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help for ^mvsampsi^ (David E. Moore)
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Sample size and power determination for multivariate regression
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^mvsampsi^ # [^, a^lpha^(^#s^) p^ower^(^#s^) n(^#s^) ny(^#^) nx(^#^) nc(^#^)^ ]
Description
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^mvsampsi^ estimates required sample size or power of tests for multivariate
F tests derived from Wilks' lambda. If ^n()^ is specified, ^mvsampsi^ computes
power; otherwise, it computes sample size. ^mvsampsi^ is an immediate command;
all of its arguments are numbers or ranges of numbers; see help @immed@.
At a given value of Wilks' lambda, ^mvsampsi^ computes power for each combina-
tion of alpha and n, or sample size for each combination of alpha and power.
Options
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Options that accept a range of values understand single values, a comma and/or
space delimited list of values, or entries of the form: #1 - #2 / #3. The
latter specification acts as if you had entered every value between #1 and #2
at intervals of #3. If #2 > #1, #3 is added to #1, otherwise #3 is subtracted
from #1 (i.e., it takes the absolute value of #3). Thus, specifying a range
of ".01 - .05 / .01" is equivalent to ".05 - .01 / .01."
^alpha(^#s^)^ specifies the significance level of the test; the default is
1-level/100 from ^set level^, see help @level@.
^power(^#s^)^ is power of the test; the default is ^power(.90)^.
^n(^#s^)^ specifies the size(s) of the sample(s). If specified, ^mvsampsi^
reports the power calculation. If not specified, ^mvsampsi^ 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
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^mvsampsi^ 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. ^mvsampsi^ quietly
calls ^mvsamp1i^ to perform the calculations; see help @mvsamp1i@.
Examples
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Compute power with lambda = .75, ny = 8, nx = 6, nc = 0, n = 100,
alpha = .01 and .05:
. ^mvsampsi .75, n(100) ny(8) nx(6) a(.01,.05)^
Compute power with lambda = .75, ny = 8, nx = 6, nc = 0, n = 100,
alpha = .01 to .05 at every .01:
. ^mvsampsi .75, n(100) ny(8) nx(6) a(.01-.05/.01)^
Compute power with lambda = .75, ny = 8, nx = 6, nc = 0, n = 100 and 200:
. ^mvsampsi .75, n(100 200) ny(8) nx(6)^
Compute sample size with lambda = .75, ny = 8, nx = 6, nc = 0, power = .8:
. ^mvsampsi .75, ny(8) nx(6) p(.8)^
Stored results
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^mvsampsi^ 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_10^ Adjusted R squared
^S_11^ Noncentrality parameter
Author
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David E. Moore
The Hartman Group, Inc.
email: david@tinderboxthg.com
Also see
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Manual: ^[R] sampsi^
On-line: help for @mvsamp1i@
Reference: Cohen, J. 1988. Statistical Power Analysis for the Behavioral
Sciences, 2nd Ed. Hillsdale, New Jersey: LEA.