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T-tests Request different degrees of freedom #188

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T-tests Request different degrees of freedom #188

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7b490c6
allow manual df specification re #181
birm Mar 14, 2020
8a37e91
all df->dof
birm Mar 26, 2020
6afe7de
add dof to docstrings
birm Mar 26, 2020
26f51af
test df->dof
birm Mar 26, 2020
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39 changes: 20 additions & 19 deletions src/t.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -28,7 +28,7 @@ export OneSampleTTest, TwoSampleTTest, EqualVarianceTTest,
abstract type TTest <: HypothesisTest end
abstract type TwoSampleTTest <: TTest end

pvalue(x::TTest; tail=:both) = pvalue(TDist(x.df), x.t; tail=tail)
pvalue(x::TTest; tail=:both) = pvalue(TDist(x.dof), x.t; tail=tail)

default_tail(test::TTest) = :both

Expand All @@ -41,7 +41,7 @@ function StatsBase.confint(x::TTest; level::Float64=0.95, tail=:both)
elseif tail == :right
(StatsBase.confint(x, level=1-(1-level)*2)[1], Inf)
elseif tail == :both
q = quantile(TDist(x.df), 1-(1-level)/2)
q = quantile(TDist(x.dof), 1-(1-level)/2)
(x.xbar-q*x.stderr, x.xbar+q*x.stderr)
else
throw(ArgumentError("tail=$(tail) is invalid"))
Expand All @@ -54,7 +54,7 @@ end
struct OneSampleTTest <: TTest
n::Int # number of observations
xbar::Real # estimated mean
df::Int # degrees of freedom
dof::Int # degrees of freedom
stderr::Real # empirical standard error
t::Real # t-statistic
μ0::Real # mean under h_0
Expand All @@ -66,24 +66,24 @@ population_param_of_interest(x::OneSampleTTest) = ("Mean", x.μ0, x.xbar) # para
function show_params(io::IO, x::OneSampleTTest, ident="")
println(io, ident, "number of observations: $(x.n)")
println(io, ident, "t-statistic: $(x.t)")
println(io, ident, "degrees of freedom: $(x.df)")
println(io, ident, "degrees of freedom: $(x.dof)")
println(io, ident, "empirical standard error: $(x.stderr)")
end

"""
OneSampleTTest(xbar::Real, stddev::Real, n::Int, μ0::Real = 0)
OneSampleTTest(xbar::Real, stddev::Real, n::Int, μ0::Real = 0, dof::Int = n-1)

Perform a one sample t-test of the null hypothesis that `n` values with mean `xbar` and
sample standard deviation `stddev` come from a distribution with mean `μ0` against the
alternative hypothesis that the distribution does not have mean `μ0`.
alternative hypothesis that the distribution does not have mean `μ0`. Degrees of freedom
`dof` may be specified.

Implements: [`pvalue`](@ref), [`confint`](@ref)
"""
function OneSampleTTest(xbar::Real, stddev::Real, n::Int, μ0::Real=0)
function OneSampleTTest(xbar::Real, stddev::Real, n::Int, μ0::Real=0, dof::Int=n-1)
stderr = stddev/sqrt(n)
t = (xbar-μ0)/stderr
df = n-1
OneSampleTTest(n, xbar, df, stderr, t, μ0)
OneSampleTTest(n, xbar, dof, stderr, t, μ0)
end

"""
Expand Down Expand Up @@ -119,7 +119,7 @@ struct EqualVarianceTTest <: TwoSampleTTest
n_x::Int # number of observations
n_y::Int # number of observations
xbar::Real # estimated mean difference
df::Int # degrees of freedom
dof::Int # degrees of freedom
stderr::Real # empirical standard error
t::Real # t-statistic
μ0::Real # mean difference under h_0
Expand All @@ -128,30 +128,31 @@ end
function show_params(io::IO, x::TwoSampleTTest, ident="")
println(io, ident, "number of observations: [$(x.n_x),$(x.n_y)]")
println(io, ident, "t-statistic: $(x.t)")
println(io, ident, "degrees of freedom: $(x.df)")
println(io, ident, "degrees of freedom: $(x.dof)")
println(io, ident, "empirical standard error: $(x.stderr)")
end

testname(::EqualVarianceTTest) = "Two sample t-test (equal variance)"
population_param_of_interest(x::TwoSampleTTest) = ("Mean difference", x.μ0, x.xbar) # parameter of interest: name, value under h0, point estimate

