fix(analyze): write an undefined paired p-value as null, not as NaN

A paired contrast where censoring orders no pair has no p-value, and JSON has
no NaN, so --json failed with 'marshal summary: json: unsupported value: NaN'
and wrote no summary at all after printing a complete report. The two fields
join the medians and the rates already carried as pointers, undefined reading
as null in the summary and n/a in the report.

Reachable since a clean run started being censored where it stopped: an arm
the wall clock stops before its partner ever violates orders nothing.

cmd/internal-tools/analyze/analysis.go

@@ -105,8 +105,9 @@ func analysePaired(arms []arm, now time.Time) (analysis, error) {
 		return analysis{}, fmt.Errorf("arms %q and %q share no seed with a usable run in both",
 			testable[0].Name, testable[1].Name)
 	}
-	if !math.IsNaN(comparison.PValue) {
-		comparison.HolmPValue = holm([]float64{comparison.PValue})[0]
+	if comparison.PValue != nil {
+		adjusted := holm([]float64{*comparison.PValue})[0]
+		comparison.HolmPValue = &adjusted
 		result.HolmFamilySize = 1
 	}
 	result.Paired = &comparison

cmd/internal-tools/analyze/censoring_test.go

@@ -1,8 +1,11 @@
 package main
 
 import (
+	"bytes"
+	"io"
 	"math"
 	"path/filepath"
+	"strings"
 	"testing"
 )
 
@@ -116,3 +119,30 @@ func TestRun_PairedContrastFollowsWhatCensoringDetermines(t *testing.T) {
 		t.Errorf("a12 within pairs %.4f, want above 0.5", paired.A12)
 	}
 }
+
+// Nothing orders any pair here, so there is no test to report. The summary has
+// to say that rather than failing to write a number that does not exist: a
+// NaN p-value is not JSON and the whole summary went unwritten behind it.
+func TestRun_PairedContrastWithNoOrderedPairSaysSo(t *testing.T) {
+	earlyDirectory, lateDirectory := wallClockArms(t, stoppedShort(20, 12), violatedAt(20, 100))
+	result := analyseCampaigns(t, "--paired", earlyDirectory, lateDirectory)
+
+	paired := *result.Paired
+	if paired.Pairs != 20 || paired.Unordered != 20 {
+		t.Fatalf("paired %+v, want twenty pairs and all of them unordered", paired)
+	}
+	if paired.PValue != nil || paired.HolmPValue != nil {
+		t.Errorf("p %v and holm p %v, want both undefined", paired.PValue, paired.HolmPValue)
+	}
+	if result.HolmFamilySize != 0 {
+		t.Errorf("holm family of %d, want none where nothing was tested", result.HolmFamilySize)
+	}
+
+	var stdout bytes.Buffer
+	if err := run([]string{"--paired", earlyDirectory, lateDirectory}, &stdout, io.Discard); err != nil {
+		t.Fatal(err)
+	}
+	if !strings.Contains(stdout.String(), "sign test over the 0 ordered pair(s), p n/a, holm p n/a") {
+		t.Errorf("report does not say the test was not run:\n%s", stdout.String())
+	}
+}

cmd/internal-tools/analyze/paired.go

@@ -65,9 +65,12 @@ type pairedComparison struct {
 	// of matched seeds on which the first arm took more steps, an unordered pair
 	// counting as half. A matched design has no reason to compare the two arms
 	// as pooled bags of runs when each seed has a partner.
-	A12        float64 `json:"a12_within_pairs"`
-	PValue     float64 `json:"p_value"`
-	HolmPValue float64 `json:"holm_p_value"`
+	A12 float64 `json:"a12_within_pairs"`
+	// PValue is undefined, and null in the summary, when censoring left no pair
+	// ordered: there is nothing for the test to be a test of, and JSON has no
+	// way to write the number that is not there.
+	PValue     *float64 `json:"p_value"`
+	HolmPValue *float64 `json:"holm_p_value"`
 }
 
 // pairArms matches the two arms by seed and contrasts them pair by pair. A seed
@@ -84,13 +87,7 @@ func pairArms(first, second arm) (pairedComparison, error) {
 		return pairedComparison{}, err
 	}
 
-	comparison := pairedComparison{
-		First:      first.Name,
-		Second:     second.Name,
-		A12:        math.NaN(),
-		PValue:     math.NaN(),
-		HolmPValue: math.NaN(),
-	}
+	comparison := pairedComparison{First: first.Name, Second: second.Name, A12: math.NaN()}
 	var differences []float64
 	for _, seed := range sortedSeeds(firstBySeed, secondBySeed) {
 		left, inFirst := firstBySeed[seed]
@@ -130,7 +127,9 @@ func pairArms(first, second arm) (pairedComparison, error) {
 		comparison.Sign = -1
 	}
 	comparison.A12 = (float64(comparison.SecondSooner) + 0.5*float64(comparison.Unordered)) / float64(comparison.Pairs)
-	comparison.PValue = signTest(comparison.FirstSooner, comparison.SecondSooner)
+	if tested := signTest(comparison.FirstSooner, comparison.SecondSooner); !math.IsNaN(tested) {
+		comparison.PValue = &tested
+	}
 	return comparison, nil
 }
 

