Adding the arcsine binomial proportion confidence interval (#86)

* Added arcsine transformation CI calculation

* Fixed typo & replaced alpha by unicode equivalent

* Keep typofix, revert Unicode replacement

* Change sigma to z for semantic purposes

* Fix brackets, add information link

* Added tests for arcsine transformation CI

* Fixing arcsine test

Entered wrong values

* Left != right

src/binomial.jl

@@ -85,6 +85,8 @@ function StatsBase.confint(x::BinomialTest, alpha::Float64=0.05; tail=:both, met
             ci_jeffrey(x, alpha)
         elseif method == :agresti_coull
             ci_agresti_coull(x, alpha)
+        elseif method == :arcsine
+            ci_arcsine(x, alpha)
         else
             throw(ArgumentError("method=$(method) is not implemented yet"))
         end
@@ -131,6 +133,13 @@ function ci_wilson(x::BinomialTest, alpha::Float64=0.05)
     (μ-q*σ, μ+q*σ)
 end
 
+# Arcsine transformation interval as based on Cohen's H: https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Arcsine_transformation
+function ci_arcsine(x::BinomialTest, alpha::Float64=0.05)
+    q = quantile(Normal(), 1-alpha/2)
+    p = x.x / x.n
+    z = q/(2*sqrt(x.n))
+    (sin(asin(sqrt(p))-z)^2, sin(asin(sqrt(p))+z)^2)
+end
 
 ## SIGN TEST
 

test/binomial.jl

@@ -19,6 +19,10 @@ t = BinomialTest(26, 78)
 @test_ci_approx confint(t, method=:agresti_coull) (0.2384423809121706, 0.44387022232522744)
 @test_ci_approx confint(t, tail=:left, method=:agresti_coull) (0.0, 0.42558712894362222)
 @test_ci_approx confint(t, tail=:right, method=:agresti_coull) (0.25225408385003706, 1.0)
+@test_ci_approx confint(t, method=:arcsine) (0.23366209634204066,0.44117918327686334)
+@test_ci_approx confint(t, tail=:left, method=:arcsine) (0.0,0.4235046425920888)
+@test_ci_approx confint(t, tail=:right, method=:arcsine) (0.2489264087216164,1.0)
+
 show(IOBuffer(), t)
 
 t = BinomialTest([trues(6); falses(3)])
@@ -40,6 +44,9 @@ t = BinomialTest([trues(6); falses(3)])
 @test_ci_approx confint(t, method=:agresti_coull) (0.350905767251112,0.88271254994237336)
 @test_ci_approx confint(t, tail=:left, method=:agresti_coull) (0.0,0.86049746046629294)
 @test_ci_approx confint(t, tail=:right, method=:agresti_coull) (0.39579136642712159,1.0)
+@test_ci_approx confint(t, method=:arcsine) (0.345812446615087,0.9188773496172281)
+@test_ci_approx confint(t, tail=:left, method=:arcsine) (0.0,0.8879439981269358)
+@test_ci_approx confint(t, tail=:right, method=:arcsine) (0.3965293068864491,1.0)
 show(IOBuffer(), t)
 
 x = [55, 58, 61, 61, 62, 62, 62, 63, 63, 64, 66, 68, 68, 69, 69, 69, 70, 71, 72, 72]