Hi,
I am getting confused about the assumption of some statistical tests. In my field (archaeology) normally researchers do not inform about the fulfillment of these assumptions in, for instance, ANCOVA. In some other cases they just say "since the residuals are not normally distributed we used the non-parametric versión of this test", but digging more I have found that the assumptions of ANCOVA are not just that one, but also that:
-There needs to be homogeneity of variances, and that,
-The covariate should be linearly related to the dependent variable at each level of the independent variable, and,
-That there needs to be homogeneity of regression slopes,
So, in the first place, I wonder how strict must we really be with the assumptions for ANCOVA?. It is really necessary that all assumptions are met? are some assumptions more important than others?
In the second place, I have a sample of 300 teeth, but some of the groups of my covariate are small: 7 teeth, for instance. So, I don't know if the number of observations by covariate is too small to use a parametric test or if this is not a problem.
Hello Ana. I'll address part of what you asked (homogeneity of regression slopes).
Statistical terminology can vary by discipline. In the dialect of statistical terminology I speak, ANCOVA refers to a linear model with (at least) one categorical explanatory variable (often called a factor variable) and (at least) one quantitative explanatory variable, with the latter being the covariate. Importantly, in the dialect I speak, the ANCOVA model does not include the interaction between the factor variable and the covariate. Therefore, the fitted values from this model are forced to fall on k parallel lines, where k = the number of levels of the factor variable. So rather than saying the model assumes homogeneity of regression slopes, I would say it imposes it on the fitted values.
What I would suggest is that you create a scatter-plot with X = the covariate, Y = the outcome variable, and different colours (or symbols) for the k levels of your factor variable; and plot the regression lines for each group separately. If this plot shows that the k lines have fairly similar slopes, then the ANCOVA model (which forces the fitted values to fall on parallel lines) probably makes some sense. But if the k lines are departing too much from being parallel, you should consider including the factor*covariate term in your model. In the statistical dialect I speak, this should no longer be called ANCOVA; but there is nothing wrong with it as a linear model. By including the factor*covariate interaction, you are relaxing the constraint that the k lines must be parallel to each other. But notice that when you do this, you can no longer make a single assessment of how much the means for the k levels of the factor variable differ from each other; if the lines are not parallel, how and how much they differ from each other will depend on the value of X, the covariate. If you want to describe the effect of the factor variable X, you'll have to do so at selected values of X (e.g., low, medium and high values of X; or at the quartiles, etc.).
HTH.
Dear Ana,
I would recommend starting with a grouped scatter plot to decide whether ANCOVA or a regression with non-parallel slopes is more appropriate. There is a test for it in SPSS under Univariate model. The assumption you can violate is normality.
Peter Samuels
Would you please discuss the details of:
How to visualize scatter plot matrix to "decide whether ANCOVA or a regression with non-parallel slopes is more appropriate "?
2. There is a test for it in SPSS under Univariate model. Which test?
TIA
Dear Dr. Bruce Weaver,
I have a question in a similar line. In my experiment all ANCOVA assumptions are fine except one. I did not find the correlation between my dependent variable and co-variate. Can I still do the ANCOVA? If not, what is the solution?
This has been bothering me as well. I have a not normally distributed dependent variable and did not find significant correlations between my dependent variable and covariates (using pearson correlation).
May I ask Peter Samuels how can normality is the only assumption that can be violated?
Hello Rashmi Gupta . I didn't see your question until Ida Bagus Yorky Brahmantya resurrected this thread today. Perhaps you will find this discussion on The Analysis Factor website helpful (if it's not too late).
- https://www.theanalysisfactor.com/assumptions-of-ancova/
Peter Samuels
Bruce Weaver
Hello, I am testing the assumption of homogeneity of variance and have found that by assessment of scatter plots (method 1) one of my covariates does not meet the parallel assumption. However, when conducting a correlation analysis (method 2) between the DV and that covariate, the assumption is met because the p-value is insignificant. As method 1 is generally considered more 'casual' and method 2 is more 'professional, should I be removing or keeping that covariate in the analysis?
Thank you in advance,
Luca
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