group differences following an intervention, which the baseline scores entered as the covariate.

There were no significant group differences at baseline. I tested the assumption of homogenity of rgresion slopes: The interaction between baseline variable interest and group was statistically significant, F(1, 28) = 6.807, p =0.015, indicating that the assumption of ANCOVA were violated.  

It is my understanding that this significant interaction suggests that any group differences in the postintervention score vary as a function of the covariate (in this case the baseline variable of interest) rather than the group .    BUT how can that be if there were not differences at baseline?  I should note that small sample size is any issue and that the groups differ in sample size.  I am wondering if this could be statisical anomoly related to sample size and/or spread of the distribution on the variable of interest.

Thanks in advance for any thoughts/help.

[Bruce Weaver]

Make a scatter-plot with X = Baseline, Y = Follow-up, and separate lines (called "fit lines" in the chart editor dialog IIRC) for the two groups.  The significant interaction you report below should lead you to expect non-parallel lines.  The no significant differences on baseline leads you to expect the two means for the X-axis variable to be fairly similar.  Because the lines are not parallel, you will need to compare the groups at various points (e.g., low, medium and high values of the baseline variable).  If you run your model via UNIANOVA, you can make those comparisons via EMMEANS sub-commands where you specify the desired values of the baseline variable (see WITH in the help for EMMEANS).  The default is WITH X=mean, but you can specify any value you want.

HTH.

jiupui wrote

Hello,

Would someone please help me to understand the strange ANCOVA result below?  This is from an anaylsis in which I'm using ANCOVA to look at group differences following an intervention, which the baseline scores entered as the covariate.

There were no significant group differences at baseline. I tested the assumption of homogenity of rgresion slopes: The interaction between baseline variable interest and group was statistically significant, F(1, 28) = 6.807, p =0.015, indicating that the assumption of ANCOVA were violated.  

It is my understanding that this significant interaction suggests that any group differences in the postintervention score vary as a function of the covariate (in this case the baseline variable of interest) rather than the group .    BUT how can that be if there were not differences at baseline?  I should note that small sample size is any issue and that the groups differ in sample size.  I am wondering if this could be statisical anomoly related to sample size and/or spread of the distribution on the variable of interest.

Thanks in advance for any thoughts/help.