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The following plots are available for one-way ANOVA folios. For general information on working with plots, see Plots.
Level Plots
Level plots allow you to compare the visually evaluate the effects of different factor levels on the selected response.
The Comparison Chart shows the standardized difference for each paired comparison of factor levels.
The Response vs. Level plot shows the observed output, or response, as well as the calculated mean output, at each level of the factor.
The Level Mean plot shows the mean output at each level of the factor. The center point of each level line is the calculated mean and the end points represent the high and low confidence bounds on the mean based on the alpha (risk) value specified on the Analysis Settings page of the control panel.
The Box Plot shows the output at each level of the factor. The height of each box represents the spread of output values at that level.
The Mean PDFs plot shows the pdf of the mean response at each level of the factor.
Residual Plots
Residuals are the differences between the observed response values and the response values predicted by the model at each combination of factor values. Residual plots help to determine the validity of the model for the currently selected response. When applicable, a residual plot allows the user to select the type of residual to be used:
Regular Residual is the difference between the observed Y and the predicted Y.
Standardized Residual is the regular residual divided by the constant standard deviation.
Studentized Residual is the regular residual divided by an estimate of its standard deviation.
External Studentized Residual is the regular residual divided by an estimate of its standard deviation, where the observation in question is omitted from the estimation.
The plots are described next.
The Residual Probability* plot is the normal probability plot of the residuals. If all points fall on the line, the model fits the data well (i.e., the residuals follow a normal distribution). Some scatter is to be expected, but noticeable patterns may indicate that a transformation should be used for further analysis. Two additional measures of how well the normal distribution fits the data are provided by default in the lower title of this plot. Smaller values for the Anderson-Darling test indicate a better fit. Smaller p values indicate a worse fit.
The Residual vs. Fitted* plot shows the residuals plotted against the fitted, or predicted, values of the selected response. If the points are randomly distributed around the "0" line in the plot, the model fits the data well. If a pattern or trend is apparent, it can mean either that the model does not provide a good fit or that Y is not normally distributed, in which case a transformation should be used for further analysis. Points outside the critical value lines, which are calculated based on the specified alpha (risk) value, may be outliers and should be examined to determine the cause of their variation.
The Residual Histogram* is used to demonstrate whether the residual is normally distributed by dividing the residuals into equally spaced groups and plotting the frequency of the groups. The Residual Histogram Settings area allows you to:
Select Custom Bins to specify the number of groups, or bins, into which the residuals will be divided. Otherwise, DOE++ will automatically select a default number of bins based on the number of observations.
Select Superimpose pdf to display the probability density function line on top of the bins.
Diagnostic Plots
The Box-Cox Transformation* plot can help determine, for the currently selected response and model, what transformation, if any, should be applied. The plot shows the sum of squares of the residuals plotted against lambda. The value of lambda at the minimum point of this curve is considered the "best value" of lambda, and indicates the appropriate transformation, which is also noted by default in the lower title of the plot.
* These plots are available only when there is error in the design, as indicated when sum of squares for Residual has a positive value in the ANOVA table of the analysis results.
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