Chi Squared

Chi-squared test for 2x2 contingency tables derived from two count vectors.

chi_squared(
    first_column::AbstractVector{<:Real},
    second_column::AbstractVector{<:Real};
    yates::Bool = true,
)::Matrix{Float64}

chi_squared(
    matrix::AbstractMatrix{<:Real};
    yates::Bool = true,
)::Matrix{Float64}

Compute chi-squared statistics and p-values for 2x2 contingency tables. The two input vectors (or the two columns of the input matrix) contain non-negative counts. Each entry defines one 2x2 table together with the column sums:

	First	Second
Current entry	a	c
Other entries	sum1 - a	sum2 - c

If yates is true (the default), Yates' continuity correction is applied. The inputs must not contain NaN values. The function works with both dense and sparse inputs.

Returns an n x 3 matrix where the first column contains the chi-squared statistics, the second column contains the p-values (for chi-squared with 1 degree of freedom, computed as erfc(sqrt(chi2 / 2)) ), and the third column contains the FDR-corrected p-values (Benjamini-Hochberg procedure).

result = chi_squared([10, 30, 50], [20, 40, 60])
@assert size(result) == (3, 3)
@views @assert all(result[:, 1] .>= 0)
@views @assert all(0 .<= result[:, 2] .<= 1)
@views @assert all(0 .<= result[:, 3] .<= 1)
@views @assert all(result[:, 3] .>= result[:, 2] .- 1e-12)

# output

result_yates = chi_squared([10, 30], [20, 40]; yates = true)
result_no_yates = chi_squared([10, 30], [20, 40]; yates = false)
@views @assert all(result_yates[:, 1] .<= result_no_yates[:, 1] .+ 1e-12)
@views @assert all(result_yates[:, 2] .>= result_no_yates[:, 2] .- 1e-12)
@views @assert all(result_yates[:, 3] .>= result_yates[:, 2] .- 1e-12)

# output

result = chi_squared([10 20; 30 40; 50 60])
@assert size(result) == (3, 3)

# output