A small statistics tool for gauging the statistical significance

of data from benchmarks etc.  Implements "Student's t" for various
confidence levels, defaults to 95%.

If your benchmarks are not significant at the 95% confidence level,
we don't want to hear about it.
This commit is contained in:
phk 2003-08-13 07:21:54 +00:00
parent b35539c7d2
commit b3803c0021
10 changed files with 1242 additions and 0 deletions

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# $FreeBSD$
PROG= ministat
NOMAN= yes
LDADD= -lm
.include <bsd.prog.mk>
test: ${PROG}
./${PROG} < ${.CURDIR}/chameleon
./${PROG} ${.CURDIR}/chameleon
./${PROG} ${.CURDIR}/chameleon ${.CURDIR}/iguana
./${PROG} -c 80 ${.CURDIR}/chameleon ${.CURDIR}/iguana

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$FreeBSD$
A small tool to do the statistics legwork on benchmarks etc.
Prepare your data into two files, one number per line
run
./ministat data_before data_after
and see what it says.
You need at least three data points in each data set, but the more
you have the better your result generally gets.
Here are two typical outputs:
x _1
+ _2
+--------------------------------------------------------------------------+
|x + x+ x x x + ++ |
| |_________|______AM_______________|__A___________M_______________||
+--------------------------------------------------------------------------+
N Min Max Median Avg Stddev
x 5 36060 36138 36107 36105.6 31.165686
+ 5 36084 36187 36163 36142.6 49.952978
No difference proven at 95.0% confidence
Here nothing can be concluded from the numbers. It _may_ be possible to
prove something if many more measurements are made, but with only five
measurements, nothing is proven.
x _1
+ _2
+--------------------------------------------------------------------------+
| + |
| x + +|
|x x x x + +|
| |_______________A_____M_________| |_M___A____| |
+--------------------------------------------------------------------------+
N Min Max Median Avg Stddev
x 5 0.133 0.137 0.136 0.1354 0.0015165751
+ 5 0.139 0.14 0.139 0.1394 0.00054772256
Difference at 95.0% confidence
0.004 +/- 0.00166288
2.95421% +/- 1.22812%
(Student's t, pooled s = 0.00114018)
Here we have a clearcut difference, not very big, but clear and unambiguous.

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# $FreeBSD$
150
400
720
500
930

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# $FreeBSD$
50
200
150
400
750
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150

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/*
* ----------------------------------------------------------------------------
* "THE BEER-WARE LICENSE" (Revision 42):
* <phk@FreeBSD.ORG> wrote this file. As long as you retain this notice you
* can do whatever you want with this stuff. If we meet some day, and you think
* this stuff is worth it, you can buy me a beer in return. Poul-Henning Kamp
* ----------------------------------------------------------------------------
*
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
#include <stdio.h>
#include <math.h>
#include <err.h>
#include <string.h>
#include <stdlib.h>
#include <unistd.h>
#include <sys/queue.h>
#define NSTUDENT 100
#define NCONF 6
double const studentpct[] = { 80, 90, 95, 98, 99, 99.5 };
double student [NSTUDENT + 1][NCONF] = {
/* inf */ { 1.282, 1.645, 1.960, 2.326, 2.576, 3.090 },
/* 1. */ { 3.078, 6.314, 12.706, 31.821, 63.657, 318.313 },
/* 2. */ { 1.886, 2.920, 4.303, 6.965, 9.925, 22.327 },
/* 3. */ { 1.638, 2.353, 3.182, 4.541, 5.841, 10.215 },
/* 4. */ { 1.533, 2.132, 2.776, 3.747, 4.604, 7.173 },
/* 5. */ { 1.476, 2.015, 2.571, 3.365, 4.032, 5.893 },
/* 6. */ { 1.440, 1.943, 2.447, 3.143, 3.707, 5.208 },
/* 7. */ { 1.415, 1.895, 2.365, 2.998, 3.499, 4.782 },
/* 8. */ { 1.397, 1.860, 2.306, 2.896, 3.355, 4.499 },
/* 9. */ { 1.383, 1.833, 2.262, 2.821, 3.250, 4.296 },
/* 10. */ { 1.372, 1.812, 2.228, 2.764, 3.169, 4.143 },
/* 11. */ { 1.363, 1.796, 2.201, 2.718, 3.106, 4.024 },
