Abstract: The validity of inferences drawn from statistical test results depends on how well data meet associated assumptions. Yet, research (e.g., Hoekstra et al., 2012) indicates that such assumptions are rarely reported in literature and that some researchers might be unfamiliar with the techniques and remedies that are pertinent to the statistical tests they conduct. This article seeks to support researchers by concisely reviewing key statistical assumptions associated with substantive statistical tests across the general linear model. Additionally, the article reviews techniques to check for statistical assumptions and identifies remedies and problems if data do not meet the necessary assumptions.
The degree to which valid inferences may be drawn from the results of inferential statistics depends upon the sampling technique and the characteristics of population data. This dependency stems from the fact that statistical analyses assume that sample(s) and population(s) meet certain conditions. These conditions are called statistical assumptions. If violations of statistical assumptions are not appropriately addressed, results may be interpreted incorrectly. In particular, when statistical assumptions are violated, the probability of a test statistic may be inaccurate, distorting Type I or Type II error rates.
This article focuses on the assumptions associated with substantive statistical analyses across the general linear model (GLM), as research indicates they are reported with more frequency in educational and psychological research than analyses focusing on measurement (cf. Kieffer et al., 2001; Zientek et al., 2008). This review is organized around Table 1, which relates key statistical assumptions to associated analyses and classifies them into the following categories: randomization, independence, measurement, normality, linearity, and variance. Note that the assumptions of independence, measurement, normality, linearity, and variance apply to population data and are tested by examining sample data and using test statistics to draw inferences about the population(s) from which the sample(s) were selected.
