ANCOVA is a procedure like ANOVA except researchers can study the effects of one or more independent variables on a dependent variable after adjusting for other variables, called covariates, which were not a primary focus of the study. The letter C in ANCOVA stands for covariate. There can be several covariates in a study. In testing for differences among groups experiencing different leadership styles, we could study the effects on employee satisfaction after adjusting for a covariate of years of employment. A key word in ANCOVA studies is adjusting. Analysts adjust the scores based on information about the covariate before testing for significant differences.
Basic features of an ANCOVA:
Independent or grouping Variable = 1 or more
Dependent or criterion Variable = 1
Covariates = 1 or more
An F test indicates significance overall and for specific effects or relationships.
A commonly reported measure of effect size is eta squared.
A p value reveals the probability of a significant relationship-- one that is not due to chance factors.
Read more about ANCOVA in the following books.
Analysis of Covariance
Geoffrey W. Sutton, Ph.D.
The analysis of covariance is a research strategy that is based upon a two or more groups design that yields at least interval data and could be analyzed using ANOVA. We use the term ANCOVA as an acronym. The letter C in the acronym represents a covariate. We usually refer to the covariate as a CV. A covariate is a variable that is significantly correlated with the dependent variable.
In experimental research, the covariate helps reduce error variance and makes the F-test more sensitive to any main or interaction effects. The correlation between the covariate and the DV allows for the removal of the effects of a CV on a DV and represents a known source of systematic bias.
In nonexperimental research, researchers can use the covariate to statistically remove the influence of a variable to help equate groups that could not be formed by random assignment or to better understand another relationships of interest.
A third purpose is to examine group differences by controlling for the influence of a DV when there are several DVs in an analysis. This latter use is known as multivariate analysis of variance or, MANCOVA.
You can use more than one CV in a research design or ANCOVA procedure. However, if there is a correlation greater than r = .80 between two CVs, you should use only one of the CVs because they appear to be measuring a lot of the same variance.
As with all statistical procedures, there are several assumptions to meet. The first three are basic assumptions for ANOVA and the next three are additional assumptions for ANCOVA.
1. All data are from random samples and independent of other data.
2. The scores on the DV are normally distributed in the population.
3. The distributions of scores on the DV have equal variances.
Additional assumptions for ANCOVA
4. There is a linear relationship between the CV and the DV.
5. The slope for the regression line (for the CV) is the same in each group.
6. The CV has high reliability and was measured without error.
Research questions and hypotheses
We generally use a key phrase to identify the CV in a research study. That key phrase can be controlling for or adjusted for. Here are some examples.
1. What is the difference between memory scores for people with right and left hemisphere stroke when adjusted for age?
2. What is the effect of a marriage enrichment program when controlling for years of marriage?
The research hypothesis states there is an effect or a difference when adjusting for the CV and the null hypothesis assumes the usual no difference, or no effect result, when adjusting for the CV.
Following is a hypothesis based on question number one.
H1: When adjusting for age, there is a significant difference between the means on verbal memory between patients who experience right and left hemisphere strokes.
H01: When adjusting for age, there is no significant difference between the means on verbal memory in the population between patients who experienced right and left hemisphere strokes (p < .05).
The research method with a CV
We would follow usual procedures for delivering the IV (independent variable) or measuring a QIV (quasi-independent variable) along with the DVs. We would consider what variables might affect the DVs and collect data to measure those CVs. After all the data have been entered into our database, we would obtain the descriptive statistics. Next, make any adjustments to the data and calculate correlations between the measured variables. Those variables that were not the primary focus of the experiment or study will be entered as CVs in the ANOVA procedure if they are highly correlated with the DVs. We will perform the usual post hoc analyses, if applicable.
When interpreting the results of an ANCOVA, we will refer to the adjusted means. SPSS reports the results of the analysis. In the Test of Between Subjects Effects table, SPSS reports the CV along with an F-test. If the CV made a significant contribution to the analysis, the p-value for the CV will be less than .05 (or your preferred level of significance). The output will also include adjusted and unadjusted means. When reporting the results, you should report both sets of means. In a small study, the means can be reported in a paragraph. In a larger study, the means should be placed in a table.
Example of ANCOVA reporting for a fictitious study.
IV = communication skills training vs. a no skills training control (2 groups)
DV = some measure of communication on a continuous scale
CV = years of employment-- a continuous scale
Workplace communication skills training for employees significantly improved positive statements when adjusted for years of employment, F(2,38) = 4.56, p = .03, eta2 = .42, Observed Power = .67.
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