/* 12. */ { 1.356, 1.782, 2.179, 2.681, 3.055, 3.929 },
/* 13. */ { 1.350, 1.771, 2.160, 2.650, 3.012, 3.852 },
/* 14. */ { 1.345, 1.761, 2.145, 2.624, 2.977, 3.787 },
/* 15. */ { 1.341, 1.753, 2.131, 2.602, 2.947, 3.733 },
/* 16. */ { 1.337, 1.746, 2.120, 2.583, 2.921, 3.686 },
/* 17. */ { 1.333, 1.740, 2.110, 2.567, 2.898, 3.646 },
/* 18. */ { 1.330, 1.734, 2.101, 2.552, 2.878, 3.610 },
/* 19. */ { 1.328, 1.729, 2.093, 2.539, 2.861, 3.579 },
/* 20. */ { 1.325, 1.725, 2.086, 2.528, 2.845, 3.552 },
/* 21. */ { 1.323, 1.721, 2.080, 2.518, 2.831, 3.527 },
/* 22. */ { 1.321, 1.717, 2.074, 2.508, 2.819, 3.505 },
/* 23. */ { 1.319, 1.714, 2.069, 2.500, 2.807, 3.485 },
/* 24. */ { 1.318, 1.711, 2.064, 2.492, 2.797, 3.467 },
/* 25. */ { 1.316, 1.708, 2.060, 2.485, 2.787, 3.450 },
/* 26. */ { 1.315, 1.706, 2.056, 2.479, 2.779, 3.435 },
/* 27. */ { 1.314, 1.703, 2.052, 2.473, 2.771, 3.421 },
/* 28. */ { 1.313, 1.701, 2.048, 2.467, 2.763, 3.408 },
/* 29. */ { 1.311, 1.699, 2.045, 2.462, 2.756, 3.396 },
/* 30. */ { 1.310, 1.697, 2.042, 2.457, 2.750, 3.385 },
/* 31. */ { 1.309, 1.696, 2.040, 2.453, 2.744, 3.375 },
/* 32. */ { 1.309, 1.694, 2.037, 2.449, 2.738, 3.365 },
/* 33. */ { 1.308, 1.692, 2.035, 2.445, 2.733, 3.356 },
/* 34. */ { 1.307, 1.691, 2.032, 2.441, 2.728, 3.348 },
/* 35. */ { 1.306, 1.690, 2.030, 2.438, 2.724, 3.340 },
/* 36. */ { 1.306, 1.688, 2.028, 2.434, 2.719, 3.333 },
/* 37. */ { 1.305, 1.687, 2.026, 2.431, 2.715, 3.326 },
/* 38. */ { 1.304, 1.686, 2.024, 2.429, 2.712, 3.319 },
/* 39. */ { 1.304, 1.685, 2.023, 2.426, 2.708, 3.313 },
/* 40. */ { 1.303, 1.684, 2.021, 2.423, 2.704, 3.307 },
/* 41. */ { 1.303, 1.683, 2.020, 2.421, 2.701, 3.301 },
/* 42. */ { 1.302, 1.682, 2.018, 2.418, 2.698, 3.296 },
/* 43. */ { 1.302, 1.681, 2.017, 2.416, 2.695, 3.291 },
/* 44. */ { 1.301, 1.680, 2.015, 2.414, 2.692, 3.286 },
/* 45. */ { 1.301, 1.679, 2.014, 2.412, 2.690, 3.281 },
/* 46. */ { 1.300, 1.679, 2.013, 2.410, 2.687, 3.277 },
/* 47. */ { 1.300, 1.678, 2.012, 2.408, 2.685, 3.273 },
/* 48. */ { 1.299, 1.677, 2.011, 2.407, 2.682, 3.269 },
/* 49. */ { 1.299, 1.677, 2.010, 2.405, 2.680, 3.265 },
/* 50. */ { 1.299, 1.676, 2.009, 2.403, 2.678, 3.261 },
/* 51. */ { 1.298, 1.675, 2.008, 2.402, 2.676, 3.258 },
/* 52. */ { 1.298, 1.675, 2.007, 2.400, 2.674, 3.255 },
/* 53. */ { 1.298, 1.674, 2.006, 2.399, 2.672, 3.251 },
/* 54. */ { 1.297, 1.674, 2.005, 2.397, 2.670, 3.248 },
/* 55. */ { 1.297, 1.673, 2.004, 2.396, 2.668, 3.245 },
/* 56. */ { 1.297, 1.673, 2.003, 2.395, 2.667, 3.242 },
/* 57. */ { 1.297, 1.672, 2.002, 2.394, 2.665, 3.239 },
/* 58. */ { 1.296, 1.672, 2.002, 2.392, 2.663, 3.237 },
/* 59. */ { 1.296, 1.671, 2.001, 2.391, 2.662, 3.234 },
/* 60. */ { 1.296, 1.671, 2.000, 2.390, 2.660, 3.232 },
/* 61. */ { 1.296, 1.670, 2.000, 2.389, 2.659, 3.229 },
/* 62. */ { 1.295, 1.670, 1.999, 2.388, 2.657, 3.227 },
/* 63. */ { 1.295, 1.669, 1.998, 2.387, 2.656, 3.225 },
/* 64. */ { 1.295, 1.669, 1.998, 2.386, 2.655, 3.223 },
/* 65. */ { 1.295, 1.669, 1.997, 2.385, 2.654, 3.220 },
/* 66. */ { 1.295, 1.668, 1.997, 2.384, 2.652, 3.218 },
/* 67. */ { 1.294, 1.668, 1.996, 2.383, 2.651, 3.216 },
/* 68. */ { 1.294, 1.668, 1.995, 2.382, 2.650, 3.214 },
/* 69. */ { 1.294, 1.667, 1.995, 2.382, 2.649, 3.213 },
/* 70. */ { 1.294, 1.667, 1.994, 2.381, 2.648, 3.211 },
/* 71. */ { 1.294, 1.667, 1.994, 2.380, 2.647, 3.209 },
/* 72. */ { 1.293, 1.666, 1.993, 2.379, 2.646, 3.207 },
/* 73. */ { 1.293, 1.666, 1.993, 2.379, 2.645, 3.206 },
/* 74. */ { 1.293, 1.666, 1.993, 2.378, 2.644, 3.204 },
/* 75. */ { 1.293, 1.665, 1.992, 2.377, 2.643, 3.202 },
/* 76. */ { 1.293, 1.665, 1.992, 2.376, 2.642, 3.201 },
/* 77. */ { 1.293, 1.665, 1.991, 2.376, 2.641, 3.199 },
/* 78. */ { 1.292, 1.665, 1.991, 2.375, 2.640, 3.198 },
/* 79. */ { 1.292, 1.664, 1.990, 2.374, 2.640, 3.197 },
/* 80. */ { 1.292, 1.664, 1.990, 2.374, 2.639, 3.195 },
/* 81. */ { 1.292, 1.664, 1.990, 2.373, 2.638, 3.194 },
/* 82. */ { 1.292, 1.664, 1.989, 2.373, 2.637, 3.193 },
