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*[[Normality|Multivariate normality]]: Independent variables are normal for each level of the grouping variable.<ref name="buy"/><ref name="green"/>
*Homogeneity of variance/covariance ([[homoscedasticity]]): Variances among group variables are the same across levels of predictors. Can be tested with Box's M statistic.<ref name="green"/>{{pn|date=April 2012}} It has been suggested, however, that [[linear discriminant analysis]] be used when covariances are equal, and that [[quadratic classifier#quadratic discriminant analysis|quadratic discriminant analysis]] may be used when covariances are not equal.<ref name="buy"/>
*[[Multicollinearity]]: Predictive power can decrease with an increased correlation between predictor variables.<ref name="buy"/>
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Each function is given a discriminant score to determine how well it predicts group placement.
*Structure Correlation Coefficients: The correlation between each predictor and the discriminant score of each function. This is a whole{{clarify|date=April 2012}} correlation.<ref name="buy"/><ref name="garson">Garson, G. D. (2008). Discriminant function analysis. http://www2.chass.ncsu.edu/garson/pa765/discrim.htm .</ref>
*Standardized Coefficients: Each predictor’s unique contribution to each function, therefore this is a [[partial correlation]]. Indicates the relative importance of each predictor in predicting group assignment from each function.<ref name="garson"/><ref name="buy"/>
*Functions at Group Centroids: Mean discriminant scores for each grouping variable are given for each function. The farther apart the means are, the less error there will be in classification.<ref name="garson"/><ref name="buy"/>
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==Eigenvalues==
An [[eigenvalues and eigenvectors|eigenvalue]] in discriminant analysis is the characteristic root of each function.{{clarify|date=April 2012}} It is an indication of how well that function differentiates the groups, where the larger the eigenvalue, the better the function differentiates.<ref name="buy"/> This however, should be interpreted with caution, as eigenvalues have no upper limit.<ref name="buy"/><ref name="green"/>
The eigenvalue can be viewed as a ratio of ''SS''<sub>between</sub> and ''SS''<sub>within</sub> as in ANOVA when the dependent variable is the discriminant function, and the groups are the levels of the IV{{clarify|date=April 2012}}.<ref name="green"/> This means that the largest eigenvalue is associated with the first function, the second largest with the second, etc..
==Effect size==
Some suggest the use of eigenvalues as [[effect size]] measures, however, this is generally not supported.<ref name="green"/> Instead, the [[canonical correlation]] is the preferred measure of effect size. It is similar to the eigenvalue, but is the square root of the ratio of ''SS''<sub>between</sub> and ''SS''<sub>total</sub>. It is the correlation between groups and the function.<ref name="green"/>
Another popular measure of effect size is the percent of variance{{clarify|date=April 2012}} for each function. This is calculated by: (''λ<sub>x</sub>/Σλ<sub>i</sub>'') X 100 where ''λ<sub>x</sub>'' is the eigenvalue for the function and Σ''λ<sub>i</sub>'' is the sum of all eigenvalues. This tells us how strong the prediction is for that particular function compared to the others.<ref name="green"/>
Percent correctly classified can also be analyzed as an effect size. The kappa value{{clarify|date=April 2012}} can describe this while correcting for chance agreement.<ref name="green"/>
==Variations==
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==Comparison to logistic regression==
Discriminant function analysis is very similar to [[logistic regression]], and both can be used to answer the same research questions.<ref name="green"/> Logistic regression does not have as many assumptions and restrictions as discriminant analysis. However, when discriminant analysis’ assumptions are met, it is more powerful than logistic regression.{{cn|date=April 2012}} Unlike logistic regression, discriminant analysis can be used with small sample sizes. It has been shown that when sample sizes are equal, and homogeneity of variance/covariance holds, discriminant analysis is more accurate.<ref name="buy"/> With all this being considered, logistic regression is the common choice nowadays, since the assumptions of discriminant analysis are rarely met.<ref name="buy"/><ref name="cohen"/>
==See also==
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