I have a data set of 543 participants with one dependent variable of a score and three independent variables of teacher age, student age, and teacher self-efficacy. When carrying out the tests for the assumptions, there are several outliers and extreme points, several dependent variables are not normally distributed and the assumption of homogeneity variances was violated. Where do I go from here?
Do you have multiple students per teacher? If so, you need to use the MIXED command to estimate a multilevel model (aka., hierarchical linear model, aka., mixed linear model) with students clustered within teachers. If you are not already familiar with such models, there are many good resources online. Try a Google search on , , , , etc. HTH.
Thanks for responding Bruce Weaver but no, the teacher scored student engagement for their class as a whole.
Just to check, you have 543 teachers, correct? Does each teacher have one and only one class?
Note that the iid assumption is usually more important than things like the distribution of residuals.
Simply answered, since the assumption of homogeneity of variance was not met, you should use a nonparametric statistical procedure, such as the Aligned Rank Transform (ART) ANOVA, which is a non-parametric approach to factorial ANOVA. For elaboration on ART, you could check out the following publications.
Harrar, S. W., Ronchi, F., & Salmaso, L. (2019). A comparison of recent nonparametric methods for testing effects in two-by-two factorial designs. Journal of Applied Statistics, 46(9), 1649–1670. https://doi.org/10.1080/02664763.2018.1555575
Luepsen, H. (2018). Comparison of nonparametric analysis of variance methods: A vote for van der Waerden. Communications in Statistics - Simulation and Computation, 47(9), 2547–2576. https://doi.org/10.1080/03610918.2017.1353613
Mansouri, H., Paige, R. L., & Surles, J. G. (2004). Aligned rank transform techniques for analysis of variance and multiple comparisons. Communications in Statistics - Theory and Methods, 33(9), 2217–2232. https://doi.org/10.1081/STA-200026599
Wobbrock, J. O., Findlater, L., Gergle, D., & Higgins, J. J. (2011). The aligned rank transform for nonparametric factorial analyses using only ANOVA procedures. Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, 143–146. https://doi.org/10.1145/1978942.1978963
Good luck,
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