/* 83. */ { 1.292, 1.663, 1.989, 2.372, 2.636, 3.191 },
/* 84. */ { 1.292, 1.663, 1.989, 2.372, 2.636, 3.190 },
/* 85. */ { 1.292, 1.663, 1.988, 2.371, 2.635, 3.189 },
/* 86. */ { 1.291, 1.663, 1.988, 2.370, 2.634, 3.188 },
/* 87. */ { 1.291, 1.663, 1.988, 2.370, 2.634, 3.187 },
/* 88. */ { 1.291, 1.662, 1.987, 2.369, 2.633, 3.185 },
/* 89. */ { 1.291, 1.662, 1.987, 2.369, 2.632, 3.184 },
/* 90. */ { 1.291, 1.662, 1.987, 2.368, 2.632, 3.183 },
/* 91. */ { 1.291, 1.662, 1.986, 2.368, 2.631, 3.182 },
/* 92. */ { 1.291, 1.662, 1.986, 2.368, 2.630, 3.181 },
/* 93. */ { 1.291, 1.661, 1.986, 2.367, 2.630, 3.180 },
/* 94. */ { 1.291, 1.661, 1.986, 2.367, 2.629, 3.179 },
/* 95. */ { 1.291, 1.661, 1.985, 2.366, 2.629, 3.178 },
/* 96. */ { 1.290, 1.661, 1.985, 2.366, 2.628, 3.177 },
/* 97. */ { 1.290, 1.661, 1.985, 2.365, 2.627, 3.176 },
/* 98. */ { 1.290, 1.661, 1.984, 2.365, 2.627, 3.175 },
/* 99. */ { 1.290, 1.660, 1.984, 2.365, 2.626, 3.175 },
/* 100. */ { 1.290, 1.660, 1.984, 2.364, 2.626, 3.174 }
};
TAILQ_HEAD(pointlist, point);
struct dataset {
struct pointlist list;
double sy, syy;
int n;
};
static struct dataset *
NewSet(void)
{
struct dataset *ds;
ds = calloc(1, sizeof *ds);
TAILQ_INIT(&ds->list);
return(ds);
}
struct point {
TAILQ_ENTRY(point) list;
double val;
};
static void
AddPoint(struct dataset *ds, double a)
{
struct point *pp, *pp2;
pp = calloc(1, sizeof *pp);
pp->val = a;
ds->n++;
ds->sy += a;
ds->syy += a * a;
if (TAILQ_EMPTY(&ds->list)) {
TAILQ_INSERT_HEAD(&ds->list, pp, list);
return;
}
TAILQ_FOREACH(pp2, &ds->list, list) {
if (pp->val < pp2->val) {
TAILQ_INSERT_BEFORE(pp2, pp, list);
return;
}
}
TAILQ_INSERT_TAIL(&ds->list, pp, list);
}
static double
Min(struct dataset *ds)
{
return (TAILQ_FIRST(&ds->list)->val);
}
static double
Max(struct dataset *ds)
{
return(TAILQ_LAST(&ds->list, pointlist)->val);
}
static double
Avg(struct dataset *ds)
{
return(ds->sy / ds->n);
}
static double
Median(struct dataset *ds)
{
int i;
struct point *pp;
i = ds->n / 2;
TAILQ_FOREACH(pp, &ds->list, list) {
if (i--)
continue;
return (pp->val);
}
}
static double
Var(struct dataset *ds)
{
return (ds->syy - ds->sy * ds->sy / ds->n) / (ds->n - 1.0);
}
static double
Stddev(struct dataset *ds)
{
return sqrt(Var(ds));
}
static void
VitalsHead(void)
{
printf(" N Min Max Median Avg Stddev\n");
}
static void
Vitals(struct dataset *ds, int flag)
{
double a;
printf("%c %3d %13.8g %13.8g %13.8g %13.8g %13.8g",
flag == 1 ? 'x' : '+',
ds->n, Min(ds), Max(ds), Median(ds), Avg(ds), Stddev(ds));
printf("\n");
}
static void
Relative(struct dataset *ds, struct dataset *rs, int confidx)
{
double spool, s, d, e, t;
int i, c;
i = ds->n + rs->n - 2;
if (i > NSTUDENT)
t = student[0][confidx];
else
t = student[i][confidx];
spool = (ds->n - 1) * Var(ds) + (rs->n - 1) * Var(rs);
spool /= ds->n + rs->n - 2;
spool = sqrt(spool);
s = spool * sqrt(1.0 / ds->n + 1.0 / rs->n);
d = Avg(ds) - Avg(rs);
e = t * s;
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(" (Student's t, pooled s = %g)\n", spool);
} else {
printf("No difference proven at %.1f%% confidence\n",
studentpct[confidx]);
}
}
struct plot {
double min;
double max;
double span;
int width;
double x0, dx;
int height;
char *data;
};
static struct plot plot;
static void
SetupPlot(int width)
{
struct plot *pl;
pl = &plot;
pl->width = width;
pl->height = 0;
pl->data = NULL;
pl->min = 999e99;
pl->max = -999e99;
}
static void
AdjPlot(double a)
{
struct plot *pl;
pl = &plot;
if (a < pl->min)
pl->min = a;
if (a > pl->max)
pl->max = a;
pl->span = pl->max - pl->min;
pl->dx = pl->span / (pl->width - 1.0);
pl->x0 = pl->min - .5 * pl->dx;
}
static void
DimPlot(struct dataset *ds)
{
AdjPlot(Min(ds));
AdjPlot(Max(ds));
AdjPlot(Avg(ds) - Stddev(ds));
AdjPlot(Avg(ds) + Stddev(ds));
}
static void
PlotSet(struct dataset *ds, int val)
{
struct plot *pl;
struct point *pp;
int i, j, m, x;
pl = &plot;
m = 1;
i = -1;
j = 0;
TAILQ_FOREACH(pp, &ds->list, list) {
x = (pp->val - pl->x0) / pl->dx;
if (x == i) {
j++;
if (j > m)
