Add stderror and meandiff functions for TTest

src/HypothesisTests.jl

@@ -29,9 +29,9 @@ using Distributions, Roots, StatsBase
 using Combinatorics: combinations, permutations
 using Rmath: pwilcox, psignrank
 
-import StatsBase.confint
+import StatsBase.confint, StatsBase.stderror
 
-export testname, pvalue, confint
+export testname, pvalue, confint, stderror
 abstract type HypothesisTest end
 
 check_same_length(x::AbstractVector, y::AbstractVector) = if length(x) != length(y)
@@ -68,6 +68,13 @@ If `tail` is `:both` (default), then the p-value for the two-sided test is retur
 """
 function pvalue end
 
+"""
+    stderror(test::HypothesisTest)
+
+Compute the standard error for the point estimate of interest for a test. 
+"""
+function stderror end
+
 # Basic function for finding a p-value given a distribution and tail
 pvalue(dist::ContinuousUnivariateDistribution, x::Number; tail=:both) =
     if tail == :both

src/binomial.jl

@@ -45,7 +45,7 @@ probability is not equal to `p`.
 
 Computed confidence intervals ([`confint`](@ref)) by default are Clopper-Pearson intervals.
 
-Implements: [`pvalue`](@ref), [`confint(::BinomialTest)`](@ref)
+Implements: [`pvalue`](@ref), [`confint(::BinomialTest)`](@ref), [`stderror`](@ref)
 """
 BinomialTest(x::AbstractVector{Bool}, p=0.5) =
     BinomialTest(sum(x), length(x), p)
@@ -65,6 +65,11 @@ function show_params(io::IO, x::BinomialTest, ident="")
 end
 
 pvalue(x::BinomialTest; tail=:both) = pvalue(Binomial(x.n, x.p), x.x; tail=tail)
+function StatsBase.stderror(b::BinomialTest) 
+    n = b.n
+    phat = b.x / n
+    sqrt((phat * (1 - phat)) / n)
+end
 
 # Confidence interval
 """

src/correlation.jl

@@ -16,7 +16,7 @@ of vectors `x` and `y` is zero.
 Perform a t-test for the hypothesis that ``\\text{Cor}(x,y|Z=z) = 0``, i.e. the partial
 correlation of vectors `x` and `y` given the matrix `Z` is zero.
 
-Implements `pvalue` for the t-test.
+Implements `pvalue` for the t-test, as well as `stderror`. 
 Implements `confint` using an approximate confidence interval based on Fisher's
 ``z``-transform.
 
@@ -82,6 +82,7 @@ end
 
 default_tail(::CorrelationTest) = :both
 pvalue(test::CorrelationTest; tail=:both) = pvalue(TDist(dof(test)), test.t, tail=tail)
+StatsBase.stderror(test::CorrelationTest) = sqrt(1/dof(test))
 
 function show_params(io::IO, test::CorrelationTest, indent="")
     println(io, indent, "number of observations:          ", nobs(test))

src/t.jl

@@ -48,6 +48,8 @@ function StatsBase.confint(x::TTest; level::Float64=0.95, tail=:both)
     end
 end
 
+# The standard error of the difference
+StatsBase.stderror(x::TTest) = x.stderr
 
 ## ONE SAMPLE T-TEST
 
@@ -77,7 +79,7 @@ Perform a one sample t-test of the null hypothesis that `n` values with mean `xb
 sample standard deviation `stddev`  come from a distribution with mean `μ0` against the
 alternative hypothesis that the distribution does not have mean `μ0`.
 
-Implements: [`pvalue`](@ref), [`confint`](@ref)
+Implements: [`pvalue`](@ref), [`confint`](@ref), [`stderror`](@ref)
 """
 function OneSampleTTest(xbar::Real, stddev::Real, n::Int, μ0::Real=0)
     stderr = stddev/sqrt(n)
@@ -93,7 +95,7 @@ Perform a one sample t-test of the null hypothesis that the data in vector `v` c
 a distribution with mean `μ0` against the alternative hypothesis that the distribution
 does not have mean `μ0`.
 
