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 the assumptions of your analysis are not met, 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.
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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. There are non-parametric alternatives to the common parametric analyses so you will not be limited in the type of analysis you can conduct. However, although non-parametric analyses are beneficial because they are free of the assumptions of parametric analyses, they are generally considered less powerful than parametric analyses.
Alternative statistics for determining significance: Finally, you may consider using more conservative statistics for determining significance if your assumptions are violated. For example, if the assumption of homogeneity of variance was violated in your analysis of variance (ANOVA), you can use alternative F statistics (Welch’s or Brown-Forsythe; see Field, 2013) to determine if you have 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.
Field, A. (2013). Discovering statistics using SPSS (4th ed.). Sage publications.
Rummel, R. J. (1988). Applied factor analysis. Northwestern University Press.