m = j;
} else {
j = 1;
i = x;
}
}
m += 1;
if (m > pl->height) {
pl->data = realloc(pl->data, pl->width * m);
memset(pl->data + pl->height * pl->width, 0,
(m - pl->height) * pl->width);
}
pl->height = m;
i = -1;
TAILQ_FOREACH(pp, &ds->list, list) {
x = (pp->val - pl->x0) / pl->dx;
if (x == i) {
j++;
} else {
j = 1;
i = x;
}
pl->data[j * pl->width + x] |= val;
}
x = ((Avg(ds) - Stddev(ds)) - pl->x0) / pl->dx;
m = ((Avg(ds) + Stddev(ds)) - pl->x0) / pl->dx;
pl->data[m] = '|';
pl->data[x] = '|';
for (i = x + 1; i < m; i++)
if (pl->data[i] == 0)
pl->data[i] = '_';
x = (Median(ds) - pl->x0) / pl->dx;
pl->data[x] = 'M';
x = (Avg(ds) - pl->x0) / pl->dx;
pl->data[x] = 'A';
}
static void
DumpPlot(void)
{
struct plot *pl;
int i, j, k;
pl = &plot;
putchar('+');
for (i = 0; i < pl->width; i++)
putchar('-');
putchar('+');
putchar('\n');
for (i = 1; i < pl->height; i++) {
putchar('|');
for (j = 0; j < pl->width; j++) {
k = pl->data[(pl->height - i) * pl->width + j];
switch (k) {
case 0: putchar(' '); break;
case 1: putchar('x'); break;
case 2: putchar('+'); break;
case 3: putchar('*'); break;
default: printf("[%02x]", k); break;
}
}
putchar('|');
putchar('\n');
}
putchar('|');
for (j = 0; j < pl->width; j++) {
k = pl->data[j];
if (k == 0)
k = ' ';
putchar(k);
}
putchar('|');
putchar('\n');
putchar('+');
for (i = 0; i < pl->width; i++)
putchar('-');
putchar('+');
putchar('\n');
}
static struct dataset *
ReadSet(char *n)
{
FILE *f;
char buf[BUFSIZ], *p;
struct dataset *s;
double d;
int line;
if (n == NULL) {
f = stdin;
n = "<stdin>";
} else if (!strcmp(n, "-")) {
f = stdin;
n = "<stdin>";
} else {
f = fopen(n, "r");
}
if (f == NULL)
err(1, "Cannot open %s", n);
s = NewSet();
line = 0;
while (fgets(buf, sizeof buf, f) != NULL) {
line++;
p = strchr(buf, '#');
if (p != NULL)
*p = '\0';
p = buf + strlen(buf) - 1;
while (p >= buf && isspace(*p)) {
*p = '\0';
p--;
}
d = strtod(buf, &p);
if (p != NULL && *p != '\0')
err(2, "Invalid data on line %d in %s\n", line, n);
if (*buf != '\0')
AddPoint(s, d);
}
fclose(f);
if (s->n < 3) {
fprintf(stderr,
"Dataset %s must contain at least 3 data points\n", n);
exit (2);
}
return (s);
}
static void
usage(char const *whine)
{
int i;
fprintf(stderr, "%s\n", whine);
fprintf(stderr,
"Usage: ministat [ -c confidence ] [file 1 [file 2]]\n");
fprintf(stderr, "\tconfidence = {");
for (i = 0; i < NCONF; i++) {
fprintf(stderr, "%s%g%%",
i ? ", " : "",
studentpct[i]);
}
fprintf(stderr, "}\n");
exit (2);
}
int
main(int argc, char **argv)
{
struct dataset *ds1, *ds2, *ds3;
double a;
char *p;
int c, i, ci;
ci = -1;
while ((c = getopt(argc, argv, "c:")) != -1)
switch (c) {
case 'c':
a = strtod(optarg, &p);
if (p != NULL && *p != '\0')
usage("Not a floating point number");
for (i = 0; i < NCONF; i++)
if (a == studentpct[i])
ci = i;
if (ci == -1)
usage("No support for confidence level");
break;
default:
usage("Unknown option");
break;
}
if (ci == -1)
ci = 2;
argc -= optind;
argv += optind;
if (argc == 0) {
ds1 = ReadSet(NULL);
printf("x stdin\n");
} else if (argc > 0) {
ds1 = ReadSet(argv[0]);
printf("x %s\n", argv[0]);
} if (argc > 1) {
ds2 = ReadSet(argv[1]);
printf("+ %s\n", argv[1]);
}
SetupPlot(74);
DimPlot(ds1);
if (argc > 1)
DimPlot(ds2);
PlotSet(ds1, 1);
if (argc > 1)
PlotSet(ds2, 2);
DumpPlot();
VitalsHead();
Vitals(ds1, 1);
if (argc > 1) {
Vitals(ds2, 2);
Relative(ds2, ds1, ci);
}
exit(0);
}

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usr.bin/ministat/Makefile Normal file
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# $FreeBSD$
PROG= ministat
NOMAN= yes
LDADD= -lm
.include <bsd.prog.mk>
test: ${PROG}
./${PROG} < ${.CURDIR}/chameleon
./${PROG} ${.CURDIR}/chameleon
./${PROG} ${.CURDIR}/chameleon ${.CURDIR}/iguana
./${PROG} -c 80 ${.CURDIR}/chameleon ${.CURDIR}/iguana

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usr.bin/ministat/README Normal file
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$FreeBSD$
A small tool to do the statistics legwork on benchmarks etc.
