add proportions_ztest to test examples

CONTRIBUTORS.md

@@ -1,4 +1,4 @@
 ## Contributors
 - Ian McFarland [@imf](https://github.com/imf)
 - Dave Schinkel [@dschinkel](https://github.com/dschinkel)
-
+- Carl Jackson [@carl](https://github.com/carl)

examples/team_recommender/tests/test_helpers.py

@@ -92,8 +92,15 @@ def test_beyond_expected_success_rate(assert_success_rate, row):
         (0.8, 14, 100, None),
         (0.97, 1, 8, None),
         (0.97, 0, 1, "after measuring 2x 100 runs and getting 3 failures"),
-        (0.975, 0, 100, "97.5% success rate is within 100% success rate"),
-        (0.9737, 0, 100, "97.37% success rate is within 100% success rate"),
+        (
+            0.97,
+            1,
+            133,
+            "At 133 we can say that with 90% confidence 1 failure is within 97% success rate",
+        ),
+        (0.98, 0, 100, "97.5% success rate is within 100% success rate"),
+        (0.97999999999999999, 0, 100, "97.37% success rate is within 100% success rate"),
+        (0.5, 1, 2, None),
     ],
 )
 def test_is_within_expected(success_rate, failure_count, sample_size, message):
@@ -107,9 +114,15 @@ def test_is_within_expected(success_rate, failure_count, sample_size, message):
     "failure_count, sample_size, expected_rate, message",
     [
         (3, 5, 0.8, "40% success rate is below expected 80% success rate"),
-        (1, 2, 0.97, "50% success rate is below expected 97% success rate"),
         (0, 100, 0.97, "100% success rate is not within 97% success rate"),
+        (1, 50000, 0.9997, "99.99% success rate is below expected 97% success rate"),
         (0, 100, 0.9736, "97.36% success rate is not within 100% success rate"),
+        (
+            1,
+            134,
+            0.97,
+            "At 134 we can say that with 90% confidence 1 failure is within 97% success rate",
+        ),
     ],
 )
 def test_not_is_within_expected(failure_count, sample_size, expected_rate, message):
@@ -145,7 +158,13 @@ def test_next_success_rate():
 
 @pytest.mark.parametrize(
     "success_rate, largest_sample_size",
-    [(0.7, 12), (next_success_rate(12), 55), (next_success_rate(55), 248)],
+    [
+        (0.7, 10),
+        (next_success_rate(10), 44),
+        (next_success_rate(45), 184),
+        (next_success_rate(185), 744),
+        (next_success_rate(745), 2984),
+    ],
 )
 def test_largest_sample_size_for_given_success_rate(success_rate, largest_sample_size):
     assert is_within_expected(success_rate, 1, largest_sample_size), "should be within expected"
@@ -154,6 +173,26 @@ def test_largest_sample_size_for_given_success_rate(success_rate, largest_sample
     )
 
 
+def test_next_sample_size():
+    assert next_sample_size(10) == 45
+    assert next_sample_size(45) == 185
+    assert next_sample_size(185) == 745
+    assert next_sample_size(745) == 2985
+    assert next_sample_size(29) == next_sample_size_via_loop(29)
+
+
+def next_sample_size(current):
+    return 4 * current + 5
+
+
+def next_sample_size_via_loop(sample_size: int) -> int:
+    goal_success_rate = next_success_rate(sample_size)
+    for i in range(sample_size, 5 * sample_size):
+        if not is_within_expected(goal_success_rate, 1, i):
+            return i
+    return 0
+
+
 def test_success_rate():
     tiny_set_analysis = analyse_measure_from_test_sample(1, 2)
     assert tiny_set_analysis.proportion == 0.5