changes

crates/domain/tests/correlation/significance_test.rs

@@ -0,0 +1,107 @@
+use domain::correlation::{CorrelationStrategy, Observation, PValue};
+use domain::entry::{DayMood, Mood};
+
+fn day(mood: Mood) -> DayMood {
+    DayMood::of(&[mood]).unwrap()
+}
+
+fn mood_of(value: u8) -> Mood {
+    Mood::try_from(value).unwrap()
+}
+
+fn loosely_rising() -> Vec<Observation> {
+    let moods = [3, 1, 4, 2, 3, 5, 2, 4, 3, 5, 4, 3];
+
+    moods
+        .iter()
+        .enumerate()
+        .map(|(index, mood)| Observation::new(index as f64 + 1.0, day(mood_of(*mood))))
+        .collect()
+}
+
+fn significance(strategy: CorrelationStrategy, observations: &[Observation]) -> f64 {
+    strategy
+        .significance(observations)
+        .expect("a scored series has a p-value")
+        .value()
+}
+
+#[test]
+fn the_familiar_thresholds_come_out_of_the_normal_tail() {
+    assert!((PValue::from_standard_score(1.96).value() - 0.05).abs() < 1e-4);
+    assert!((PValue::from_standard_score(1.645).value() - 0.10).abs() < 1e-4);
+}
+
+#[test]
+fn a_standard_score_of_nothing_is_certain_to_be_nothing() {
+    assert!((PValue::from_standard_score(0.0).value() - 1.0).abs() < 1e-9);
+}
+
+#[test]
+fn direction_does_not_change_how_surprising_a_score_is() {
+    let positive = PValue::from_standard_score(2.5).value();
+    let negative = PValue::from_standard_score(-2.5).value();
+
+    assert!((positive - negative).abs() < 1e-12);
+}
+
+#[test]
+fn each_strategy_turns_its_own_statistic_into_a_p_value() {
+    let observations = loosely_rising();
+
+    let pearson = significance(CorrelationStrategy::Pearson, &observations);
+    let spearman = significance(CorrelationStrategy::Spearman, &observations);
+    let kendall = significance(CorrelationStrategy::Kendall, &observations);
+
+    assert!((pearson - 0.198_050_956_8).abs() < 1e-4, "got {pearson}");
+    assert!((spearman - 0.241_732_162_6).abs() < 1e-4, "got {spearman}");
+    assert!((kendall - 0.201_603_352_7).abs() < 1e-4, "got {kendall}");
+}
+
+#[test]
+fn a_relationship_that_holds_all_the_way_is_hard_to_put_down_to_chance() {
+    let tight: Vec<Observation> = (1..=12)
+        .map(|day_number| {
+            let mood = mood_of(((day_number - 1) / 3 + 1) as u8);
+            Observation::new(day_number as f64, day(mood))
+        })
+        .collect();
+
+    assert!(significance(CorrelationStrategy::Pearson, &tight) < 0.001);
+    assert!(significance(CorrelationStrategy::Spearman, &tight) < 0.001);
+    assert!(significance(CorrelationStrategy::Kendall, &tight) < 0.001);
+}
+
+#[test]
+fn a_mean_difference_is_judged_by_the_spread_within_each_group() {
+    let observations: Vec<Observation> = [
+        (1.0, Mood::Good),
+        (1.0, Mood::Rad),
+        (1.0, Mood::Good),
+        (1.0, Mood::Rad),
+        (0.0, Mood::Bad),
+        (0.0, Mood::Meh),
+        (0.0, Mood::Bad),
+        (0.0, Mood::Awful),
+    ]
+    .into_iter()
+    .map(|(value, mood)| Observation::new(value, day(mood)))
+    .collect();
+
+    let p = significance(CorrelationStrategy::MeanDifference, &observations);
+
+    assert!((p - 0.000_000_573_3).abs() < 1e-9, "got {p}");
+}
+
+#[test]
+fn a_series_that_cannot_be_scored_has_nothing_to_report() {
+    let unvarying: Vec<Observation> = (1..=10)
+        .map(|day_number| Observation::new(day_number as f64, day(Mood::Meh)))
+        .collect();
+
+    assert!(
+        CorrelationStrategy::Spearman
+            .significance(&unvarying)
+            .is_none()
+    );
+}