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Fix total mean calculation in ANOVA #273

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Fix total mean calculation in ANOVA #273

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a229016
fix #242
wildart May 28, 2022
f0ff08e
fixed ANOVA test
wildart Jul 22, 2022
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2 changes: 1 addition & 1 deletion src/var_equality.jl
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Expand Up @@ -60,7 +60,7 @@ end
function anova(scores::AbstractVector{<:Real}...)
Nᵢ = [length(g) for g in scores]
Z̄ᵢ = mean.(scores)
Z̄ = mean(Z̄ᵢ)
Z̄ = sum(Iterators.flatten(scores))/sum(Nᵢ)
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Alternatively, one could use

Suggested change
Z̄ = sum(Iterators.flatten(scores))/sum(Nᵢ)
Z̄ = dot(Z̄ᵢ, Nᵢ) / sum(Nᵢ)

In a quick benchmark this seemed to be similarly fast, and usually even marginally faster.

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You'd probably need a very large dataset to see the difference.

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Actually a tiny dataset is sufficient. Of course, the difference is very small but it seemed to be consistent:

julia> using Statistics, LinearAlgebra, BenchmarkTools

julia> function f(scores::AbstractVector{<:Real}...)
           Nᵢ = [length(g) for g in scores]
           Z̄ᵢ = mean.(scores)
           Z̄ = sum(Iterators.flatten(scores)) / sum(Nᵢ)
           return Nᵢ, Z̄ᵢ, Z̄
       end
f (generic function with 1 method)

julia> function g(scores::AbstractVector{<:Real}...)
           Nᵢ = [length(g) for g in scores]
           Z̄ᵢ = mean.(scores)
           Z̄ = dot(Z̄ᵢ, Nᵢ) / sum(Nᵢ)
           return Nᵢ, Z̄ᵢ, Z̄
       end
g (generic function with 1 method)

julia> scores = map(n -> rand(n), (3, 9, 12));

julia> @btime f($(scores...));
  33.893 ns (1 allocation: 64 bytes)

julia> @btime g($(scores...));
  33.687 ns (1 allocation: 64 bytes)

julia> scores = map(n -> rand(n), (3, 9, 12, 134));

julia> @btime f($(scores...));
  33.944 ns (1 allocation: 64 bytes)

julia> @btime g($(scores...));
  33.681 ns (1 allocation: 64 bytes)

julia> scores = map(n -> rand(n), (3, 9, 12, 134, 12, 4134, 1231, 122, 12, 1, 23, 58));

julia> @btime f($(scores...));
  34.070 ns (1 allocation: 64 bytes)

julia> @btime g($(scores...));
  33.781 ns (1 allocation: 64 bytes)

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It looks like something else from Z evaluation dominates in the function. But nanoseconds 😏.

SStᵢ = Nᵢ .* (Z̄ᵢ .- Z̄).^2
SSeᵢ = sum.( (z .- z̄).^2 for (z, z̄) in zip(scores, Z̄ᵢ) )
(Nᵢ, SStᵢ, SSeᵢ)
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3 changes: 2 additions & 1 deletion test/var_equality.jl
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Expand Up @@ -31,7 +31,8 @@ using DelimitedFiles
t = OneWayANOVATest(groups...)
@test nobs(t) == [7, 8, 8, 6]
@test dof(t) == (3,25)
@test pvalue(t) ≈ 0.072 atol=1e-3
@test pvalue(t) ≈ 0.07276 atol=1e-6
@test HypothesisTests.teststatistic(t) ≈ 2.62311 atol=1e-6
@test occursin("reject h_0", sprint(show, t))

# http://www.real-statistics.com/one-way-analysis-of-variance-anova/homogeneity-variances/levenes-test/
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