If the homogeneity of regression slopes assumption for ANCOVA (no interaction between the covariate and the independent variable) was violated, what is the next step to perform the analysis. Is there any alternative test for ANCOVA?
For instance, you want to use analysis of covariance (ANCOVA), with post-test scores as dependent, pre-test scores as covariates, and group membership as independent factor.
The SPSS UNIANOVA syntax will look something like this:
UNIANOVA
post BY grp WITH pre
/METHOD = SSTYPE(3)
/print = parameter
/emmeans = table(grp) WITH (pre=A)
/emmeans = table(grp) WITH (pre=B)
/emmeans = table(grp) WITH (pre=C)
/emmeans = table(grp) WITH (pre=D)
/DESIGN = pre grp pre*grp.
Where:
- post = outcome variable
- pre = covariate (the baseline score)
- grp = group variable
Replace A, B, C and D with selected values of the pre-test (baseline) score that span the observed range in your data.
HTH.
There is nothing stopping you from estimating a model that includes the Group x Covariate interaction. Just don't call it ANCOVA, because the ANCOVA model excludes that product term, and therefore forces the lines to be parallel.
Also, if you include the interaction, looking at differences among group (adjusted) means at the overall mean of the covariate is not terribly informative. The variability in those group (adjusted) means will depend on the value of the covariiate. What people sometimes do, therefore, is show the adjusted means at 3 or 4 selected values of the covariate (e.g., low, medium and high values for the observed data). Depending on what software you use, this can be done quite easily. (E.g., with the SPSS UNIANOVA procedure, you can do it with a series of EMMEANS sub-commands.)
HTH.
Thank you so much dear Bruce Weaver for your answer. I am using SPSS. Do you suggest me to use a model that includes the Group x Covariate interaction and report the results? Kindly, let me know what I will call this analysis. Also, I am not sure if it is a usual practice to present the adjusted means at 3 or 4 selected values of the covariate (e.g., low, medium and high values for the observed data), and report the outcomes.
The SPSS UNIANOVA syntax will look something like this:
UNIANOVA
post BY grp WITH pre
/METHOD = SSTYPE(3)
/print = parameter
/emmeans = table(grp) WITH (pre=A)
/emmeans = table(grp) WITH (pre=B)
/emmeans = table(grp) WITH (pre=C)
/emmeans = table(grp) WITH (pre=D)
/DESIGN = pre grp pre*grp.
Where:
- post = outcome variable
- pre = covariate (the baseline score)
- grp = group variable
Replace A, B, C and D with selected values of the pre-test (baseline) score that span the observed range in your data.
HTH.
Highly appreciated dear Bruce Weaver. Hope you the best...
Regards, Ahmad.
Well, an answer 2 years later, why not?
For ANCOVA for statistical control the assumption is neglible interaction term. For ANCOVA for comparison of slopes, the next step is to report the gradient (slope of the regression) at each level of the categorical variable. So if the interaction term is substantial, as with a frequentist's pvalue, the data are trying to tell us something important--different gradients with respect to the 'control' variable, across levels of the categorical variable. So tell us about the regression term at each level of the categorical variable. And give us the gradient (slope) at each level of the categorical variable. And to top it off, as good frequentists, give us a confidence limit on the regression (slope) estimate at each level the categorical variable.
Just a thought,
David S
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