General MANOVA

Univariate Statistics - S, R-Sq and R-Sq(Adj) Values for Usability

  

S, Rimage\squared.gif and adjusted Rimage\squared.gif are measures of how well the model fits the data. These values can help you select the model with the best fit.

·    S is measured in the units of the response variable and represents the standard distance data values fall from the fitted values. For a given study, the better the model predicts the response, the lower S is.

·    Rimage\squared.gif (R-Sq) describes the amount of variation in the observed response values that is explained by the predictor(s). Rimage\squared.gif always increases with additional predictors. For example, the best five-predictor model will always have a higher Rimage\squared.gif than the best four-predictor model. Therefore, Rimage\squared.gif is most useful when comparing models of the same size.

·    Adjusted Rimage\squared.gif is a modified Rimage\squared.gif that has been adjusted for the number of terms in the model. If you include unnecessary terms, Rimage\squared.gif can be artificially high. Unlike Rimage\squared.gif, adjusted Rimage\squared.gif may get smaller when you add terms to the model. Use adjusted Rimage\squared.gif to compare models with different numbers of predictors.

Example Output

S = 0.942587   R-Sq = 44.40%   R-Sq(adj) = 39.43%

Interpretation

For the door lock data, S is 0.942587, Rimage\squared.gif is 44.40%, and the adjusted Rimage\squared.gif equals 39.43%. If you are comparing different door lock usability models, then you generally look for models that minimize S and maximize the two Rimage\squared.gif values.