ANOVA_exact {Superpower}

Simulates an exact dataset (mu, sd, and r represent empirical, not population, mean and covariance matrix) from the design to calculate power

Description

Simulates an exact dataset (mu, sd, and r represent empirical, not population, mean and covariance matrix) from the design to calculate power

Usage

ANOVA_exact(
  design_result,
  correction = Superpower_options("correction"),
  alpha_level = Superpower_options("alpha_level"),
  verbose = Superpower_options("verbose"),
  emm = Superpower_options("emm"),
  emm_model = Superpower_options("emm_model"),
  contrast_type = Superpower_options("contrast_type"),
  liberal_lambda = Superpower_options("liberal_lambda"),
  emm_comp
)

ANOVA_exact2(
  design_result,
  correction = Superpower_options("correction"),
  alpha_level = Superpower_options("alpha_level"),
  verbose = Superpower_options("verbose"),
  emm = Superpower_options("emm"),
  emm_model = Superpower_options("emm_model"),
  contrast_type = Superpower_options("contrast_type"),
  emm_comp,
  liberal_lambda = Superpower_options("liberal_lambda")
)

Arguments

design_result

Output from the ANOVA_design function

correction

Set a correction of violations of sphericity. This can be set to "none", "GG" Greenhouse-Geisser, and "HF" Huynh-Feldt

alpha_level

Alpha level used to determine statistical significance

verbose

Set to FALSE to not print results (default = TRUE)

emm

Set to FALSE to not perform analysis of estimated marginal means

emm_model

Set model type ("multivariate", or "univariate") for estimated marginal means

contrast_type

Select the type of comparison for the estimated marginal means. Default is pairwise. See ?emmeans::'contrast-methods' for more details on acceptable methods.

liberal_lambda

Logical indicator of whether to use the liberal (cohen_f^2\*(num_df+den_df)) or conservative (cohen_f^2\*den_df) calculation of the noncentrality (lambda) parameter estimate. Default is FALSE.

emm_comp

Set the comparisons for estimated marginal means comparisons. This is a factor name (a), combination of factor names (a+b), or for simple effects a | sign is needed (a|b)

Value

Returns dataframe with simulation data (power and effect sizes!), anova results and simple effect results, plot of exact data, and alpha_level. Note: Cohen's f = sqrt(pes/1-pes) and the noncentrality parameter is = f^2*df(error)

"dataframe"

A dataframe of the simulation result.

"aov_result"

aov object returned from aov_car.

"aov_result"

emmeans object returned from emmeans.

"main_result"

The power analysis results for ANOVA level effects.

"pc_results"

The power analysis results for the pairwise (t-test) comparisons.

"emm_results"

The power analysis results of the pairwise comparison results.

"manova_results"

Default is "NULL". If a within-subjects factor is included, then the power of the multivariate (i.e. MANOVA) analyses will be provided.

"alpha_level"

The alpha level, significance cut-off, used for the power analysis.

"method"

Record of the function used to produce the simulation

"plot"

A plot of the dataframe from the simulation; should closely match the meansplot in ANOVA_design

Functions

• ANOVA_exact2: An extension of ANOVA_exact that uses the effect sizes calculated from very large sample size empirical simulation. This allows for small sample sizes, where ANOVA_exact cannot, while still accurately estimating power. However, model objects (emmeans and aov) are not included as output, and pairwise (t-test) results are not currently supported.

Warnings

Varying the sd or r (e.g., entering multiple values) violates assumptions of homoscedascity and sphericity respectively

Examples

## Set up a within design with 2 factors, each with 2 levels,
## with correlation between observations of 0.8,
## 40 participants (who do all conditions), and standard deviation of 2
## with a mean pattern of 1, 0, 1, 0, conditions labeled 'condition' and
## 'voice', with names for levels of "cheerful", "sad", amd "human", "robot"
design_result <- ANOVA_design(design = "2w*2w", n = 40, mu = c(1, 0, 1, 0),
      sd = 2, r = 0.8, labelnames = c("condition", "cheerful",
      "sad", "voice", "human", "robot"))
exact_result <- ANOVA_exact(design_result, alpha_level = 0.05)