help rdpower
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Title

    rdpower --   Power calculations for random designs

Syntax
        rdpower design_type, es(#) [options]

    where elements of design_type may be

      rd1                        A simple 1-level design whereby half of the
                                  subjects are assigned treatment and half
                                  are assigned control.  Sample size is n *
                                  2.

      crd2                       A 2-level cluster randomized design where
                                  treatment is at level 2. Sample size is n *
                                  m * 2.

      crd3                       A 3-level cluster randomized design where
                                  treatment is at level 3.  Sample size is n
                                  * p * m * 2.

      rbd2                       A 2-level randomized block design where
                                  treatment is at level 1. Sample size is n *
                                  m * 2.

      rbd3                       A 3-level randomized block design where
                                  treatment is at level 2. Sample size is n *
                                  p * m * 2.

 Description

    rdpower computes power for a variety of randomized designs: a single
    level randomized design where there is no clustering, a two-level cluster
    randomized design where treatment is at level 2, a three-level cluster
    randomized design where treatment is at level 2, a two-level block
    randomized design where treatment is at level 1, and a three-level
    randomized block design where treatment is at level 2.

IMPORTANT: For each design type, the options mean something different so be sur
> e to take note 
of the definitions below.

    options                     Description
    -------------------------------------------------------------------------
    Required for all designs
      es(#)                      A standardized effect size.

    Optional for all designs
      alpha(#)                   The alpha for a two-tailed test.  Default is
                                  0.05.

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    Required for rd1

      n(#)                       The number of cases per treatment

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    Required for crd2

      m(#)                       The number level-2 clusters per treatment.

      n(#)                       The number of cases per level-2 cluster.

      icc2(#)                    The level-2 intraclass correlation (ICC). If
                                  none is specified, an ICC of 0 is assumed,
                                  and the result is the same as rd1.

    Required for crd2 when specifying covariates

      pre1(#)                    The proportion of level-1 variance explained
                                  (R-square) by level 2 covariates.

      pre2(#)                    The proportion of level-2 variance explained
                                  (R-square) by level 2 covariates.

      l2vars(#)                  The number of level-2 covariates.

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    Required for crd3

      m(#)                       The number level-3 clusters per treatment.

      p(#)                       The number level-2 clusters per level-3
                                  cluster

      n(#)                       The number of cases per level-2 cluster.

      icc2(#)                    The level-2 intraclass correlation (ICC).

      icc3(#)                    The level-3 intraclass correlation (ICC).

    Required for crd3 when specifying covariates

      pre1(#)                    The proportion of level-1 variance explained
                                  (R-square) by level-3 covariates.

      pre2(#)                    The proportion of level-2 variance explained
                                  (R-square) by level-3 covariates.

      pre3(#)                    The proportion of level-3 variance explained
                                  (R-square) by level-3 covariates.

      l3vars(#)                  The number of level-3 covariates.

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    Required for rbd2

      m(#)                       The number level-2 clusters.

      n(#)                       The number of cases per treatment per
                                  level-2 cluster.

      icc2(#)                    The level-2 intraclass correlation (ICC).

      v(#)                       The ratio of the variance in treatment
                                  effects across clusters to the total
                                  variance across clusters.

    Required for rbd2 when specifying covariates

      pre1(#)                    The proportion of level-1 variance explained
                                  (R-square) by level 2 covariates.

      pre2(#)                    The proportion of level-2 variance in
                                  treatment effects explained (R-square) by
                                  level 2 covariates.

      l2vars(#)                  The number of level-2 covariates.

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    Required for rbd3

      m(#)                       The number level-3 clusters.

      p(#)                       The number level-2 clusters per treatment
                                  per level-3 cluster

      n(#)                       The number of cases per level-2 cluster.

      icc2(#)                    The level-2 intraclass correlation (ICC).

      icc3(#)                    The level-3 intraclass correlation (ICC).

      v(#)                       The ratio of the variance in treatment
                                  effects across clusters to the total
                                  variance across clusters

    Required for rbd3 when specifying covariates

      pre1(#)                    The proportion of level-1 variance explained
                                  (R-square) by level-3 covariates.

      pre2(#)                    The proportion of level-2 variance explained
                                  (R-square) by level-3 covariates.

      pre3(#)                    The proportion of level-3 variance in the
                                  treatment effects explained (R-square) by
                                  level-3 covariates.

      l3vars(#)                  The number of level-3 covariates.

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Examples

    For a single level design with 80 subjects per treatment group and an
        effect size of 0.40

    . rdpower rd1, es(.4) n(80)

    For a two-level cluster randomized design with 8 clusters per treatment
        group, 50 subjects per cluster, an ICC of 0.2, and an effect size of
        0.50.  Treatment is at level 2.

