diff --git a/Project.toml b/Project.toml
index e36f8e5..6d9b061 100644
--- a/Project.toml
+++ b/Project.toml
@@ -9,10 +9,12 @@ ThickNumbers = "b57aa878-5b76-4266-befc-f8e007760995"
 
 [compat]
 SpecialFunctions = "2"
+ThickNumbers = "1"
 julia = "1"
 
 [extras]
+HypothesisTests = "09f84164-cd44-5f33-b23f-e6b0d136a0d5"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Test"]
+test = ["HypothesisTests", "Test"]
diff --git a/test/runtests.jl b/test/runtests.jl
index 55ba4a1..089f354 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,7 +1,17 @@
 using GaussianRandomVariables
 using ThickNumbers
+using HypothesisTests
 using Test
 
+function testscalar(f, μ, σ; n=1000, pval = 0.001)
+    x = μ .+ σ .* randn(n)
+    y = f.(x)
+    g = GVar(μ, σ)
+    fg = f(g)
+    z = mid(fg) .+ rad(fg) .* randn(n)
+    return pvalue(EqualVarianceTTest(y, z)) > pval && pvalue(LeveneTest(y, z)) > pval
+end
+
 @testset "GaussianRandomVariables.jl" begin
     x = 3 ± 1
     e = GVar(0, -1)          # empty
@@ -19,4 +29,12 @@ using Test
     @test rad(1/x)^2 ≈ rad(x)^2 / mid(x)^4 + 2 * rad(x)^4 / mid(x)^6
     @test sqrt(x) ⩪ exp(0.5 * log(x)) rtol=1e-3
     @test sqrt(x) ⩪ x^0.5
+
+    for μ in (2, 3, 10), σ in (0.25,)
+        @test testscalar(x -> x^2, μ, σ)
+        @test testscalar(x -> x^1.8, μ, σ)
+        @test testscalar(exp, μ, σ)
+        @test testscalar(log, μ, σ)
+        @test testscalar(sqrt, μ, σ)
+    end
 end