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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_10^ Adjusted 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.