ANOVA POWER ANALYSIS

The user interface uses sliders that are convertible
to text input; see the Help menu item "GUI Help" for 
more information.  Basic layout is as follows:

Left panel
    This is used to vary the numbers of factor levels,
    and whether each factor is fixed or random.

Right panel(s)
    Here, we specify the effect size (quantified as 
    the SD) for each term in the model, and observe
    the power of the F test for an effect of that size.
    (If you change the power, the effect size is set to
    that which achieves that power.)  At the bottom
    is a selector for specifying the size of all tests.

Options menu
  Graph 
    Provides for simple graphics output based on the values
    in the dialog.  It "plays" the dialog for the values 
    you specify, and plots the results.
    
  Contrasts/Comparisons
    Creates a companion dialog for studying comparisons or
    contrasts among levels of the fixed effects, and links
    parameter values so that they stay in correspondence.
    
  Show EMS
    Displays the expected mean squares (unrestricted model)
    for the ANOVA associated with this model.
    
  Report
    Generates a report for the current settings of factor 
    levels, fixed/random, etc.

  Quit
    Close the dialog and all of its dependents.


SOME DETAILS

THE "UNRESTRICTED MODEL" is currently used in all
power calculations.  This means that any mixed effects
are modeled as independent normal random variables.
Maybe some day the restricted model will be supported.

EFFECT SIZE is measured by the SD of the effects in the
ANOVA model.  In the case of a random effect, the SD^2
is its variance component.  In the case of a fixed effect, 
the SD^2 is defined as the sum of the squares of the
effects, divided by the degrees of freedom.  For example,
consider a two-way fixed-effects model:

    Y_{ijk} = mu + a_i + b_j + ab_{ij} + E_{ijk}

where i = 1,2,...,A, j=1,2,...,B, k=1,2,...n, with the
usual constraints that sum a_i = sum b_j = sum_i ab_{ij}
= sum_j ab_{ij} = 0.  Then the effect sizes are:

    SD^2(a) = sum_i  a_i^2 / (A-1)
    
    SD^2(b) = sum_j  b_j^2 / (B-1)
    
    SD^2(ab) = sum_i sum_j  ab_{ij}^2 / [(A-1)(B-1)]

Some people prefer the cell-means model:

    Y_{ijk} = mu_{ij} + E_{ijk}

in which case

    SD^2(a) = sum_i (mu_{i.} - mu_{..})^2 / (A-1)

    SD^2(b) = sum_j (mu_{.j} - mu_{..})^2 / (B-1)
    
    SD^2(ab) = sum_i sum_j  (mu_{ij} - mu_{i.} - mu_{.j} 
                   + mu_{..})^2 / [(A-1)(B-1)]

where any subscript of "." indicates averaging.