    . rdpower crd2, es(.5) n(50) m(8) icc2(.2)

    For a two-level cluster randomized design with 8 clusters per treatment
        group, 50 subjects per cluster, an ICC of 0.2, an effect size of
        0.50, with a single level-2 covariate that accounts for 20 percent of
        the variance at level 1 and 20 percent of the variance at level 2.
        Treatment is at level 2.

    . rdpower crd2, es(.5) n(50) m(8) icc2(.2) pre1(.2) pre2(.2) l2vars(1)

    For a three-level cluster randomized design with 8 level-3 clusters per
        treatment group, 2 level-2 clusters per level-3 cluster, 15 subjects
        per level-2 cluster, a level-2 ICC of 0.1, a level-3 icc of 0.20, and
        an effect size of 0.50.  Treatment is at level 3.

    . rdpower crd3, es(.5) n(15) p(2) m(8) icc2(.1) icc3(.2)

    For a three-level cluster randomized design with 8 level-3 clusters per
        treatment group, 2 level-2 clusters per level-3 cluster, 15 subjects
        per level-2 cluster, a level-2 ICC of 0.1, a level-3 icc of 0.20, an
        effect size of 0.50, with a covariate at level 3 that accounts for 10
        percent of the variance at level 1, 20 percent of the variance at
        level 2, and 25 percent of the variance at level 3.  Treatment is at
        level 3.

    . rdpower crd3, es(.5) n(15) p(2) m(8) icc2(.1) icc3(.2) pre1(.1)
        pre2(.2) pre3(.25) l3vars(1)

    For a two-level randomized block design with 8 clusters, 50 subjects per
        treatment and control per cluster, an ICC of 0.2, an effect size of
        0.50, and an estimated variance of the effect of 0.15.

    . rdpower rbd2, es(.5) n(50) m(8) icc2(.2) v(.15)

    For a two-level randomized block design with 8 clusters, 50 subjects per
        treatment group per cluster, an ICC of 0.2, an effect size of 0.50,
        and an estimated variance ratio of 0.15, with a single level 2
        covariate that accounts for 10 percent of the variation at level 1
        and 20 percent of the variation in treatment effects at level 2.

    . rdpower rbd2, es(.5) n(50) m(8) icc2(.2) v(.15) pre1(.1) pre2(.2)
        l2vars(1)

    For a three-level randomized block design with 8 level-3 clusters, 2
        level-2 clusters per treatment, 15 subjects per level-2 cluster, a
        level-2 ICC of 0.1, a level-3 ICC of 0.2, an effect size of 0.50, and
        an estimated variance of the effect of 0.15.

    . rdpower rbd3, es(.5) n(15) p(2) m(8) icc2(.1) icc3(.2) v(.15)

    For a three-level randomized block design with 8 level-3 clusters, 2
        level-2 clusters per treatment, 15 subjects per level-2 cluster, a
        level-2 ICC of 0.1, a level-3 ICC of 0.2, an effect size of 0.50, an
        estimated variance ratio of 0.15, with a single level-3 covariate
        that accounts for 10 percent of the variation at level 1 and 20
        percent of the variation at level 2, and 25 percent of the variance
        in the treatment effects at level 3.

    . rdpower rbd3, es(.5) n(15) p(2) m(8) icc2(.1) icc3(.2) v(.15) pre1(.1)
        pre2(.2) pre3(.25) l3vars(1)

Saved results

    rdpower saves the following in r():

    Scalars        
      r(samplesize)       calculated sample size
      r(n)                n
      r(m)                m
      r(p)                p
      r(icc2)             the specified level-2 ICC
      r(icc3)             the specified level-3 ICC
      r(level2vars)       the specified number of level-2 covariates
      r(level3vars)       the specified number of level-3 covariates
      r(r2_level3)        the specified proportion of explained varinace at
                            level 3
      r(r2_level2)        the specified proportion of explained varinace at
                            level 2
      r(r2_level1)        the specified proportion of explained varinace at
                            level 1
      r(designeffect)     the calculated design effect
      r(treatmentvariance)
                            the specified variance of the treatment effect
      r(alpha)            the alpha level
      r(effectsize)       the specified effect size
      r(noncentral)       the calculated non-centrality parameter of the
                            non-cental t distribution
      r(critical)         the critical t value
      r(power)            the calcuated power

    Macros         
      r(type)             design_type

References

    Hedges, Larry and Rhoads, Christopher. 2009. Statistical Power Analysis
        in Education Research (NCSER 2010-3006). Washington, DC: National
        Center for Special Education Research, Institute of Education
        Sciences, U.S. Department of Education.

    Konstantopoulos, Spyros. 2008. The Power of the Test for Treatment
        Effects in Three-Level Cluster Randomized Designs.  Journal of
        Research on Educational Effectiveness.  1:1, 66-88.

    Konstantopoulos, Spyros. 2008. The Power of the Test for Treatment
        Effects in Three-Level Block Randomized Designs.  Journal of Research
        on Educational Effectiveness.  1:4, 265-288.