"""
EqualVarianceTTest(x::AbstractVector{T<:Real}, y::AbstractVector{T<:Real})
EqualVarianceTTest(x::AbstractVector{T<:Real}, y::AbstractVector{T<:Real},
dof::Int = length(x)+length(y)-2)

Perform a two-sample t-test of the null hypothesis that `x` and `y` come from distributions
with equal means and variances against the alternative hypothesis that the distributions
have different means but equal variances.
have different means but equal variances. Degrees of freedom `dof` may be specified.

Implements: [`pvalue`](@ref), [`confint`](@ref)
"""
function EqualVarianceTTest(x::AbstractVector{T}, y::AbstractVector{S}, μ0::Real=0) where {T<:Real,S<:Real}
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function EqualVarianceTTest(x::AbstractVector{<:Real}, y::AbstractVector{<:Real}, μ0::Real=0,
dof::Int=length(x)+length(y)-2)
nx, ny = length(x), length(y)
xbar = mean(x) - mean(y)
stddev = sqrt(((nx - 1) * var(x) + (ny - 1) * var(y)) / (nx + ny - 2))
stderr = stddev * sqrt(1/nx + 1/ny)
t = (xbar - μ0) / stderr
df = nx + ny - 2
EqualVarianceTTest(nx, ny, xbar, df, stderr, t, μ0)
EqualVarianceTTest(nx, ny, xbar, dof, stderr, t, μ0)
end


Expand All @@ -161,7 +162,7 @@ struct UnequalVarianceTTest <: TwoSampleTTest
n_x::Int # number of observations
n_y::Int # number of observations
xbar::Real # estimated mean
df::Real # degrees of freedom
dof::Real # degrees of freedom
stderr::Real # empirical standard error
t::Real # t-statistic
μ0::Real # mean under h_0
Expand Down Expand Up @@ -192,6 +193,6 @@ function UnequalVarianceTTest(x::AbstractVector{T}, y::AbstractVector{S}, μ0::R
varx, vary = var(x), var(y)
stderr = sqrt(varx/nx + vary/ny)
t = (xbar-μ0)/stderr
df = (varx / nx + vary / ny)^2 / ((varx / nx)^2 / (nx - 1) + (vary / ny)^2 / (ny - 1))
UnequalVarianceTTest(nx, ny, xbar, df, stderr, t, μ0)
dof = (varx / nx + vary / ny)^2 / ((varx / nx)^2 / (nx - 1) + (vary / ny)^2 / (ny - 1))
UnequalVarianceTTest(nx, ny, xbar, dof, stderr, t, μ0)
end
4 changes: 2 additions & 2 deletions test/t.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -47,15 +47,15 @@ end
a2 = [29.89, 29.93, 29.72, 29.98, 30.02, 29.98]

tst = EqualVarianceTTest(a1, a2)
@test tst.df == 10
@test tst.dof == 10
@test abs(tst.t - 1.959) <= 1e-3
@test abs(pvalue(tst) - 0.078) <= 1e-3
@test all(abs.([confint(tst)...] - [-0.0131, 0.2031]) .<= 1e-4)
@test default_tail(tst) == :both
show(IOBuffer(), tst)

tst = UnequalVarianceTTest(a1, a2)
@test abs(tst.df - 7.03) <= 0.01
@test abs(tst.dof - 7.03) <= 0.01
@test abs(tst.t - 1.959) <= 1e-3
@test abs(pvalue(tst) - 0.091) <= 1e-3
@test all(abs.([confint(tst)...] - [-0.0196, 0.2096]) .<= 1e-4)
Expand Down