Sample size and power determination for multivariate regression ---------------------------------------------------------------
^mvsamp1i^ # [^, a^lpha^(^#^) p^ower^(^#^) n(^#^) ny(^#^) nx(^#^) nc(^#^) > ^ ]
^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.
^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.
^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.
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
David E. Moore The Hartman Group, Inc. email: email@example.com
Also see --------
Manual: ^[R] sampsi^ Reference: Cohen, J. 1988. Statistical Power Analysis for the Behavioral Sciences, 2nd Ed. Hillsdale, New Jersey: LEA.