add mean difference scaling?

[garner-code]

Info in PsyR documentation:

Scaling Options allow you to change the scale of contrast coefficients so that each contrast can
be expressed as a mean difference contrast (a difference between the means of two subsets of
means), or in a form appropriate for the interpretation of a first-order or higher-order product
interaction contrast. Contrast coefficient scaling has no effect on contrast sums of squares or on
test statistics, so if you are interested in using confidence intervals only to carry out significance
tests (by seeing whether zero is or is not inside an interval), then you may as well use the
default. Correct scaling is critical for the correct interpretation of contrast values as effect sizes,
and of confidence intervals on contrast values. The default option (mean difference contrasts) is
appropriate for the analysis of most single factor designs (trend analysis being the most obvious
exception). If the design has one between-subjects and one within-subjects factor, the default
option produces mean difference scaling for main effect contrasts, and expresses each
Between × Within (BW) interaction contrast as a Between mean difference in a Within mean
difference. This scaling is generally appropriate for main and interaction effect contrasts in
two-factor designs.
Rescaled contrast coefficients are printed in the output immediately above tables of confidence
intervals. If you do not want the coefficients to be rescaled, select the No Rescaling option.

Designs with more than one factor of a particular type (Between or Within) will generally require
more than one run through PSY to produce appropriately scaled confidence intervals for all
contrasts. In general, mean difference scaling is appropriate for simple and main effect
contrasts. (Appropriately scaled individual confidence intervals on all such contrasts can be
constructed in one run; more than one run may be required for the construction of appropriately
scaled simultaneous confidence intervals.) The scaling of interaction contrasts depends (or
should depend) on the order of the interaction. The Interaction Contrasts option allows you to
specify a scaling appropriate for Between × Between contrasts of a given order (a two-factor
interaction involving only Between factors is of order 1) and/or a scaling appropriate for Within ×
Within contrasts of a given order (a three-factor interaction involving only Within factors is of
order 2). The default order (0) is appropriate for main effect mean difference contrasts. Any
higher-order Between × Within contrast defined by PSY will be scaled appropriately if the
Between and Within contrasts on which it is based are both scaled appropriately.

Example: Data from a 2 × 3 × (4) design (two Between factors, called here U and V; one Within
factor; 6 groups, 4 measurements per subject) are submitted to PSY with 3 Between main effect
contrasts (U, V1 and V2), 2 Between product interaction contrasts (UV1 and UV2), and 3 Within
contrasts (W1, W2 and W3). The user provides coefficients for the 5 Between contrasts (U, V1,
V2, UV1 and UV2) and the 3 Within contrasts. PSY defines 15 Between × Within product
interaction contrasts [9 first-order (double) interaction contrasts UW1, UW2, UW3, V1W1,
V1W2, V1W3, V2W1, V2W2 and V2W3 and 6 second-order (triple) interaction contrasts
UV1W1, UV1W2, UV1W3, UV2W1, UV2W2 and UV2W3]. A PSY run with all default options in
place will produce 95% individual confidence intervals for all 23 contrasts, with the 8
user-defined contrasts scaled as mean difference contrasts, and the 15 PSY-defined BW
contrasts scaled as first-order interaction contrasts. The main effect contrasts U, V1, V2, W1,
W2 and W3 will be scaled appropriately, as will the (PSY-defined) first-order Between × Within
interaction contrasts derived from them (UW1, UW2, UW3, V1W1, V1W2, V1W3, V2W1, V2W2
and V2W3). User-defined Between × Between interaction contrasts (UV1 and UV2) will be
scaled inappropriately, if the user wishes to interpret each of these contrasts as a mean
difference in a mean difference (perhaps a difference between two effect sizes). Higher-order
interaction contrasts based on these contrasts (namely UV1W1, UV1W2, UV1W3, UV2W1,
UV2W2 and UV2W3) will also be scaled inappropriately, if the user wishes to interpret each as
a mean difference in the magnitude of a properly scaled first-order interaction. After the first
PSY run is completed, pressing the Run Analysis button brings up the Analysis Options screen
again, and the user should select Interaction Contrasts, Between order = 1, retaining the Within
order default option of 0. In the second run all Between contrasts will be scaled as first-order
interaction contrasts, so the contrasts UV1 and UV2 will be scaled appropriately, as will the
second-order Between × Within contrasts UV1W1, UV1W2, UV1W3, UV2W1, UV2W2 and
UV2W3.