```.-
help for ^mvsamp1i^                                              (David E. Moor
> e)
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Sample size and power determination for multivariate regression
---------------------------------------------------------------

^mvsamp1i^ # [^, a^lpha^(^#^) p^ower^(^#^) n(^#^) ny(^#^) nx(^#^) nc(^#^)
> ^ ]

Description
-----------

^mvsamp1i^ estimates required sample size or power of tests for multivariate
F tests derived from Wilks' lambda.  If ^n()^ is specified, ^mvsamp1i^ computes
>
power; otherwise, it computes sample size.  ^mvsamp1i^ is an immediate command;
>
all of its arguments are numbers; see help @immed@.

At a given value of Wilks' lambda, ^mvsamp1i^ computes power for alpha and n,
or sample size for alpha and power.

Options
-------

^alpha(^#^)^ specifies the significance level of the test; the default is
1-level/100 from ^set level^, see help @level@.

^power(^#^)^ is power of the test; the default is ^power(.90)^.

^n(^#^)^ specifies the size of the sample.  If specified, ^mvsamp1i^
reports the power calculation.  If not specified, ^mvsamp1i^ computes
sample size.

^ny(^#^)^ specifies the number of dependent variables.  Default is 1.

^nx(^#^)^ specifies the number of independent variables.  Count all but one
category of any categorical variable as separate independent variables
(e.g., a five category variable counts as four independent variables).
Default is 1.

^nc(^#^)^ specifies the number of control variables; categorical variables
treated as in ^nx()^.  Default is 0.

Remarks
-------

^mvsamp1i^ follows Cohen's method of calculating power for multivariate
F tests based on Wilks' lambda (Cohen, 1988: 550-552).  A square root
normal approximation of the noncentral F distribution is used to obtain
power values.  The noncentrality parameter is a function of effect size,
sample size, and numerator df; effect size depends on Wilks' lambda, and
the number of dependent and independent variables.

Examples
--------

Compute power with lambda = .75, ny = 8, nx = 6, nc = 0, n = 100,
alpha = .01:

. ^mvsamp1i .75, n(100) ny(8) nx(6) a(.01)^

Compute sample size with lambda = .75, ny = 8, nx = 6, nc = 0, power = .8:

. ^mvsamp1i .75, ny(8) nx(6) p(.8)^

Stored results
--------------

^mvsamp1i^ stores in the ^\$S_^# macros:

^S_1^    Sample size
^S_2^    Alpha
^S_3^    Power
^S_4^    Wilks' lambda
^S_5^    Effect size
^S_6^    F associated with Wilks' lambda
^S_7^    df1 for F associated with Wilks' lambda
^S_8^    df2 for F associated with Wilks' lambda
^S_9^    R squared
^S_11^    Noncentrality parameter

Author
------

David E. Moore
The Hartman Group, Inc.
email: david@tinderboxthg.com

Also see
--------

Manual:  ^[R] sampsi^
Reference:  Cohen, J.  1988.  Statistical Power Analysis for the Behavioral
Sciences, 2nd Ed.  Hillsdale, New Jersey: LEA.
```