Stata 15 help for power

[PSS] power -- Power and sample-size analysis for hypothesis tests

Syntax

Compute sample size

power method ... [, power(numlist) power_options ...]

Compute power

power method ..., n(numlist) [power_options ...]

Compute effect size and target parameter

power method ..., n(numlist) power(numlist) [power_options ...]

method Description ------------------------------------------------------------------------- One sample onemean One-sample mean test (one-sample t test) oneproportion One-sample proportion test onecorrelation One-sample correlation test onevariance One-sample variance test

Two independent samples twomeans Two-sample means test (two-sample t test) twoproportions Two-sample proportions test twocorrelations Two-sample correlations test twovariances Two-sample variances test

Two paired samples pairedmeans Paired-means test (paired t test) pairedproportions Paired-proportions test (McNemar's test)

Analysis of variance oneway One-way ANOVA twoway Two-way ANOVA repeated Repeated-measures ANOVA

Linear regression oneslope Slope test in a simple linear regression rsquared R^2 test in a multiple linear regression pcorr Partial-correlation test in a multiple linear regression

Contingency tables cmh Cochran-Mantel-Haenszel test (stratified 2 x 2 tables) mcc Matched case-control studies trend Cochran-Armitage trend test (linear trend in J x 2 table)

Survival analysis cox Cox proportional hazards model exponential Two-sample exponential test logrank Log-rank test

Cluster randomized design (CRD) onemean, cluster One-sample mean test in a CRD oneproportion, cluster One-sample proportion test in a CRD twomeans, cluster Two-sample means test in a CRD twoproportions, cluster Two-sample proportions test in a CRD logrank, cluster Log-rank test in a CRD

User-define methods usermethod Add your own method to power -------------------------------------------------------------------------

power_options Description ------------------------------------------------------------------------- Main * alpha(numlist) significance level; default is alpha(0.05) * power(numlist) power; default is power(0.8) * beta(numlist) probability of type II error; default is beta(0.2) * n(numlist) sample size; required to compute power or effect size * n1(numlist) sample size of the control group * n2(numlist) sample size of the experimental group * nratio(numlist) ratio of sample sizes, N2/N1; default is nratio(1), meaning equal group sizes compute(N1|N2) solve for N1 given N2 or for N2 given N1 nfractional allow fractional sample size direction(upper|lower) direction of the effect for effect-size determination; default is direction(upper), which means that the postulated value of the parameter is larger than the hypothesized value onesided one-sided test; default is two sided parallel treat number lists in starred options or in command arguments as parallel when multiple values per option or argument are specified (do not enumerate all possible combinations of values)

Table [no]table[(tablespec)] suppress table or display results as a table; see [PSS] power, table saving(filename [, replace]) save the table data to filename; use replace to overwrite existing filename

Graph graph[(graphopts)] graph results; see [PSS] power, graph

Iteration init(#) initial value of the estimated parameter; default is method specific iterate(#) maximum number of iterations; default is iterate(500) tolerance(#) parameter tolerance; default is tolerance(1e-12) ftolerance(#) function tolerance; default is ftolerance(1e-12) [no]log suppress or display iteration log [no]dots suppress or display iterations as dots

notitle suppress the title ------------------------------------------------------------------------- * Specifying a list of values in at least two starred options, or at least two command arguments, or at least one starred option and one argument results in computations for all possible combinations of the values; see numlist. Also see the parallel option. Options n1(), n2(), nratio(), and compute() are available only for two-independent-samples methods. Iteration options are available only with computations requiring iteration. notitle does not appear in the dialog box.

Menu

Statistics > Power and sample size

Description

The power command is useful for planning studies. It performs power and sample-size analysis for studies that use hypothesis testing to form inferences about population parameters. You can compute sample size given power and effect size, power given sample size and effect size, or the minimum detectable effect size and the corresponding target parameter given power and sample size. You can display results in a table ([PSS] power, table) and on a graph ([PSS] power, graph).

