Can I add more than 2 independent groups to an Ancova and if so, do I need to create dummy variables in SPSS

Question

I want to analyze the difference between 4 groups on one dependent variable while controlling for my covariate, age, and 3 different independent variables (sex, cancer type, metastasis) in SPSS. Can I use an ANCOVA with this many independent variables and if so, do I need to create dummy variables? Alternatively, what test should I perform?

Answer 1

Well given ANCOVA is just an extension of ANOVA (Navarro, 2013), this means it can handle omnibus NHST tests of groups that are greater than or equal to two, which fits your use case. Note that one can achieve the same thing by simply adding a single categorical predictor (your four levels of your factor), your three other control variables, and your DV into a linear regression. The only difference is that this takes a coefficient-based approach to estimating the conditional mean comparisons between groups (usually using the intercept as a reference group and additional slopes as comparison groups). For conceptual comparisons of ANOVA and regression, see Slinker & Glantz, 1988). Whether you use an ANCOVA or regression, you can simply dummy code your variables to get group comparisons if SPSS doesn't do that already.

Given the ANOVA and ANCOVA are omnibus tests, they only test the hypothesis of whether the difference between means in every group is exactly the same, but doesn't say where these differences lie. To achieve this under an NHST framework, you would need to do additional t-tests on each pair of groups. Common practice is to use adjusted pairwise comparisons (Midway et al., 2020) but I generally don't find them to be all that useful (see Nakagawa, 2004 for a short but thorough criticism). You can also just simply compare the means and explain differences in this way.

NHST tests are useless on their own. Make sure to include effect sizes (such as Cohen's $d$ or Hedge's $g$ for pairwise comparisons) and the raw estimates (like I mentioned with the means) if you report your results (Lakens, 2013).

References

• Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for t-tests and ANOVAs. Frontiers in Psychology, 4. https://doi.org/10.3389/fpsyg.2013.00863
• Midway, S., Robertson, M., Flinn, S., & Kaller, M. (2020). Comparing multiple comparisons: Practical guidance for choosing the best multiple comparisons test. PeerJ, 8, e10387. https://doi.org/10.7717/peerj.10387
• Nakagawa, S. (2004). A farewell to Bonferroni: The problems of low statistical power and publication bias. Behavioral Ecology, 15(6), 1044–1045. https://doi.org/10.1093/beheco/arh107
• Navarro, D. (2013). Learning statistics with R: A tutorial for psychology students and other beginners: Vol. 0.3. University of Adelaide.
• Slinker, B. K., & Glantz, S. A. (1988). Multiple linear regression is a useful alternative to traditional analyses of variance. American Journal of Physiology-Regulatory, Integrative and Comparative Physiology, 255(3), R353–R367. https://doi.org/10.1152/ajpregu.1988.255.3.R353