What to do When the Assumptions of Your Analysis are Violated
Violations of the assumptions of your analysis impact your ability to trust your results and validly draw inferences about your results. For a brief overview of the importance of assumption testing, check out our previous blog. When you don’t meet the assumptions of your analysis, you have a few options as a researcher.
Data transformation:
A common issue that researchers face is a violation of the assumption of normality. Numerous statistics texts recommend data transformations, such as natural log or square root transformations, to address this violation (see Rummel, 1988). Data transformations are not without consequence; for example, once you transform a variable and conduct your analysis, you can only interpret the transformed variable. You cannot provide an interpretation of the results based on the untransformed variable values.
Non-parametric analysis:
You may encounter issues where multiple assumptions are violated, or a data transformation does not correct the violated assumption. In these cases, you may opt to use non-parametric analyses. If you are not familiar with parametric and non-parametric, please check out our previous blog that discusses this topic. Non-parametric alternatives to common parametric analyses exist, allowing you to conduct a variety of analyses. Although non-parametric analyses are beneficial because they don’t rely on the assumptions of parametric analyses, they are generally less powerful.
Alternative statistics for determining significance:
Although non-parametric analyses are beneficial because they don’t rely on the assumptions of parametric analyses, they are generally less powerful. For example, if your analysis of variance (ANOVA) violates the homogeneity of variance assumption, you can use alternative F statistics, like Welch’s or Brown-Forsythe (see Field, 2013), to determine statistical significance. Calculating these F values and their related p values will not require any difficult steps on your part. SPSS offers the option of calculating these statistics as part of the ANOVA analysis.
These are just a few of your options when your assumptions are violated. There are a variety of approaches you can take to enhance the validity of your findings.
References
Field, A. (2013). Discovering statistics using SPSS (4th ed.). Sage publications.
Rummel, R. J. (1988). Applied factor analysis. Northwestern University Press.