-Implements: [`pvalue`](@ref), [`confint`](@ref)
+Implements: [`pvalue`](@ref), [`confint`](@ref), [`stderror`](@ref)
 """
 OneSampleTTest(v::AbstractVector{T}, μ0::Real=0) where {T<:Real} = OneSampleTTest(mean(v), std(v), length(v), μ0)
 
@@ -104,7 +106,7 @@ Perform a paired sample t-test of the null hypothesis that the differences betwe
 values in vectors `x` and `y` come from a distribution with mean `μ0` against the
 alternative hypothesis that the distribution does not have mean `μ0`.
 
-Implements: [`pvalue`](@ref), [`confint`](@ref)
+Implements: [`pvalue`](@ref), [`confint`](@ref), [`stderror`](@ref)
 """
 function OneSampleTTest(x::AbstractVector{T}, y::AbstractVector{S}, μ0::Real=0) where {T<:Real, S<:Real}
     check_same_length(x, y)
@@ -142,7 +144,7 @@ Perform a two-sample t-test of the null hypothesis that `x` and `y` come from di
 with equal means and variances against the alternative hypothesis that the distributions
 have different means but equal variances.
 
-Implements: [`pvalue`](@ref), [`confint`](@ref)
+Implements: [`pvalue`](@ref), [`confint`](@ref), [`stderror`](@ref)
 """
 function EqualVarianceTTest(x::AbstractVector{T}, y::AbstractVector{S}, μ0::Real=0) where {T<:Real,S<:Real}
     nx, ny = length(x), length(y)
@@ -184,7 +186,7 @@ equation:
         \\frac{(k_i s_i^2)^2}{ν_i}}
 ```
 
-Implements: [`pvalue`](@ref), [`confint`](@ref)
+Implements: [`pvalue`](@ref), [`confint`](@ref), [`stderror`](@ref)
 """
 function UnequalVarianceTTest(x::AbstractVector{T}, y::AbstractVector{S}, μ0::Real=0) where {T<:Real,S<:Real}
     nx, ny = length(x), length(y)

src/z.jl

@@ -48,6 +48,8 @@ function StatsBase.confint(x::ZTest; level::Float64=0.95, tail=:both)
     end
 end
 
+# The standard error of the difference
+StatsBase.stderror(x::ZTest) = x.stderr
 
 ## ONE SAMPLE Z-TEST
 
@@ -75,7 +77,7 @@ Perform a one sample z-test of the null hypothesis that `n` values with mean `xb
 population standard deviation `stddev`  come from a distribution with mean `μ0` against the
 alternative hypothesis that the distribution does not have mean `μ0`.
 
-Implements: [`pvalue`](@ref), [`confint`](@ref)
+Implements: [`pvalue`](@ref), [`confint`](@ref), [`stderror`](@ref)
 """
 function OneSampleZTest(xbar::Real, stddev::Real, n::Int, μ0::Real=0)
     stderr = stddev/sqrt(n)
@@ -90,7 +92,7 @@ Perform a one sample z-test of the null hypothesis that the data in vector `v` c
 a distribution with mean `μ0` against the alternative hypothesis that the distribution
 does not have mean `μ0`.
 
-Implements: [`pvalue`](@ref), [`confint`](@ref)
+Implements: [`pvalue`](@ref), [`confint`](@ref), [`stderror`](@ref)
 """
 OneSampleZTest(v::AbstractVector{T}, μ0::Real=0) where {T<:Real} = OneSampleZTest(mean(v), std(v), length(v), μ0)
 
@@ -101,7 +103,7 @@ Perform a paired sample z-test of the null hypothesis that the differences betwe
 values in vectors `x` and `y` come from a distribution with mean `μ0` against the
 alternative hypothesis that the distribution does not have mean `μ0`.
 
