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an-ethz/pwr4exp: Power Analysis for Research Experiments

pwr4exp supports statistical power calculations for diverse experimental designs analyzed using linear mixed models.

It provides approximate F-tests for omnibus hypothesis tests and t-tests for specific contrasts, employing the Satterthwaite method for approximating degrees of freedom.

Various correlation structures (R-side) defined in the nlme package can be used to model residuals.

# You can install pwr4exp from CRAN
install.packages("pwr4exp")

# Or the development version from GitHub:
# install.packages("devtools")
devtools::install_github("an-ethz/pwr4exp")

# Load the library
library(pwr4exp)

Performing a power analysis in pwr4exp involves two main steps:

mkdesign is the most flexible function for defining an experimental design based on its data structure, statistical model, treatment effects, and variance-covariance components.

For example, the following code defines a completely randomized design with repeated measures:

# Create a data frame reflecting the data structure
n_trt = 3 # Number of treatments
trt = c("CON", "TRT1", "TRT2")
n_subject = 6 # Number of subjects per treatment
n_hour = 8 # Number of repeated measures (time points)

df.rep <- data.frame(
  subject = as.factor(rep(seq_len(n_trt*n_subject), each = n_hour)),
  hour = as.factor(rep(seq_len(n_hour), n_subject*n_trt)),
  trt = rep(trt, each = n_subject*n_hour)
)

# Create the design object
crd.rep <- mkdesign(
  formula = ~ trt*hour, # model
  data = df.rep, # a data frame reflecting the data structure
  # treatment means at each hour reflecting effects
  means =  c(1, 2.50, 3.5,
             1, 3.50, 4.54,
             1, 3.98, 5.80,
             1, 4.03, 5.4,
             1, 3.68, 5.49,
             1, 3.35, 4.71,
             1, 3.02, 4.08,
             1, 2.94, 3.78), 
  sigma2 = 2, # residual variance
  # residual correlation structure, AR1
  correlation = corAR1(value = 0.6, form = ~ hour|subject) 
)

pwr4exp also provides functions for some common standard designs, allowing a design to be defined by specifying key characteristics like treatment structure and replications, without manually creating a data frame.

# Create a completely randomized design
crd <- designCRD(
  treatments = 4, # one treatment factor with 4 levels
  replicates = 12, # 12 experimental units per treatment
  means = c(30, 28, 33, 35), # treatment means
  sigma2 = 10 # error variance
)

# Create a randomized complete block design
rcbd <- designRCBD(
  # two factors, each with 2 levels (2x2 factorial)
  treatments = c(2, 2), 
  blocks = 10, # 10 blocks
  means = c(30, 28, 33, 35), # treatment means (cell means)
  vcomp = 6, # block variance
  sigma2 = 4 # error variance
)

# Create a Latin Square design
lsd <- designLSD(
  # two factors, with 2 and 3 levels, respectively (2x3 factorial)
  treatments = c(2, 3), 
  squares = 4, # four squares
  reuse = "col", # column blocks are identical acorss squares
  means = c(30, 28, 33, 35, 34, 35), # treatment means (cell means)
  vcomp = c(5, 2), # variances of blocking factor (row and column)
  sigma2 = 3 # error variance
)

# Create a split-plot design
spd <- designSPD(
  trt.main = 2, # one factor with two levels at main plot
  trt.sub = 2, # one factor with two levels at subplot
  # 10 units per main plot factor (blocks at subplot level)
  replicates = 10, 
  means = c(30, 28, 33, 35), # treatment means (cell means)
  vcomp = 7, # main plot error
  sigma2 = 3 # residual error (subplot error)
)

# If not specified, these functions internally use a default model formula that includes main effects and all interactions, with block factors fitted as random effects.

Once the design has been correctly defined, the design object can be passed to power calculation functions, including:

Computes the power of F-tests for omnibus hypotheses.

Computes the power of t-tests for specific contrasts.

pwr.contrast(crd.rep, which = "trt", by = "hour", contrast = "trt.vs.ctrl")

To learn more about power analysis with pwr4exp, refer to the vignette which contains:

• Instructions on preparing and providing the required inputs.
• Examples of power calculations for standard designs available in the package.
• Examples of power analysis for customized designs.
• Fundamental concepts of statistical power in linear mixed models.

For questions or suggestions, please open an issue on our GitHub repository or contact the package maintainer.

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