added two sample t-test

Author: msharp

lib/statistics/tests/t_test.ex

@@ -25,14 +25,65 @@ defmodule Statistics.Tests.TTest do
   def one_sample(list, popmean) do
     df = length(list)-1
     t = (mean(list) - popmean) / (stdev(list) / sqrt(length(list)))
+    p = get_t_prob(t, df)
+    %{t: t, p: p}
+  end
+
+ 
+  @doc """
+  A two-sided test for the null hypothesis that the 
+  mean of `list1` is different to the mean of `list2`.
+
+  The variance of the lists should be equal but the 
+  sample size of each last can be different.
+
+  Returns the _t_ statistic, and the _p_ value.
+
+  ## Example
+
+      iex> Statistics.Tests.TTest.ind_samples([1,2,3,2,1], [3,2,4,3,5])
+      %{p: 0.022802155958137702, t: -2.82842712474619}
+
+      iex> Statistics.Tests.TTest.ind_samples([1,2,3,2,1], [3,2,4,3,5,4,5,6])
+      %{p: 0.0044530673387188, t: -3.5858542135407596}
+
+  """
+  def ind_samples(list1, list2) do
+    df = length(list1) + length(list2) - 2
+    mu1 = mean(list1)
+    mu2 = mean(list2)
+    # calculate pooled standard deviation and
+    # sample proportion differently when 
+    # sample sizes are unequal
+    {sp, sz} = case length(list1) == length(list2) do
+      true ->
+        spt = sqrt((variance(list1) + variance(list2)) / 2)
+        szt = sqrt(2/length(list1))
+        {spt, szt}
+      false ->
+        # weight variances by sample size
+        adj_var1 = (length(list1)-1) * variance(list1)
+        adj_var2 = (length(list2)-1) * variance(list2)
+        spf = sqrt((adj_var1 + adj_var2) / df)
+        szf = sqrt((1 / length(list1)) + (1 / length(list2)))
+        {spf, szf}
+    end
+    t = (mu1 - mu2) / (sp * sz)
+    p = get_t_prob(t, df)
+    %{t: t, p: p}
+  end
+
+
+  defp get_t_prob(t, df) do
     c = T.cdf(df).(t) 
-    p1 = case t < 0.0 do 
+    p = case t < 0.0 do 
       true -> c
       false -> 1 - c
     end
-    p = 2 * p1 # two-sided test
-    %{t: t, p: p}
+    case p < 0.5 do # two-sided test
+      true -> 2 * p
+      false -> 1.0
+    end
   end
 
-
 end

test/t_test_test.exs

@@ -4,8 +4,13 @@ defmodule TTestTest do
 
   alias Statistics.Tests.TTest
 
-  test "one sample t test" do
+  test "one sample t-test" do
+    assert TTest.one_sample([1,2,1,2,1,2],1.5) == %{p: 1.0, t: 0.0}
     assert TTest.one_sample([4,1,2,3,1,2,3,4],2) == %{p: 0.23032680249555892, t: 1.2649110640673518}
   end
 
+  test "independent samples t-test" do
+    assert TTest.ind_samples([1,2,1,2,1,2],[2,1,2,1,2,1]) == %{t: 0.0, p: 1.0} 
+    assert TTest.ind_samples([1,2,1,2,1,2],[5,6,7,6,7,5]) == %{p: 4.3244470028110745e-7, t: -11.512838683202965}
+  end
 end