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

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)
#> Power and Effect sizes for ANOVA tests
#>                 power partial_eta_squared cohen_f non_centrality
#> condition           5              0.0000  0.0000              0
#> voice             100              0.5618  1.1323             50
#> condition:voice     5              0.0000  0.0000              0
#> 
#> Power and Effect sizes for pairwise comparisons (t-tests)
#>                                                                 power
#> p_condition_cheerful_voice_human_condition_cheerful_voice_robot 99.82
#> p_condition_cheerful_voice_human_condition_sad_voice_human       5.00
#> p_condition_cheerful_voice_human_condition_sad_voice_robot      99.82
#> p_condition_cheerful_voice_robot_condition_sad_voice_human      99.82
#> p_condition_cheerful_voice_robot_condition_sad_voice_robot       5.00
#> p_condition_sad_voice_human_condition_sad_voice_robot           99.82
#>                                                                 effect_size
#> p_condition_cheerful_voice_human_condition_cheerful_voice_robot       -0.79
#> p_condition_cheerful_voice_human_condition_sad_voice_human             0.00
#> p_condition_cheerful_voice_human_condition_sad_voice_robot            -0.79
#> p_condition_cheerful_voice_robot_condition_sad_voice_human             0.79
#> p_condition_cheerful_voice_robot_condition_sad_voice_robot             0.00
#> p_condition_sad_voice_human_condition_sad_voice_robot                 -0.79