We touch on the notion of independence in Definition 3 of Basic Probability Concepts. Generally, linearity can be tested graphically using scatter diagrams or via other techniques explored in Correlation, Regression and Multiple Regression. Regression) require that there be a linear correlation between the dependent and independent variables. In Homogeneity of Variances we provide some tests for determining whether groups of data have the same variance. ANOVA) require that the groups of data being studied have the same variance. In Testing for Normality and Symmetry we provide tests to determine whether data meet this assumption. Such data is symmetric around its mean and has kurtosis equal to zero. We explore in detail what it means for data to be normally distributed in Normal Distribution, but in general, it means that the graph of the data has the shape of a bell curve. Linearity: Data have a linear relationship.Homogeneity of variances: Data from multiple groups have the same variance.Normality: Data have a normal distribution (or at least is symmetric).When these assumptions are violated the results of the analysis can be misleading or completely erroneous. As we can see throughout this website, most of the statistical tests we perform are based on a set of assumptions.
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