Prepare your data into two files, one number per line
run
./ministat data_before data_after
and see what it says.
You need at least three data points in each data set, but the more
you have the better your result generally gets.
Here are two typical outputs:
x _1
+ _2
+--------------------------------------------------------------------------+
|x + x+ x x x + ++ |
| |_________|______AM_______________|__A___________M_______________||
+--------------------------------------------------------------------------+
N Min Max Median Avg Stddev
x 5 36060 36138 36107 36105.6 31.165686
+ 5 36084 36187 36163 36142.6 49.952978
No difference proven at 95.0% confidence
Here nothing can be concluded from the numbers. It _may_ be possible to
prove something if many more measurements are made, but with only five
measurements, nothing is proven.
x _1
+ _2
+--------------------------------------------------------------------------+
| + |
| x + +|
|x x x x + +|
| |_______________A_____M_________| |_M___A____| |
+--------------------------------------------------------------------------+
N Min Max Median Avg Stddev
x 5 0.133 0.137 0.136 0.1354 0.0015165751
+ 5 0.139 0.14 0.139 0.1394 0.00054772256
Difference at 95.0% confidence
0.004 +/- 0.00166288
2.95421% +/- 1.22812%
(Student's t, pooled s = 0.00114018)
Here we have a clearcut difference, not very big, but clear and unambiguous.

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/*
* ----------------------------------------------------------------------------
* "THE BEER-WARE LICENSE" (Revision 42):
* <phk@FreeBSD.ORG> wrote this file. As long as you retain this notice you
* can do whatever you want with this stuff. If we meet some day, and you think
* this stuff is worth it, you can buy me a beer in return. Poul-Henning Kamp
* ----------------------------------------------------------------------------
*
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
#include <stdio.h>
#include <math.h>
#include <err.h>
#include <string.h>
#include <stdlib.h>
#include <unistd.h>
#include <sys/queue.h>
#define NSTUDENT 100
#define NCONF 6
double const studentpct[] = { 80, 90, 95, 98, 99, 99.5 };
double student [NSTUDENT + 1][NCONF] = {
/* inf */ { 1.282, 1.645, 1.960, 2.326, 2.576, 3.090 },
/* 1. */ { 3.078, 6.314, 12.706, 31.821, 63.657, 318.313 },
/* 2. */ { 1.886, 2.920, 4.303, 6.965, 9.925, 22.327 },
/* 3. */ { 1.638, 2.353, 3.182, 4.541, 5.841, 10.215 },
/* 4. */ { 1.533, 2.132, 2.776, 3.747, 4.604, 7.173 },
/* 5. */ { 1.476, 2.015, 2.571, 3.365, 4.032, 5.893 },
/* 6. */ { 1.440, 1.943, 2.447, 3.143, 3.707, 5.208 },
/* 7. */ { 1.415, 1.895, 2.365, 2.998, 3.499, 4.782 },
/* 8. */ { 1.397, 1.860, 2.306, 2.896, 3.355, 4.499 },
/* 9. */ { 1.383, 1.833, 2.262, 2.821, 3.250, 4.296 },
/* 10. */ { 1.372, 1.812, 2.228, 2.764, 3.169, 4.143 },
/* 11. */ { 1.363, 1.796, 2.201, 2.718, 3.106, 4.024 },
/* 12. */ { 1.356, 1.782, 2.179, 2.681, 3.055, 3.929 },
/* 13. */ { 1.350, 1.771, 2.160, 2.650, 3.012, 3.852 },
/* 14. */ { 1.345, 1.761, 2.145, 2.624, 2.977, 3.787 },
/* 15. */ { 1.341, 1.753, 2.131, 2.602, 2.947, 3.733 },
/* 16. */ { 1.337, 1.746, 2.120, 2.583, 2.921, 3.686 },
/* 17. */ { 1.333, 1.740, 2.110, 2.567, 2.898, 3.646 },
/* 18. */ { 1.330, 1.734, 2.101, 2.552, 2.878, 3.610 },
/* 19. */ { 1.328, 1.729, 2.093, 2.539, 2.861, 3.579 },
/* 20. */ { 1.325, 1.725, 2.086, 2.528, 2.845, 3.552 },
/* 21. */ { 1.323, 1.721, 2.080, 2.518, 2.831, 3.527 },
/* 22. */ { 1.321, 1.717, 2.074, 2.508, 2.819, 3.505 },
/* 23. */ { 1.319, 1.714, 2.069, 2.500, 2.807, 3.485 },