Options

+------+ ----+ Main +-------------------------------------------------------------

alpha(numlist) sets the significance level of the test. The default is alpha(0.05).

power(numlist) sets the power of the test. The default is power(0.8). If beta() is specified, this value is set to be 1 - beta(). Only one of power() or beta() may be specified.

beta(numlist) sets the probability of a type II error of the test. The default is beta(0.2). If power() is specified, this value is set to be 1 - power(). Only one of beta() or power() may be specified.

n(numlist) specifies the total number of subjects in the study to be used for power or effect-size determination. If n() is specified, the power is computed. If n() and power() or beta() are specified, the minimum effect size that is likely to be detected in a study is computed.

n1(numlist) specifies the number of subjects in the control group to be used for power or effect-size determination.

n2(numlist) specifies the number of subjects in the experimental group to be used for power or effect-size determination.

nratio(numlist) specifies the sample-size ratio of the experimental group relative to the control group, N2/N1, for power or effect-size determination for two-sample tests. The default is nratio(1), meaning equal allocation between the two groups.

compute(N1|N2) requests that the power command compute one of the group sample sizes given the other one instead of the total sample size for two-sample tests. To compute the control-group sample size, you must specify compute(N1) and the experimental-group sample size in n2(). Alternatively, to compute the experimental-group sample size, you must specify compute(N2) and the control-group sample size in n1().

nfractional specifies that fractional sample sizes be allowed. When this option is specified, fractional sample sizes are used in the intermediate computations and are also displayed in the output.

Also see the description and the use of options n(), n1(), n2(), nratio(), and compute() for two-sample tests in [PSS] unbalanced designs.

direction(upper|lower) specifies the direction of the effect for effect-size determination. For most methods, the default is direction(upper), which means that the postulated value of the parameter is larger than the hypothesized value. For survival methods, the default is direction(lower), which means that the postulated value is smaller than the hypothesized value.

onesided indicates a one-sided test. The default is two sided.

parallel requests that computations be performed in parallel over the lists of numbers specified for at least two study parameters as command arguments, starred options allowing numlist, or both. That is, when parallel is specified, the first computation uses the first value from each list of numbers, the second computation uses the second value, and so on. If the specified number lists are of different sizes, the last value in each of the shorter lists will be used in the remaining computations. By default, results are computed over all combinations of the number lists.

For example, let a_1 and a_2 be the list of values for one study parameter, and let b_1 and b_2 be the list of values for another study parameter. By default, power will compute results for all possible combinations of the two values in two study parameters: (a_1,b_1), (a_1,b_2), (a_2,b_1), and (a_2,b_2). If parallel is specified, power will compute results for only two combinations: (a_1,b_1) and (a_2,b_2).

+-------+ ----+ Table +------------------------------------------------------------

notable, table, and table() control whether or not results are displayed in a tabular format. table is implied if any number list contains more than one element. notable is implied with graphical output -- when either the graph or the graph() option is specified. table() is used to produce custom tables. See [PSS] power, table for details.

saving(filename [, replace]) creates a Stata data file (.dta file) containing the table values with variable names corresponding to the displayed columns. replace specifies that filename be overwritten if it exists. saving() is only appropriate with tabular output.

+-------+ ----+ Graph +------------------------------------------------------------

graph and graph() produce graphical output; see [PSS] power, graph for details.

The following options control an iteration procedure used by the power command for solving nonlinear equations.

+-----------+ ----+ Iteration +--------------------------------------------------------

init(#) specifies an initial value for the estimated parameter. Each power method sets its own default value. See the documentation entry of the method for details.

iterate(#) specifies the maximum number of iterations for the Newton method. The default is iterate(500).

tolerance(#) specifies the tolerance used to determine whether successive parameter estimates have converged. The default is tolerance(1e-12). See Convergence criteria in [M-5] solvenl() for details.

ftolerance(#) specifies the tolerance used to determine whether the proposed solution of a nonlinear equation is sufficiently close to 0 based on the squared Euclidean distance. The default is ftolerance(1e-12). See Convergence criteria in [M-5] solvenl() for details.

log and nolog specify whether an iteration log is to be displayed. The iteration log is suppressed by default. Only one of log, nolog, dots, or nodots may be specified.

dots and nodots specify whether a dot is to be displayed for each iteration. The iteration dots are suppressed by default. Only one of dots, nodots, log, or nolog may be specified.

