CoDA Two Group Hypotheses

Performs the calculations for the hypothesis of equal centers and covariance (H1), of equal covariance with different centers (H2), of equal centers with different covariance (H3), and all at once All, for two diferent samples, using Compositional Data Analysis (CoDA) principles.

Usage

CoDA_2Group_H1(comp1, comp2)

CoDA_2Group_H2(comp1, comp2)

CoDA_2Group_H3(comp1, comp2)

CoDA_2Group_All(comp1, comp2)

Arguments

comp1

A matrix or data frame of observations for composition 1. Entries must be non-zero and positive.

comp2

A matrix or data frame of observations for composition 2. Entries must be non-zero and positive.

Value

A tibble with the statistic (Q), degrees of freedom (nu), p-value, and null hypothesis (H0)

References

Pawlowsky-Hlahn, V., Egozcue, J.J & Tolosna-Delgado, R. (2015). Modeling and analysis of compositional data. John Wiley & Sons.

Aitchison, J. (1986). The statistical analysis of compositional data. Chapman and Hall.

See also

Other compositional data analysis: CoDA_Atyp_Idx(), CoDA_Univariate()

Examples

data("Hongite", package = 'compositions')
data("Kongite", package = 'compositions')
CoDA_2Group_H1(Hongite,Kongite)
#> # A tibble: 1 × 4
#>       Q    nu      pval H0                          
#>   <dbl> <dbl>     <dbl> <chr>                       
#> 1  45.7    14 0.0000316 equal centers and covariance

data("Hongite", package = 'compositions')
data("Kongite", package = 'compositions')
CoDA_2Group_H2(Hongite,Kongite)
#> # A tibble: 1 × 4
#>       Q    nu  pval H0                                     
#>   <dbl> <dbl> <dbl> <chr>                                  
#> 1  10.7    10 0.384 equal covariance with different centers

data("Hongite", package = 'compositions')
data("Kongite", package = 'compositions')
CoDA_2Group_H3(Hongite,Kongite)
#> # A tibble: 1 × 4
#>       Q    nu        pval H0                                     
#>   <dbl> <int>       <dbl> <chr>                                  
#> 1  33.6     4 0.000000893 equal centers with different covariance

data("Hongite", package = 'compositions')
data("Kongite", package = 'compositions')
CoDA_2Group_All(Hongite,Kongite)
#> # A tibble: 3 × 4
#>       Q    nu        pval H0                                     
#>   <dbl> <dbl>       <dbl> <chr>                                  
#> 1  45.7    14 0.0000316   equal centers and covariance           
#> 2  10.7    10 0.384       equal covariance with different centers
#> 3  33.6     4 0.000000893 equal centers with different covariance