/* 24. */ { 1.318, 1.711, 2.064, 2.492, 2.797, 3.467 },
/* 25. */ { 1.316, 1.708, 2.060, 2.485, 2.787, 3.450 },
/* 26. */ { 1.315, 1.706, 2.056, 2.479, 2.779, 3.435 },
/* 27. */ { 1.314, 1.703, 2.052, 2.473, 2.771, 3.421 },
/* 28. */ { 1.313, 1.701, 2.048, 2.467, 2.763, 3.408 },
/* 29. */ { 1.311, 1.699, 2.045, 2.462, 2.756, 3.396 },
/* 30. */ { 1.310, 1.697, 2.042, 2.457, 2.750, 3.385 },
/* 31. */ { 1.309, 1.696, 2.040, 2.453, 2.744, 3.375 },
/* 32. */ { 1.309, 1.694, 2.037, 2.449, 2.738, 3.365 },
/* 33. */ { 1.308, 1.692, 2.035, 2.445, 2.733, 3.356 },
/* 34. */ { 1.307, 1.691, 2.032, 2.441, 2.728, 3.348 },
/* 35. */ { 1.306, 1.690, 2.030, 2.438, 2.724, 3.340 },
/* 36. */ { 1.306, 1.688, 2.028, 2.434, 2.719, 3.333 },
/* 37. */ { 1.305, 1.687, 2.026, 2.431, 2.715, 3.326 },
/* 38. */ { 1.304, 1.686, 2.024, 2.429, 2.712, 3.319 },
/* 39. */ { 1.304, 1.685, 2.023, 2.426, 2.708, 3.313 },
/* 40. */ { 1.303, 1.684, 2.021, 2.423, 2.704, 3.307 },
/* 41. */ { 1.303, 1.683, 2.020, 2.421, 2.701, 3.301 },
/* 42. */ { 1.302, 1.682, 2.018, 2.418, 2.698, 3.296 },
/* 43. */ { 1.302, 1.681, 2.017, 2.416, 2.695, 3.291 },
/* 44. */ { 1.301, 1.680, 2.015, 2.414, 2.692, 3.286 },
/* 45. */ { 1.301, 1.679, 2.014, 2.412, 2.690, 3.281 },
/* 46. */ { 1.300, 1.679, 2.013, 2.410, 2.687, 3.277 },
/* 47. */ { 1.300, 1.678, 2.012, 2.408, 2.685, 3.273 },
/* 48. */ { 1.299, 1.677, 2.011, 2.407, 2.682, 3.269 },
/* 49. */ { 1.299, 1.677, 2.010, 2.405, 2.680, 3.265 },
/* 50. */ { 1.299, 1.676, 2.009, 2.403, 2.678, 3.261 },
/* 51. */ { 1.298, 1.675, 2.008, 2.402, 2.676, 3.258 },
/* 52. */ { 1.298, 1.675, 2.007, 2.400, 2.674, 3.255 },
/* 53. */ { 1.298, 1.674, 2.006, 2.399, 2.672, 3.251 },
/* 54. */ { 1.297, 1.674, 2.005, 2.397, 2.670, 3.248 },
/* 55. */ { 1.297, 1.673, 2.004, 2.396, 2.668, 3.245 },
/* 56. */ { 1.297, 1.673, 2.003, 2.395, 2.667, 3.242 },
/* 57. */ { 1.297, 1.672, 2.002, 2.394, 2.665, 3.239 },
/* 58. */ { 1.296, 1.672, 2.002, 2.392, 2.663, 3.237 },
/* 59. */ { 1.296, 1.671, 2.001, 2.391, 2.662, 3.234 },
/* 60. */ { 1.296, 1.671, 2.000, 2.390, 2.660, 3.232 },
/* 61. */ { 1.296, 1.670, 2.000, 2.389, 2.659, 3.229 },
/* 62. */ { 1.295, 1.670, 1.999, 2.388, 2.657, 3.227 },
/* 63. */ { 1.295, 1.669, 1.998, 2.387, 2.656, 3.225 },
/* 64. */ { 1.295, 1.669, 1.998, 2.386, 2.655, 3.223 },
/* 65. */ { 1.295, 1.669, 1.997, 2.385, 2.654, 3.220 },
/* 66. */ { 1.295, 1.668, 1.997, 2.384, 2.652, 3.218 },
/* 67. */ { 1.294, 1.668, 1.996, 2.383, 2.651, 3.216 },
/* 68. */ { 1.294, 1.668, 1.995, 2.382, 2.650, 3.214 },
/* 69. */ { 1.294, 1.667, 1.995, 2.382, 2.649, 3.213 },
/* 70. */ { 1.294, 1.667, 1.994, 2.381, 2.648, 3.211 },
/* 71. */ { 1.294, 1.667, 1.994, 2.380, 2.647, 3.209 },
/* 72. */ { 1.293, 1.666, 1.993, 2.379, 2.646, 3.207 },
/* 73. */ { 1.293, 1.666, 1.993, 2.379, 2.645, 3.206 },
/* 74. */ { 1.293, 1.666, 1.993, 2.378, 2.644, 3.204 },
/* 75. */ { 1.293, 1.665, 1.992, 2.377, 2.643, 3.202 },
/* 76. */ { 1.293, 1.665, 1.992, 2.376, 2.642, 3.201 },
/* 77. */ { 1.293, 1.665, 1.991, 2.376, 2.641, 3.199 },
/* 78. */ { 1.292, 1.665, 1.991, 2.375, 2.640, 3.198 },
/* 79. */ { 1.292, 1.664, 1.990, 2.374, 2.640, 3.197 },
/* 80. */ { 1.292, 1.664, 1.990, 2.374, 2.639, 3.195 },
/* 81. */ { 1.292, 1.664, 1.990, 2.373, 2.638, 3.194 },
/* 82. */ { 1.292, 1.664, 1.989, 2.373, 2.637, 3.193 },
/* 83. */ { 1.292, 1.663, 1.989, 2.372, 2.636, 3.191 },
/* 84. */ { 1.292, 1.663, 1.989, 2.372, 2.636, 3.190 },
/* 85. */ { 1.292, 1.663, 1.988, 2.371, 2.635, 3.189 },
/* 86. */ { 1.291, 1.663, 1.988, 2.370, 2.634, 3.188 },
/* 87. */ { 1.291, 1.663, 1.988, 2.370, 2.634, 3.187 },
