Simulate Contingency Table

Simulate a contingency table with fish counts distributed across n lesion categories and n treatment groups. Probability values for generating counts in each cell (i.e. each factor level combination) can be assigned using the probs argument. This function is designed for use in power and/or false positive rate calculations; for details, see Con_Simul_PR().

Usage

Con_Simul(
  probs = "equal",
  total_count = 750,
  n_lesion = 3,
  n_Trt. = 5,
  margin_fixed_Trt. = FALSE,
  verbose = TRUE
)

Arguments

probs

Matrix of probability values created using matrix(). Each row in the matrix should represent a treatment group and each column a lesion category. All probability values in the matrix should sum to 1. Default = equal probability across all cells.

total_count

Total number of counts in the contingency table. Defaults to 750.

n_lesion

Number of lesion categories. Ignored if probs specified. Defaults to 3.

n_Trt.

Number of treatment groups. Ignored if probs specified. Defaults to 5.

margin_fixed_Trt.

Whether margins are fixed per treatment group (i.e. fixed number of fish per treatment). Default = FALSE. See Details for further information on marginals.

verbose

Whether to print the parameters and probability matrix used. Default = TRUE.

Value

Returns a list containing:

sim_tab		The simulated contingency table containing counts across different treatment groups (rows) and lesion categories (columns)
params		The simulation parameters as a vector
probs		The probability matrix used for simulation

Details

Counts are simulated from a multinomial distribution using rmultinom(). Counts may be assumed to have a fixed total in the marginals (e.g. per treatment group) or no fixed total in row or column marginals.

For further discussion into the types of marginals in contingency tables, refer to: here and the comments on Arguments.

See also

Link for executed Examples which includes any figure outputs.

Examples

# Simulate table with uniform probabilities across cells
Con_Simul(total_count = 750, n_lesion = 3, n_Trt. = 5)
#> $sim_tab
#>     Lesion_Category
#> Trt.  1  2  3
#>    A 48 59 48
#>    B 45 48 50
#>    C 43 50 43
#>    D 48 55 57
#>    E 59 45 52
#> 
#> $params
#>       total_count          n_lesion            n_Trt. margin_fixed_Trt. 
#>               750                 3                 5                 0 
#> 
#> $probs
#>            [,1]       [,2]       [,3]
#> [1,] 0.06666667 0.06666667 0.06666667
#> [2,] 0.06666667 0.06666667 0.06666667
#> [3,] 0.06666667 0.06666667 0.06666667
#> [4,] 0.06666667 0.06666667 0.06666667
#> [5,] 0.06666667 0.06666667 0.06666667
#> 

# Simulate table with specified probabilities across cells
Con_Simul(probs = matrix(nrow = 2, ncol = 3, c(1/6, 3/12, 1/6, 1/6, 1/6, 1/12)))
#> $sim_tab
#>     Lesion_Category
#> Trt.   1   2   3
#>    A 118 153 118
#>    B 175 130  56
#> 
#> $params
#>       total_count          n_lesion            n_Trt. margin_fixed_Trt. 
#>               750                 3                 2                 0 
#> 
#> $probs
#>           [,1]      [,2]       [,3]
#> [1,] 0.1666667 0.1666667 0.16666667
#> [2,] 0.2500000 0.1666667 0.08333333
#>