-Implements: [`pvalue`](@ref), [`confint`](@ref)
+Implements: [`pvalue`](@ref), [`confint`](@ref), [`stderror`](@ref)
 """
 function OneSampleZTest(x::AbstractVector{T}, y::AbstractVector{S}, μ0::Real=0) where {T<:Real, S<:Real}
     check_same_length(x, y)
@@ -137,7 +139,7 @@ Perform a two-sample z-test of the null hypothesis that `x` and `y` come from di
 with equal means and variances against the alternative hypothesis that the distributions
 have different means but equal variances.
 
-Implements: [`pvalue`](@ref), [`confint`](@ref)
+Implements: [`pvalue`](@ref), [`confint`](@ref), [`stderror`](@ref)
 """
 function EqualVarianceZTest(x::AbstractVector{T}, y::AbstractVector{S}, μ0::Real=0) where {T<:Real,S<:Real}
     nx, ny = length(x), length(y)
@@ -169,7 +171,7 @@ Perform an unequal variance two-sample z-test of the null hypothesis that `x` an
 from distributions with equal means against the alternative hypothesis that the
 distributions have different means.
 
-Implements: [`pvalue`](@ref), [`confint`](@ref)
+Implements: [`pvalue`](@ref), [`confint`](@ref), [`stderror`](@ref)
 """
 function UnequalVarianceZTest(x::AbstractVector{T}, y::AbstractVector{S}, μ0::Real=0) where {T<:Real,S<:Real}
     nx, ny = length(x), length(y)

test/binomial.jl

@@ -6,6 +6,7 @@ using HypothesisTests: default_tail
     @test pvalue(t) ≈ 0.004334880883507431
     @test pvalue(t, tail=:left) ≈ 0.002167440441753716
     @test pvalue(t, tail=:right) ≈ 0.9989844298129187
+    @test stderror(t) ≈ 0.05337605126836238
     @test default_tail(t) == :both
     @test_ci_approx confint(t) (0.23058523962930383, 0.4491666887959782)
     @test_ci_approx confint(t, tail=:left) (0.0, 0.4313047758370174)
@@ -32,6 +33,7 @@ using HypothesisTests: default_tail
     @test pvalue(t) ≈ 0.5078125000000002
     @test pvalue(t, tail=:left) ≈ 0.91015625
     @test pvalue(t, tail=:right) ≈ 0.2539062500000001
+    @test stderror(t) ≈ 0.15713484026367724
     @test_ci_approx confint(t) (0.2992950562085405, 0.9251453685803082)
     @test_ci_approx confint(t, tail=:left) (0.0, 0.9022531865607242)
     @test_ci_approx confint(t, tail=:right) (0.3449413659437032, 1.0)

test/correlation.jl

@@ -41,6 +41,7 @@ end
     @test nobs(w) == 37
     @test dof(w) == 33
     @test pvalue(w) < 0.00001
+    @test stderror(w) ≈ 0.17407765595569785
 
     X = [ 2 1 0
           4 2 0
@@ -52,4 +53,5 @@ end
     @test nobs(x) == 4
     @test dof(x) == 1
     @test pvalue(x) ≈ 0.25776212 atol=1e-6
+    @test stderror(x) ≈ 1.0
 end

test/t.jl

@@ -11,6 +11,7 @@ using HypothesisTests: default_tail
 	@test abs(pvalue(tst; tail=:left) - 0.9735) <= 1e-4
 	@test abs(pvalue(tst; tail=:right) - 0.0265) <= 1e-4
 	@test default_tail(tst) == :both
+	@test stderror(tst) ≈ tst.stderr ≈ 1.1902380714238083
 	show(IOBuffer(), tst)
 
 	tst = OneSampleTTest(mean(-5:10), std(-5:10), 16)
@@ -24,6 +25,7 @@ using HypothesisTests: default_tail
 	c = confint(tst; tail=:right)
 	@test abs(c[1] - 0.4135) .<= 1e-4
 	@test c[2] == Inf
