THe documentation for the MODECLUS procedure discusses this. Basically it is Euclidean distance unless you use a variable width bandwidth. If you are using variables that have incompatible scales, you should probably standardize the data. Otherwise variables with difference variance will not be handled similarly.
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ANOVA, or Analysis Of Variance, is used to compare the averages or means of two or more populations to better understand how they differ. Watch this tutorial for more.