The following option is available with power but is not shown in the dialog box:

notitle prevents the command title from displaying.

Examples

Examples: One-sample mean test

Compute the required sample size for a two-sided test of Ho: mu=2 versus Ha: mu=2.5 assuming a standard deviation of 0.8, significance level of 5% (the default) and power of 0.80 (also the default) . power onemean 2 2.5, sd(0.8)

Compute the power of the test in the previous example, assuming a sample size of 50 . power onemean 2 2.5, sd(0.8) n(50)

Same as above, reporting output in a table . power onemean 2 2.5, sd(0.8) n(50) table

Produce a table showing the power of the test for sample sizes 25, 50, and 100, using a significance level of 1% (0.01) . power onemean 2 2.5, sd(0.8) n(25 50 100) alpha(0.01)

Compute the required sample size for a one-sided test . power onemean 2 2.5, sd(0.8) onesided

Examples: Two-sample means test

Compute the required sample size for a two-sided two-sample means test assuming a control-group mean of 12, an experimental-group mean of 16, a significance level of 5%, and desired power of 80%; assume both groups have a standard deviation of 5 . power twomeans 12 16, sd(5)

Same as above but assuming a control-group standard deviation of 5 and an experimental-group standard deviation of 7 . power twomeans 12 16, sd1(5) sd2(7)

Same as above, assuming our experimental group is one-half the size of the control group . power twomeans 12 15, sd1(5) sd2(7) nratio(0.5)

Same as first example, using the diff() option to specify the mean difference under Ha . power twomeans 12, sd(5) diff(4)

Examples: ANOVA

Consider power and sample-size analysis for an overall F test of the equality of group means for a three-group one-way ANOVA model. For power and sample-size computations, the postulated group means are 260, 289, and 295; and the error variance is assumed to be 4900. The significance level is set at 5%.

Compute the required sample size given power of 80%, the default . power oneway 260 289 295, varerror(4900)

Compute power given a sample size of 300 . power oneway 260 289 295, n(300) varerror(4900)

Compute the minimum effect size detectable with a power of 80% given a sample size of 300 equally allocated among 3 groups . power oneway, n(300) power(0.8) ngroups(3)

Specify error variance to compute the corresponding between-group variance . power oneway, n(300) power(0.8) ngroups(3) varerror(4900)

Stored results

power stores the following in r():

Scalars r(alpha) significance level r(power) power r(beta) probability of a type II error r(delta) effect size r(N) total sample size r(N_a) actual sample size r(N1) sample size of the control group r(N2) sample size of the experimental group r(nratio) ratio of sample sizes, N2/N1 r(nratio_a) actual ratio of sample sizes r(nfractional) 1 if nfractional is specified, 0 otherwise r(onesided) 1 for a one-sided test, 0 otherwise r(separator) number of lines between separator lines in the table r(divider) 1 if divider is requested in the table, 0 otherwise r(init) initial value of the estimated parameter r(maxiter) maximum number of iterations r(iter) number of iterations performed r(tolerance) requested parameter tolerance r(deltax) final parameter tolerance achieved r(ftolerance) requested distance of the objective function from zero r(function) final distance of the objective function from zero r(converged) 1 if iteration algorithm converged, 0 otherwise

Macros r(type) test r(method) the name of the specified method r(direction) upper or lower r(columns) displayed table columns r(labels) table column labels r(widths) table column widths r(formats) table column formats

Matrices r(pss_table) table of results

Also see Stored results in the method-specific manual entries for additional stored results.


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