+	@test stderror(tst) ≈ tst.stderr ≈ 1.1902380714238083
 	show(IOBuffer(), tst)
 
 	tst = OneSampleTTest(-10:5)
@@ -33,6 +35,7 @@ using HypothesisTests: default_tail
 	@test all(abs.([confint(tst)...] - [-5.0369, 0.0369]) .<= 1e-4)
 	@test abs.(confint(tst; tail=:left)[2] - (-0.4135)) .<= 1e-4
 	@test abs.(confint(tst; tail=:right)[1] - (-4.5865)) .<= 1e-4
+	@test stderror(tst) ≈ tst.stderr ≈ 1.1902380714238083	
 	show(IOBuffer(), tst)
 end
 
@@ -52,6 +55,7 @@ end
 	@test abs(pvalue(tst) - 0.078) <= 1e-3
 	@test all(abs.([confint(tst)...] - [-0.0131, 0.2031]) .<= 1e-4)
 	@test default_tail(tst) == :both
+	@test stderror(tst) ≈ tst.stderr ≈ 0.048493985881413015	
 	show(IOBuffer(), tst)
 
 	tst = UnequalVarianceTTest(a1, a2)
@@ -60,6 +64,7 @@ end
 	@test abs(pvalue(tst) - 0.091) <= 1e-3
 	@test all(abs.([confint(tst)...] - [-0.0196, 0.2096]) .<= 1e-4)
 	@test default_tail(tst) == :both
+	@test stderror(tst) ≈ tst.stderr ≈ 0.048493985881413015		
 	show(IOBuffer(), tst)
 end
 end

test/z.jl

@@ -21,6 +21,7 @@ null = Normal(0.0, 1.0)
 	@test pvalue(tst; tail=:left) ≈ cdf(null, z)
 	@test pvalue(tst; tail=:right) ≈ ccdf(null, z)
 	@test default_tail(tst) == :both
+	@test stderror(tst) ≈ tst.stderr ≈ 1.1902380714238083
 	show(IOBuffer(), tst)
 
 	tst = OneSampleZTest(m, s, n)
@@ -33,6 +34,7 @@ null = Normal(0.0, 1.0)
 	@test confint(tst; tail=:left)[2] ≈ m + cquantile(null, 0.05) * se
 	@test confint(tst; tail=:right)[1] ≈ m + quantile(null, 0.05) * se
 	@test confint(tst; tail=:right)[2] ≈ Inf
+	@test stderror(tst) ≈ tst.stderr ≈ 1.1902380714238083
 	show(IOBuffer(), tst)
 
 	x = -10:5
@@ -44,6 +46,7 @@ null = Normal(0.0, 1.0)
 	@test pvalue(tst) ≈ 2 * min(cdf(null, z), ccdf(null, z))
 	@test pvalue(tst; tail=:left) ≈ cdf(null, z)
 	@test pvalue(tst; tail=:right) ≈ ccdf(null, z)
+	@test stderror(tst) ≈ tst.stderr ≈ 1.1902380714238083
 	show(IOBuffer(), tst)
 
 	tst = OneSampleZTest(m, s, n)
@@ -56,6 +59,7 @@ null = Normal(0.0, 1.0)
 	@test confint(tst; tail=:left)[2] ≈ m + cquantile(null, 0.05) * se
 	@test confint(tst; tail=:right)[1] ≈ m + quantile(null, 0.05) * se
 	@test confint(tst; tail=:right)[2] ≈ Inf
+	@test stderror(tst) ≈ tst.stderr ≈ 1.1902380714238083	
 	show(IOBuffer(), tst)
 end
 
@@ -66,6 +70,7 @@ end
 	z = (m - 0) / se
 	tst = OneSampleZTest(x, y)
 	@test pvalue(tst) ≈ 2 * min(cdf(null, z), ccdf(null, z))
+	@test stderror(tst) ≈ tst.stderr ≈ 0.24494897427831783
 end
 
 @testset "Two sample" begin
@@ -87,6 +92,7 @@ end
 	@test default_tail(tst) == :both
 	@test confint(tst)[1] ≈ xbar + quantile(null, 0.05 / 2) * se
 	@test confint(tst)[2] ≈ xbar + cquantile(null, 0.05 / 2) * se
+	@test stderror(tst) ≈ tst.stderr ≈ 0.048493985881413015
 	show(IOBuffer(), tst)
 
 	tst = UnequalVarianceZTest(a1, a2)
@@ -98,6 +104,7 @@ end
 	@test pvalue(tst; tail=:right) ≈ ccdf(null, z)
 	@test confint(tst)[1] ≈ xbar + quantile(null, 0.05 / 2) * se
 	@test confint(tst)[2] ≈ xbar + cquantile(null, 0.05 / 2) * se
+	@test stderror(tst) ≈ tst.stderr ≈ 0.048493985881413015	
 	show(IOBuffer(), tst)
 end
 end