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

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

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

^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 -------

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 -------

^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 --------

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 --------------

^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 ------

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

Also see --------

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.