Reduce the bogosity of ministat's % difference calculations.

The previous calculation used an approximation which was only valid in
cases where the means being compared were similar; this resulted in very
odd claims being made, e.g. that 0 +/- 0 is a difference of -100% +/- 1%
from 100 +/- 1.

The new calculation scales sample standard deviations by the means, and
yields approximately correct percentage difference bounds providing that
the reference population is bounded away from zero.  (In the case where
the values being compared are not sufficiently bounded away from zero,
the distribution of ratios becomes much harder to calculate, and is not
likely to be useful anyway.)

Note that when ministat is used for its intended purpose of determining
whether two samples are statistically different, this change is unlikely
to have any noticeable effect; in such cases the means will be similar
enough that the correction applied here will be minimal.

1 files changed, 7 insertions, 1 deletions

diff --git a/usr.bin/ministat/ministat.c b/usr.bin/ministat/ministat.c
index a7f7182ce420..02b5025a436c 100644
--- a/usr.bin/ministat/ministat.c
+++ b/usr.bin/ministat/ministat.c
@@ -232,6 +232,7 @@ static void
 Relative(struct dataset *ds, struct dataset *rs, int confidx)
 {
 	double spool, s, d, e, t;
+	double re;
 	int i;
 
 	i = ds->n + rs->n - 2;
@@ -246,11 +247,16 @@ Relative(struct dataset *ds, struct dataset *rs, int confidx)
 	d = Avg(ds) - Avg(rs);
 	e = t * s;
 
+	re = (ds->n - 1) * Var(ds) + (rs->n - 1) * Var(rs) *
+	    (Avg(ds) * Avg(ds)) / (Avg(rs) * Avg(rs));
+	re *= (ds->n + rs->n) / (ds->n * rs->n * (ds->n + rs->n - 2.0));
+	re = t * sqrt(re);
+
 	if (fabs(d) > e) {
 	
 		printf("Difference at %.1f%% confidence\n", studentpct[confidx]);
 		printf("	%g +/- %g\n", d, e);
-		printf("	%g%% +/- %g%%\n", d * 100 / Avg(rs), e * 100 / Avg(rs));
+		printf("	%g%% +/- %g%%\n", d * 100 / Avg(rs), re * 100 / Avg(rs));
 		printf("	(Student's t, pooled s = %g)\n", spool);
 	} else {
 		printf("No difference proven at %.1f%% confidence\n",