/* 88. */ { 1.291, 1.662, 1.987, 2.369, 2.633, 3.185 },
/* 89. */ { 1.291, 1.662, 1.987, 2.369, 2.632, 3.184 },
/* 90. */ { 1.291, 1.662, 1.987, 2.368, 2.632, 3.183 },
/* 91. */ { 1.291, 1.662, 1.986, 2.368, 2.631, 3.182 },
/* 92. */ { 1.291, 1.662, 1.986, 2.368, 2.630, 3.181 },
/* 93. */ { 1.291, 1.661, 1.986, 2.367, 2.630, 3.180 },
/* 94. */ { 1.291, 1.661, 1.986, 2.367, 2.629, 3.179 },
/* 95. */ { 1.291, 1.661, 1.985, 2.366, 2.629, 3.178 },
/* 96. */ { 1.290, 1.661, 1.985, 2.366, 2.628, 3.177 },
/* 97. */ { 1.290, 1.661, 1.985, 2.365, 2.627, 3.176 },
/* 98. */ { 1.290, 1.661, 1.984, 2.365, 2.627, 3.175 },
/* 99. */ { 1.290, 1.660, 1.984, 2.365, 2.626, 3.175 },
/* 100. */ { 1.290, 1.660, 1.984, 2.364, 2.626, 3.174 }
};
TAILQ_HEAD(pointlist, point);
struct dataset {
struct pointlist list;
double sy, syy;
int n;
};
static struct dataset *
NewSet(void)
{
struct dataset *ds;
ds = calloc(1, sizeof *ds);
TAILQ_INIT(&ds->list);
return(ds);
}
struct point {
TAILQ_ENTRY(point) list;
double val;
};
static void
AddPoint(struct dataset *ds, double a)
{
struct point *pp, *pp2;
pp = calloc(1, sizeof *pp);
pp->val = a;
ds->n++;
ds->sy += a;
ds->syy += a * a;
if (TAILQ_EMPTY(&ds->list)) {
TAILQ_INSERT_HEAD(&ds->list, pp, list);
return;
}
TAILQ_FOREACH(pp2, &ds->list, list) {
if (pp->val < pp2->val) {
TAILQ_INSERT_BEFORE(pp2, pp, list);
return;
}
}
TAILQ_INSERT_TAIL(&ds->list, pp, list);
}
static double
Min(struct dataset *ds)
{
return (TAILQ_FIRST(&ds->list)->val);
}
static double
Max(struct dataset *ds)
{
return(TAILQ_LAST(&ds->list, pointlist)->val);
}
static double
Avg(struct dataset *ds)
{
return(ds->sy / ds->n);
}
static double
Median(struct dataset *ds)
{
int i;
struct point *pp;
i = ds->n / 2;
TAILQ_FOREACH(pp, &ds->list, list) {
if (i--)
continue;
return (pp->val);
}
}
static double
Var(struct dataset *ds)
{
return (ds->syy - ds->sy * ds->sy / ds->n) / (ds->n - 1.0);
}
static double
Stddev(struct dataset *ds)
{
return sqrt(Var(ds));
}
static void
VitalsHead(void)
{
printf(" N Min Max Median Avg Stddev\n");
}
static void
Vitals(struct dataset *ds, int flag)
{
double a;
printf("%c %3d %13.8g %13.8g %13.8g %13.8g %13.8g",
flag == 1 ? 'x' : '+',
ds->n, Min(ds), Max(ds), Median(ds), Avg(ds), Stddev(ds));
printf("\n");
}
static void
Relative(struct dataset *ds, struct dataset *rs, int confidx)
{
double spool, s, d, e, t;
int i, c;
i = ds->n + rs->n - 2;
if (i > NSTUDENT)
t = student[0][confidx];
else
t = student[i][confidx];
spool = (ds->n - 1) * Var(ds) + (rs->n - 1) * Var(rs);
spool /= ds->n + rs->n - 2;
spool = sqrt(spool);
s = spool * sqrt(1.0 / ds->n + 1.0 / rs->n);
d = Avg(ds) - Avg(rs);
e = t * s;
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(" (Student's t, pooled s = %g)\n", spool);
} else {
printf("No difference proven at %.1f%% confidence\n",
studentpct[confidx]);
}
}
struct plot {
double min;
double max;
double span;
int width;
double x0, dx;
int height;
char *data;
};
static struct plot plot;
static void
SetupPlot(int width)
{
struct plot *pl;
pl = &plot;
pl->width = width;
pl->height = 0;
pl->data = NULL;
pl->min = 999e99;
pl->max = -999e99;
}
static void
AdjPlot(double a)
{
struct plot *pl;
pl = &plot;
if (a < pl->min)
pl->min = a;
if (a > pl->max)
pl->max = a;
pl->span = pl->max - pl->min;
pl->dx = pl->span / (pl->width - 1.0);
pl->x0 = pl->min - .5 * pl->dx;
}
static void
DimPlot(struct dataset *ds)
{
AdjPlot(Min(ds));
AdjPlot(Max(ds));
AdjPlot(Avg(ds) - Stddev(ds));
AdjPlot(Avg(ds) + Stddev(ds));
}
static void
PlotSet(struct dataset *ds, int val)
