This R Markdown document is used to compute the factors \(k_1\) and \(k_2\).

library(tidyverse)
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## ✔ tibble  3.1.7     ✔ dplyr   1.0.9
## ✔ tidyr   1.2.0     ✔ stringr 1.4.0
## ✔ readr   2.1.2     ✔ forcats 0.5.1
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library(furrr)
## Loading required package: future
## 
## Attaching package: 'future'
## The following object is masked from 'package:rmarkdown':
## 
##     run
library(cmstatr)
library(EquivSample)
plan(multisession, workers = 12)

factors <- expand_grid(
  alpha = c(0.05, 0.01, 0.005),
  n = c(12, 18, 24, 30, 36, 50, 100, 1000, Inf),
  m = c(3, 4, 5, 6, 7, 8, 9, 10)
) %>% 
  future_pmap(
    function(alpha, n, m) {
      if (is.infinite(n)) {
        res <- k_equiv(alpha, m)
      } else {
        res <- k_equiv_two_sample(n, m, alpha)
      }
      tibble(alpha = alpha, n = n, m = m,
             k1 = res[1],
             k2 = res[2]
      )
    }
  ) %>% 
  bind_rows()
factors
## # A tibble: 216 × 5
##    alpha     n     m    k1    k2
##    <dbl> <dbl> <dbl> <dbl> <dbl>
##  1  0.05    12     3  2.76 1.33 
##  2  0.05    12     4  2.94 1.20 
##  3  0.05    12     5  3.07 1.11 
##  4  0.05    12     6  3.18 1.05 
##  5  0.05    12     7  3.27 0.998
##  6  0.05    12     8  3.34 0.959
##  7  0.05    12     9  3.41 0.927
##  8  0.05    12    10  3.46 0.901
##  9  0.05    18     3  2.60 1.24 
## 10  0.05    18     4  2.75 1.11 
## # … with 206 more rows
write_csv(factors, file = "factors.csv")
sessionInfo()
## R version 4.2.0 (2022-04-22)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 20.04.4 LTS
## 
## Matrix products: default
## BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.9.0
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.9.0
## 
## locale:
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##  [5] LC_MONETARY=en_CA.UTF-8    LC_MESSAGES=en_CA.UTF-8   
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## [11] LC_MEASUREMENT=en_CA.UTF-8 LC_IDENTIFICATION=C       
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
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## other attached packages:
##  [1] EquivSample_1.0.0 cmstatr_0.9.1     furrr_0.3.0       future_1.25.0    
##  [5] forcats_0.5.1     stringr_1.4.0     dplyr_1.0.9       purrr_0.3.4      
##  [9] readr_2.1.2       tidyr_1.2.0       tibble_3.1.7      ggplot2_3.3.6    
## [13] tidyverse_1.3.1   rmarkdown_2.14   
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## loaded via a namespace (and not attached):
##  [1] Rcpp_1.0.8.3      lubridate_1.8.0   listenv_0.8.0     assertthat_0.2.1 
##  [5] digest_0.6.29     utf8_1.2.2        parallelly_1.31.1 R6_2.5.1         
##  [9] cellranger_1.1.0  backports_1.4.1   reprex_2.0.1      evaluate_0.15    
## [13] httr_1.4.3        pillar_1.7.0      kSamples_1.2-9    rlang_1.0.2      
## [17] readxl_1.4.0      rstudioapi_0.13   jquerylib_0.1.4   bit_4.0.4        
## [21] munsell_0.5.0     broom_0.8.0       compiler_4.2.0    modelr_0.1.8     
## [25] xfun_0.30         pkgconfig_2.0.3   globals_0.14.0    htmltools_0.5.2  
## [29] tidyselect_1.1.2  codetools_0.2-18  fansi_1.0.3       crayon_1.5.1     
## [33] tzdb_0.3.0        dbplyr_2.1.1      withr_2.5.0       SuppDists_1.1-9.7
## [37] MASS_7.3-57       grid_4.2.0        jsonlite_1.8.0    gtable_0.3.0     
## [41] lifecycle_1.0.1   DBI_1.1.2         magrittr_2.0.3    scales_1.2.0     
## [45] vroom_1.5.7       cli_3.3.0         stringi_1.7.6     fs_1.5.2         
## [49] xml2_1.3.3        bslib_0.3.1       ellipsis_0.3.2    generics_0.1.2   
## [53] vctrs_0.4.1       tools_4.2.0       bit64_4.0.5       glue_1.6.2       
## [57] hms_1.1.1         parallel_4.2.0    fastmap_1.1.0     yaml_2.3.5       
## [61] colorspace_2.0-3  rvest_1.0.2       knitr_1.39        haven_2.5.0      
## [65] sass_0.4.1