Quantitative Results

Statistical Analysis

**Analysis of Covariance (ANCOVA)** is the inclusion of a continuous variable in addition to the variables of interest (i.e., the dependent and independent variable) as means for control. Because the ANCOVA is an extension of the ANOVA, the researcher can still can assess main effects and interactions to answer their research hypotheses. The difference between an ANCOVA and an ANOVA is that an ANCOVA model includes a “covariate” that is correlated with the dependent variable and means on the dependent variable are adjusted due to the effects the covariate has on it. Covariates can be used in many ANOVA based designs – such as between-subjects, within-subjects (repeated measures), mixed (between – and within – designs) etc. Thus, this technique answers the question: Are mean differences or interactive effects likely to have occurred by chance after scores have been adjusted on the dependent variable because of the effect of the covariate?

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Tabachnick and Fidell (2013) review three general applications for an Analysis of Covariance include:

*Increasing the Power of the F-Test in Experimental Designs*: Participants are assigned to treatment and control groups in an ANOVA-based design. ANCOVA can then be used as a means to eliminate unwanted variance on the dependent variable. This allows the researcher to increase test sensitivity. Adding reliable and necessary variables to these models typically reduces the error term. By reducing the error term, the sensitivity of the F-test also increases for main and interactive effects.*Equating Non-Equivalent Groups:*Another, though controversial, use of ANCOVA is to correct for initial group differences that exists on the dependent variable. Using this method, the researcher adjusts means on the dependent variable in an effort to correct for individual differences. This allows the researcher to adjust the means on the dependent variable to what they would have been should all of the participants scored equally on the covariate. Using it for this purpose is commonly done in non-experimental situations when random assignment was not used. However, differences may have also have been due to other variables not measured or included as covariates.*Adjustment of Means of Multiple Dependent Variables*: This application is similar to the ones outlined above, but when the researcher is measuring multiple dependent variables, such as a Multivariate ANOVA (MANOVA). This application typically occurs when the researcher wants to assess the contribution of the various dependent variables by removing their effects from the analyses. This procedure is called a stepdown analysis.

The researcher can go about interpreting main effects and interactions as they typically would. The difference is that the regression of the covariate on the dependent variable is estimated first before the variance in scores is partitioned into differences between and within group; however, the error term is adjusted from the regression line derived from the covariate on the DV vs. running through the means in ANOVA designs.

References:

Tabachnick, B., & Fidell, L. (2013). Using multivariate statistics (6th ed.)Upper Saddle

River, NJ: Pearson.