Classic analysis of variance is based on the assumption that, initially, the means and variances of all components of the model are the same. In the Visual Statistics Studio, select ( Designs, Designs of Experiments ) and under the Hypothetical Experimental Designs heading click on the Initial State command. Click the Accept command.
Following some type of intervention ( Select ( Designs, Designs of Experiments ) and under the Hypothetical Experimental Designs heading click on the State After Experiment command. Click the Accept command. )
Notice that the mean of the Y1 + Exp variable and the mean and variance of the total scores changed. Also notice that variances of the Y0 and Y1 + Exp variances remained the same, that is where the assumption f homoscedascity came from. It can be observed that the change of variance of the total scores is due to the variance of the changed means. Select ( Data, Enter ) and type to the input template means of the Y0 and Y1 + Exp variables.
Thus, variance of the total scores, following the experiment, is conceptualized, for the example, as .667 + .250 = .917.
Coded Analysis of Variance
Select ( Designs, Designs of Experiments ) and under the Coded Designs headings click on the Independent Measures command.
Select ( Analysis I, Regression Analysis ) and mark the Predictor and Criterion variables. Click on the Accept command.
Note that the variance of the predicted scores (.250) equals the variance between the means, obtained earlier. Also note that the standard variance of the predicted scores is .273 and the standard variance of the error scores is .727. Using the same data
select ( Analysis II, Coded Independent Measures Design )
Notice that the top two Standard Variance Components equal the standard variance of the predicted (.272) and error (.728) variables of the regression analysis.