{
struct plot *pl;
struct point *pp;
int i, j, m, x;
pl = &plot;
m = 1;
i = -1;
j = 0;
TAILQ_FOREACH(pp, &ds->list, list) {
x = (pp->val - pl->x0) / pl->dx;
if (x == i) {
j++;
if (j > m)
m = j;
} else {
j = 1;
i = x;
}
}
m += 1;
if (m > pl->height) {
pl->data = realloc(pl->data, pl->width * m);
memset(pl->data + pl->height * pl->width, 0,
(m - pl->height) * pl->width);
}
pl->height = m;
i = -1;
TAILQ_FOREACH(pp, &ds->list, list) {
x = (pp->val - pl->x0) / pl->dx;
if (x == i) {
j++;
} else {
j = 1;
i = x;
}
pl->data[j * pl->width + x] |= val;
}
x = ((Avg(ds) - Stddev(ds)) - pl->x0) / pl->dx;
m = ((Avg(ds) + Stddev(ds)) - pl->x0) / pl->dx;
pl->data[m] = '|';
pl->data[x] = '|';
for (i = x + 1; i < m; i++)
if (pl->data[i] == 0)
pl->data[i] = '_';
x = (Median(ds) - pl->x0) / pl->dx;
pl->data[x] = 'M';
x = (Avg(ds) - pl->x0) / pl->dx;
pl->data[x] = 'A';
}
static void
DumpPlot(void)
{
struct plot *pl;
int i, j, k;
pl = &plot;
putchar('+');
for (i = 0; i < pl->width; i++)
putchar('-');
putchar('+');
putchar('\n');
for (i = 1; i < pl->height; i++) {
putchar('|');
for (j = 0; j < pl->width; j++) {
k = pl->data[(pl->height - i) * pl->width + j];
switch (k) {
case 0: putchar(' '); break;
case 1: putchar('x'); break;
case 2: putchar('+'); break;
case 3: putchar('*'); break;
default: printf("[%02x]", k); break;
}
}
putchar('|');
putchar('\n');
}
putchar('|');
for (j = 0; j < pl->width; j++) {
k = pl->data[j];
if (k == 0)
k = ' ';
putchar(k);
}
putchar('|');
putchar('\n');
putchar('+');
for (i = 0; i < pl->width; i++)
putchar('-');
putchar('+');
putchar('\n');
}
static struct dataset *
ReadSet(char *n)
{
FILE *f;
char buf[BUFSIZ], *p;
struct dataset *s;
double d;
int line;
if (n == NULL) {
f = stdin;
n = "<stdin>";
} else if (!strcmp(n, "-")) {
f = stdin;
n = "<stdin>";
} else {
f = fopen(n, "r");
}
if (f == NULL)
err(1, "Cannot open %s", n);
s = NewSet();
line = 0;
while (fgets(buf, sizeof buf, f) != NULL) {
line++;
p = strchr(buf, '#');
if (p != NULL)
*p = '\0';
p = buf + strlen(buf) - 1;
while (p >= buf && isspace(*p)) {
*p = '\0';
p--;
}
d = strtod(buf, &p);
if (p != NULL && *p != '\0')
err(2, "Invalid data on line %d in %s\n", line, n);
if (*buf != '\0')
AddPoint(s, d);
}
fclose(f);
if (s->n < 3) {
fprintf(stderr,
"Dataset %s must contain at least 3 data points\n", n);
exit (2);
}
return (s);
}
static void
usage(char const *whine)
{
int i;
fprintf(stderr, "%s\n", whine);
fprintf(stderr,
"Usage: ministat [ -c confidence ] [file 1 [file 2]]\n");
fprintf(stderr, "\tconfidence = {");
for (i = 0; i < NCONF; i++) {
fprintf(stderr, "%s%g%%",
i ? ", " : "",
studentpct[i]);
}
fprintf(stderr, "}\n");
exit (2);
}
int
main(int argc, char **argv)
{
struct dataset *ds1, *ds2, *ds3;
double a;
char *p;
int c, i, ci;
ci = -1;
while ((c = getopt(argc, argv, "c:")) != -1)
switch (c) {
case 'c':
a = strtod(optarg, &p);
if (p != NULL && *p != '\0')
usage("Not a floating point number");
for (i = 0; i < NCONF; i++)
if (a == studentpct[i])
ci = i;
if (ci == -1)
usage("No support for confidence level");
break;
default:
usage("Unknown option");
break;
}
if (ci == -1)
ci = 2;
argc -= optind;
argv += optind;
if (argc == 0) {
ds1 = ReadSet(NULL);
printf("x stdin\n");
} else if (argc > 0) {
ds1 = ReadSet(argv[0]);
printf("x %s\n", argv[0]);
} if (argc > 1) {
ds2 = ReadSet(argv[1]);
printf("+ %s\n", argv[1]);
}
SetupPlot(74);
DimPlot(ds1);
if (argc > 1)
DimPlot(ds2);
PlotSet(ds1, 1);
if (argc > 1)
PlotSet(ds2, 2);
DumpPlot();
VitalsHead();
Vitals(ds1, 1);
if (argc > 1) {
Vitals(ds2, 2);
Relative(ds2, ds1, ci);
}
exit(0);
}