cmd/internal-tools/analyze/paired_test.go

@@ -87,7 +87,7 @@ func TestPairArms_ScoresEachPairByWhichRunOutlivedTheOther(t *testing.T) {
 		t.Errorf("median difference %v over %d pair(s), want 10 over 2",
 			comparison.MedianDifference, comparison.BothViolated)
 	}
-	if want := signTest(0, 2); comparison.PValue != want {
+	if want := signTest(0, 2); comparison.PValue == nil || *comparison.PValue != want {
 		t.Errorf("p %v, want the sign test's %v over the two ordered pairs", comparison.PValue, want)
 	}
 }
@@ -105,8 +105,8 @@ func TestPairArms_PairsOfCleanRunsAreNotEvidence(t *testing.T) {
 	if comparison.Unordered != 2 || comparison.Sign != 0 {
 		t.Errorf("comparison %+v, want both pairs unordered and no direction", comparison)
 	}
-	if !math.IsNaN(comparison.PValue) {
-		t.Errorf("p %v, want undefined with no ordered pair", comparison.PValue)
+	if comparison.PValue != nil {
+		t.Errorf("p %v, want undefined with no ordered pair", *comparison.PValue)
 	}
 	if comparison.MedianDifference != nil {
 		t.Errorf("median difference %v, want undefined where no pair has two violations",
@@ -181,8 +181,8 @@ func TestPairArms_DirectionReversesWithTheArms(t *testing.T) {
 		t.Errorf("median differences %v and %v, want opposites",
 			*forward.MedianDifference, *reversed.MedianDifference)
 	}
-	if math.Abs(forward.PValue-reversed.PValue) > 1e-12 {
-		t.Errorf("p-values %v and %v, want the same two-sided value", forward.PValue, reversed.PValue)
+	if math.Abs(*forward.PValue-*reversed.PValue) > 1e-12 {
+		t.Errorf("p-values %v and %v, want the same two-sided value", *forward.PValue, *reversed.PValue)
 	}
 	if math.Abs(forward.A12+reversed.A12-1) > 1e-12 {
 		t.Errorf("a12 %v and %v, want them to sum to 1", forward.A12, reversed.A12)

cmd/internal-tools/analyze/planted_test.go

@@ -647,11 +647,11 @@ func TestPlanted_PairedComparisonRecoversTheShiftAndItsSign(t *testing.T) {
 	if want := 0.5 * float64(unordered) / 30; paired.A12 != want {
 		t.Errorf("a12 within pairs %v, want %v where no pair favours the first arm", paired.A12, want)
 	}
-	if paired.PValue > 0.001 {
+	if paired.PValue == nil || *paired.PValue > 0.001 {
 		t.Errorf("p-value %v for a shift planted in every pair", paired.PValue)
 	}
-	if paired.HolmPValue != paired.PValue {
-		t.Errorf("holm p %v in a family of one, want the raw %v", paired.HolmPValue, paired.PValue)
+	if *paired.HolmPValue != *paired.PValue {
+		t.Errorf("holm p %v in a family of one, want the raw %v", *paired.HolmPValue, *paired.PValue)
 	}
 }
 
@@ -665,7 +665,7 @@ func TestPlanted_PairedNullIsNotCalledSignificantAboveItsLevel(t *testing.T) {
 	for replicate := 0; replicate < replicates; replicate++ {
 		first, second := plantTwoArms(t, int64(5000+replicate), 30, model, model)
 		result := analyseCampaigns(t, "--paired", first, second)
-		if result.Paired.PValue < 0.05 {
+		if *result.Paired.PValue < 0.05 {
 			rejected++
 		}
 	}

cmd/internal-tools/analyze/report.go

@@ -149,7 +149,7 @@ func writePaired(out io.Writer, comparison pairedComparison) {
 		formatStepDifference(comparison.MedianDifference), comparison.BothViolated, comparison.Sign, comparison.A12)
 	fmt.Fprintf(out, "sign test over the %d ordered pair(s), p %s, holm p %s\n",
 		comparison.FirstSooner+comparison.SecondSooner,
-		formatPValue(comparison.PValue), formatPValue(comparison.HolmPValue))
+		formatOptionalPValue(comparison.PValue), formatOptionalPValue(comparison.HolmPValue))
 	if len(comparison.UnpairedSeeds) > 0 {
 		fmt.Fprintf(out, "%d seed(s) usable in one arm only and left out of the pairing: %v\n",
 			len(comparison.UnpairedSeeds), comparison.UnpairedSeeds)
@@ -209,6 +209,13 @@ func formatSingletons(summary armSummary) string {
 	return fmt.Sprintf("%d/%d (%.3f)", summary.SingletonDefects, summary.DistinctDefects, *summary.SingletonFraction)
 }
 
+func formatOptionalPValue(value *float64) string {
+	if value == nil {
+		return "n/a"
+	}
+	return formatPValue(*value)
+}
+
 func formatPValue(value float64) string {
 	switch {
 	case math.IsNaN(value):