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Power Analysis for One-, Two-, Three-Way ANCOVA Contrasts and Multiple Comparisons (T-Tests)

Source: R/ancova.R
power.t.contrast.Rd

Calculates power or sample size for a single one-, two-, three-Way ANCOVA contrast.

Formulas are validated using examples and tables in Shieh (2017).

Usage

power.t.contrast(
  mu.vector,
  sd.vector,
  n.vector = NULL,
  p.vector = NULL,
  contrast.vector,
  r.squared = 0,
  k.covariates = 1,
  power = NULL,
  alpha = 0.05,
  tukey.kramer = FALSE,
  ceiling = TRUE,
  verbose = 1,
  utf = FALSE
)

Arguments

mu.vector

vector; adjusted means (or estimated marginal means) for each level of a factor.

sd.vector

vector; unadjusted standard deviations for each level of a factor.

n.vector

vector; sample sizes for each level of a factor.

p.vector

vector; proportion of total sample size in each level of a factor. These proportions should sum to one.

contrast.vector

vector; a single contrast in the form of a vector with as many elements as number of levels or groups (or cells in factorial designs). Ignored when 'x' is specified.

r.squared

explanatory power of covariates (R-squared) in the ANCOVA model.

k.covariates

Number of covariates in the ANCOVA model.

power

statistical power, defined as the probability of correctly rejecting a false null hypothesis, denoted as \(1 - \beta\).

alpha

type 1 error rate, defined as the probability of incorrectly rejecting a true null hypothesis, denoted as \(\alpha\).

tukey.kramer

logical; FALSE by default. If TRUE adjustments will be made to control Type 1 error.

ceiling

logical; TRUE by default. If FALSE sample sizes in each cell are NOT rounded up.

verbose

1 by default (returns test, hypotheses, and results), if 2 a more detailed output is given (plus key parameters and definitions), if 0 no output is printed on the console.

utf

logical; whether the output should show Unicode characters (if encoding allows for it). FALSE by default.

Value

parms

list of parameters used in calculation.

test

type of the statistical test (T-Test).

psi

contrast-weighted mean difference.

d

contrast-weighted standardized mean difference.

df

degrees of freedom.

t.alpha

critical values.

ncp

non-centrality parameter for the alternative.

null.ncp

non-centrality parameter for the null.

power

statistical power \((1-\beta)\).

n.vector

sample sizes for each level of a factor.

n.total

total sample size.

Details

Note that R has a partial matching feature which allows you to specify shortened versions of arguments, such as mu or mu.vec instead of mu.vector, or such as k or k.cov instead of k.covariates.

References

Shieh, G. (2017). Power and sample size calculations for contrast analysis in ANCOVA. Multivariate Behavioral Research, 52(1), 1-11. https://doi.org/10.1080/00273171.2016.1219841

Examples

# dummy coding example (uses the first contrast from a three-level- / two-contrasts-design)
contrast.object <- factorial.contrasts(factor.levels = 3, coding = "treatment", verbose = 0)
contrast.vector <- contrast.object[["contrast.matrix"]][1, ]
power.t.contrast(mu.vector = c(0.15, 0.30, 0.20),
                 sd.vector = c(1,    1,    1),
                 p.vector  = c(1/3,  1/3,  1/3),
                 r.squared = 0.50, k.covariates = 1,
                 contrast.vector = contrast.vector,
                 power = 0.80, alpha = 0.05)
#> +--------------------------------------------------+
#> |             SAMPLE SIZE CALCULATION              |
#> +--------------------------------------------------+
#> 
#> Single Contrast Analysis (T-Test)
#> 
#> ----------------------------------------------------
#> Hypotheses
#> ----------------------------------------------------
#>   H0 (Null)        : psi  = 0
#>   H1 (Alternative) : psi != 0
#> 
#> ----------------------------------------------------
#> Results
#> ----------------------------------------------------
#>   Total Sample Size    = 9423  <<
#>   Type 1 Error (alpha) = 0.050
#>   Type 2 Error (beta)  = 0.200
#>   Statistical Power    = 0.800
#>