Common Assumptions in Statistics
Usually in inferential statistics, certain assumptions need to be assessed prior to analysis. Depending on the statistical analysis, the assumptions may differ. A few of the most common assumptions in statistics are normality, linearity, and equality of variance.
Normality assumes that the continuous variables to be used in the analysis are normally distributed. Normal distributions are symmetric around the center (a.k.a., the mean) and follow a ‘bell-shaped’ distribution. Normality is typically assessed in the examination of mean differences (e.g., t-tests and analyses of variance – ANOVAs/MANOVAs) and prediction analyses (e.g., linear regression analyses). Normality can be examined by several methods, two of which are the Kolmogorov Smirnov (KS) test and the examination of skew and kurtosis. The KS test utilizes the z test statistic, and if the corresponding p value is less than .05 (statistical significance), then the assumption of normality is not met. Also, normality can be defined as skew below ± 2.0 and kurtosis below ± 7.0, and if the observed values exceed these boundaries, then the assumption of normality is not met.
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Linearity refers to a linear, or straight line, relationship between the independent variable(s) and the dependent variable. If the assumption of linearity is not met, then predictions may be inaccurate. Linearity is typically assessed in Pearson correlation analyses and regression analyses. Linearity can be assessed by the examination of scatter plots.
Equality of variance (a.k.a., homogeneity of variance) refers to equal variances across different groups or samples. Equality of variance is usually examined when assessing for mean differences on an independent grouping variable (e.g., t-tests and analyses of variance – ANOVAs/MANOVAs). Equality of variance can be assessed by utilizing Levene’s test for each continuous, dependent variable. Levene’s test utilizes the F test, and if the corresponding p value is less than .05 (statistical significance), then the assumption of equality of variance is not met.