OneWayANOVATest seems to differ with different group sizes

[andevellicus]

I'm a bit of a stats noob so I'm not sure if this is expected behavior or not, but when using GLM's ftest to do ANOVA calculations, and HypothesisTests OneWayANOVATest, I get different results with different sample sizes (see below)

MWE:

using GLM, StatsKit
# This set of data results in the same F-score and p-value
#=
g1 = [51, 87, 50, 48, 79, 61, 53, 54]
g2 = [82, 91, 92, 80, 52, 79, 73, 74]
g3 = [79, 84, 74, 98, 63, 83, 85, 58]
g4 = [85, 80, 65, 71, 67, 51, 63, 93]
=#

# This set of data results in a different F-score and p-value
g1 = [51, 87, 50, 48, 79, 61, 53]
g2 = [82, 91, 92, 80, 52, 79, 73, 74]
g3 = [79, 84, 74, 98, 63, 83, 85, 58]
g4 = [85, 80, 65, 71, 67, 51]

groups = [g1, g2, g3, g4]
println(OneWayANOVATest(groups...))

df1 = DataFrame(method = 0, scores=g1)
df2 = DataFrame(method = 1, scores=g2)
df3 = DataFrame(method = 2, scores=g3)
df4 = DataFrame(method = 3, scores=g4)

df = vcat(df1, df2, df3, df4)
df.method = categorical(df.method)

nullModel = lm(@formula(scores ~ 1), df)
methodModel = lm(@formula(scores ~ method), df)

println(nullModel)
println(methodModel)
ftest(nullModel.model, methodModel.model)

[wildart]

It's a bug. The overall sample mean computed as mean of means, which is true only if samples of the equal size.

HypothesisTests.jl/src/var_equality.jl

Lines 62 to 63 in dd35ae0

	Z̄ᵢ = mean.(scores)
	Z̄ = mean(Z̄ᵢ)

Fix:

Z̄ = sum(Iterators.flatten(groups))/sum(Nᵢ)