Generate a Design Efficient under ANCOVA

This menu generates a design that is efficient under analysis of covariance (ANCOVA).

When a covariate is fitted in an analysis of variance, there can be a loss of efficiency in the estimation of the treatment effects due to the treatments having different means for the covariates. A measure of this loss of efficiency is printed in a column of the analysis of variance table headed. "cov. ef." (an abbreviation for the covariance efficiency factor, CEF). A value of the CEF close to one represents very little loss in efficiency through fitting the covariate. In good designs, the treatment means for a covariate will be similar, so that only small adjustments will be required in estimating the response-variate treatment means in the analysis of covariance. Where the covariates are available before the allocation of treatments to units, the randomization of the design may be restricted to ensure high covariate efficiency for all treatment factors. To enable randomization, the proportion of good designs kept is from the overall randomization set is specified in the Proportion of the Design Set to use: edit box. Simulation is used to estimate the cut off for the CEF that will give this proportion of good designs, and then a design which has a CEF is above this cut off is randomly generated.

Covariates

A list of the covariates to be used in the analysis of covariance (ANCOVA). The covariate's names should be separated by spaces or commas. Covariate names can be entered from the available data list by double clicking their names in the Available Data list when this edit box has focus.

Order of Polynomial to fit for each covariate

The covariates can be fitted as linear terms (the default) or at higher orders (quadratic, cubic or quartic) to allow for curvature in the relationship between the covariate and the response variate. Specifying a linear term will make the generation balance the means of the covariates across the treatment factors, and higher order terms will balance the variances, skewness and kurtosis respectively for quadratic, cubic and quartic terms.

Treatments

A formula giving the treatment structure to be fitted in an analysis of covariance (ANCOVA). The formula is made up by a list of factors combined with formula operators. Factors can be entered from the Available Data list by double clicking their names when this edit box has focus, and similarly the operators can be entered by double clicking the entries in the Operators list.

Blocks

A formula giving the block structure to be fitted in an analysis of covariance (ANCOVA). The formula is made up by a list of factors combined with formula operators. Factors can be entered from the Available Data list by double clicking their names when this edit box has focus, and similarly the operators can be entered by double clicking the entries in the Operators list.

Interactions

For designs with more than one treatment factor you can specify whether interactions can be fitted in addition to main effects.

Unit Identifiers

A variate, factor or text that identifies each unit in the design. This will be printed with the design and added to a spreadsheet containing the design.

Number of Simulations

Specifies the number of designs generated when looking for the estimated cut off in the covariate efficiency factor.

Randomization Seed

A value used to initialize the random number generator. If a value of zero is used, the computers clock will be used to initialize the random numbers. If this is reset to a particular value used in a previous design, you will obtain the identical design a second time (i.e. units will have the same factor combinations). If providing your own seed, it should be a large integer (i.e. > 9999).

Proportion of the Design Set to use

This specifies the proportion of good designs to be kept from the overall randomization set. Decreasing this towards zero increases the minimum covariate efficiency factor that can be acceptable, but increases the number of designs that must be generated to find one that meets this criteria. Values between 0.01 and 0.20 are generally appropriate. For values close to zero, a larger value for the number of simulations should be used.

Use Best Design

When selected, only the best design found after generating the specified number of simulations will be returned. This does not provide a randomized design from a well specified design set, so that no randomization analysis would be possible.

Available Data

This lists data structures appropriate to the current input field. The contents of this box will change as you move from one field to the next. You can double-click a name in the list box to copy it to the current input field.

Operators

This provides a list of operators that can be used in the treatment and block model formulas. Double-click on the required symbol to copy it to the current input field. You can also type in operators directly. See model formula for a description of each.

Action Buttons

Run	Generate the design.
Cancel	Close the menu without further changes.
Options	Opens a dialog where additional options can be specified for the designs.
Store	Opens a dialog where additional results can be stored for the design.
Defaults	Set the menu settings back to the default settings. Clicking the right mouse on this button produces a pop-up menu where you can choose to set the menu using the currently stored defaults or the GenStat default settings.