The next sections are an extension of the analysis of variance.

First, we will look at analysis of covariance, or ANCOVA. It is similar to ANOVA but is used to compare two or more means after they are adjusted for the effect of one or more variables (covariates). We will then turn to two-way between-subjects design.

Analysis of Covariance

As stated already, ANCOVA is similar to ANOVA. However, the group means in an ANCOVA are adjusted to the values that they theoretically might have had if the treatment groups had equal means on the covariate. Basically, they are adjusted for one or more covariates.

(View the first two minutes)

ANCOVA is often used in quasi-experimental designs as a form of statistical control. Basically, if one or more individual participant characteristics or covariates are measured and statistically controlled for, we can predict how the outcome variable for the groups might have differed if the groups had been identical in terms of pre-existing participant characteristics. ANCOVA has the ability to increase statistical control and power as compared to ANOVA.

For a clear definition of ANCOVA, refer to: http://oak.ucc.nau.edu/rh232/courses/eps625/handouts/ancova/understanding%20ancova.pdf

Additional information:

• A review of ANCOVA: https://youtu.be/DRLi-jQXe78
• General use of ANCOVA: https://www.statisticssolutions.com/general-uses-of-analysis-of-covariance-ancova/
• Introduction to ANCOVA: https://www.youtube.com/watch?v=0e8BI2u6DU0
• ANOVA vs. ANCOVA: https://www.youtube.com/watch?v=p7fU02WRQ7Y

Two-way Between-subjects Design

In two-way between-subjects ANOVA, you can examine the main effects of the independent variables. The design includes one continuous dependent or outcome variable and two independent variables (also called factors). Furthermore, there are different subjects in each combination of the independent variables.

The two main reasons for using two-way between-subjects ANOVA, is to clarify generalizability and increase the power of the study. For example, this design allows for further clarification of whether there is an interaction effect (i.e., the effect of one independent variable on the dependent variable depends on the level of another independent variable) or if there is no significant interaction effect. If there is no interaction effect, you can then interpret the main effects.

Additional information:

• Two-way ANOVA in SPSS: https://statistics.laerd.com/spss-tutorials/two-way-anova-using-spss-statistics.php
• The breakdown of the total sum of squares: https://www.itl.nist.gov/div898/handbook/prc/section4/prc437.htm
• Main effects vs. interaction effects: https://stats.libretexts.org/Bookshelves/Applied_Statistics/Book%3A_Natural_Resources_Biometrics_(Kiernan)/06%3A_Two-way_Analysis_of_Variance/6.01%3A_Main_Effects_and_Interaction_Effect

Final Thoughts

As I move into the final topics of this course, I am distinctly reminded of how statistical procedures build on each other. If I did not understand regression and multiple regression, then ANOVA and ANCOVA would have confused me. And if the logic and use cases for ANOVA and ANCOVA escaped me, then adding additional factors would be beyond me as well. In order to maintain my level of understanding going forward, I believe it will be essential to develop a better idea of when and why different designs and tests should be used.

References

Field, A. (2017). Discovering statistics using IBM SPSS statistics (5th ed.). SAGE Publications.

Howell, D. C. (2017). Fundamental Statistics for the Behavioral Sciences (9th ed.). Cengage Learning.