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25 | <div class="section"> | |
26 | <div class="titlepage"><div><div><h5 class="title"> | |
27 | <a name="math_toolkit.stat_tut.weg.nccs_eg.nccs_power_eg"></a><a class="link" href="nccs_power_eg.html" title="Tables of the power function of the chi2 test.">Tables | |
28 | of the power function of the chi<sup>2</sup> test.</a> | |
29 | </h5></div></div></div> | |
30 | <p> | |
31 | This example computes a table of the power of the χ<sup>2</sup> | |
32 | test at the 5% significance | |
33 | level, for various degrees of freedom and non-centrality parameters. | |
34 | The table is deliberately the same as Table 6 from "The Non-Central | |
35 | χ<sup>2</sup> and F-Distributions and their applications.", P. B. Patnaik, Biometrika, | |
36 | Vol. 36, No. 1/2 (June 1949), 202-232. | |
37 | </p> | |
38 | <p> | |
39 | First we need some includes to access the non-central chi squared distribution | |
40 | (and some basic std output of course). | |
41 | </p> | |
42 | <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">non_central_chi_squared</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> | |
43 | <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">chi_squared</span><span class="special">;</span> | |
44 | <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">non_central_chi_squared</span><span class="special">;</span> | |
45 | ||
46 | <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> | |
47 | <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> | |
48 | <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">;</span> | |
49 | ||
50 | <span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> | |
51 | <span class="special">{</span> | |
52 | </pre> | |
53 | <p> | |
54 | Create a table of the power of the χ<sup>2</sup> test at 5% significance level, start | |
55 | with a table header: | |
56 | </p> | |
57 | <pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"[table\n[[[nu]]"</span><span class="special">;</span> | |
58 | <span class="keyword">for</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">lam</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> <span class="identifier">lam</span> <span class="special"><=</span> <span class="number">20</span><span class="special">;</span> <span class="identifier">lam</span> <span class="special">+=</span> <span class="number">2</span><span class="special">)</span> | |
59 | <span class="special">{</span> | |
60 | <span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"[[lambda]="</span> <span class="special"><<</span> <span class="identifier">lam</span> <span class="special"><<</span> <span class="string">"]"</span><span class="special">;</span> | |
61 | <span class="special">}</span> | |
62 | <span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"]\n"</span><span class="special">;</span> | |
63 | </pre> | |
64 | <p> | |
65 | (Note: the enclosing [] brackets are to format as a table in Boost.Quickbook). | |
66 | </p> | |
67 | <p> | |
68 | Enumerate the rows and columns and print the power of the test for each | |
69 | table cell: | |
70 | </p> | |
71 | <pre class="programlisting"><span class="keyword">for</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">n</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> <span class="identifier">n</span> <span class="special"><=</span> <span class="number">20</span><span class="special">;</span> <span class="special">++</span><span class="identifier">n</span><span class="special">)</span> | |
72 | <span class="special">{</span> | |
73 | <span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"[["</span> <span class="special"><<</span> <span class="identifier">n</span> <span class="special"><<</span> <span class="string">"]"</span><span class="special">;</span> | |
74 | <span class="keyword">for</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">lam</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> <span class="identifier">lam</span> <span class="special"><=</span> <span class="number">20</span><span class="special">;</span> <span class="identifier">lam</span> <span class="special">+=</span> <span class="number">2</span><span class="special">)</span> | |
75 | <span class="special">{</span> | |
76 | </pre> | |
77 | <p> | |
78 | Calculate the χ<sup>2</sup> statistic for a 5% significance: | |
79 | </p> | |
80 | <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">cs</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">chi_squared</span><span class="special">(</span><span class="identifier">n</span><span class="special">),</span> <span class="number">0.05</span><span class="special">));</span> | |
81 | </pre> | |
82 | <p> | |
83 | The power of the test is given by the complement of the CDF of the non-central | |
84 | χ<sup>2</sup> distribution: | |
85 | </p> | |
86 | <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">beta</span> <span class="special">=</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">non_central_chi_squared</span><span class="special">(</span><span class="identifier">n</span><span class="special">,</span> <span class="identifier">lam</span><span class="special">),</span> <span class="identifier">cs</span><span class="special">));</span> | |
87 | </pre> | |
88 | <p> | |
89 | Then output the cell value: | |
90 | </p> | |
91 | <pre class="programlisting"> <span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"["</span> <span class="special"><<</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">beta</span> <span class="special"><<</span> <span class="string">"]"</span><span class="special">;</span> | |
92 | <span class="special">}</span> | |
93 | <span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"]"</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> | |
94 | <span class="special">}</span> | |
95 | <span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"]"</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> | |
96 | <span class="special">}</span> | |
97 | </pre> | |
98 | <p> | |
99 | The output from this program is a table in Boost.Quickbook format as | |
100 | shown below. | |
101 | </p> | |
102 | <p> | |
103 | We can interpret this as follows - for example if ν=10 and λ=10 then the | |
104 | power of the test is 0.542 - so we have only a 54% chance of correctly | |
105 | detecting that our null hypothesis is false, and a 46% chance of incurring | |
106 | a type II error (failing to reject the null hypothesis when it is in | |
107 | fact false): | |
108 | </p> | |
109 | <div class="informaltable"><table class="table"> | |
110 | <colgroup> | |
111 | <col> | |
112 | <col> | |
113 | <col> | |
114 | <col> | |
115 | <col> | |
116 | <col> | |
117 | <col> | |
118 | <col> | |
119 | <col> | |
120 | <col> | |
121 | <col> | |
122 | </colgroup> | |
123 | <thead><tr> | |
124 | <th> | |
125 | <p> | |
126 | ν | |
127 | </p> | |
128 | </th> | |
129 | <th> | |
130 | <p> | |
131 | λ=2 | |
132 | </p> | |
133 | </th> | |
134 | <th> | |
135 | <p> | |
136 | λ=4 | |
137 | </p> | |
138 | </th> | |
139 | <th> | |
140 | <p> | |
141 | λ=6 | |
142 | </p> | |
143 | </th> | |
144 | <th> | |
145 | <p> | |
146 | λ=8 | |
147 | </p> | |
148 | </th> | |
149 | <th> | |
150 | <p> | |
151 | λ=10 | |
152 | </p> | |
153 | </th> | |
154 | <th> | |
155 | <p> | |
156 | λ=12 | |
157 | </p> | |
158 | </th> | |
159 | <th> | |
160 | <p> | |
161 | λ=14 | |
162 | </p> | |
163 | </th> | |
164 | <th> | |
165 | <p> | |
166 | λ=16 | |
167 | </p> | |
168 | </th> | |
169 | <th> | |
170 | <p> | |
171 | λ=18 | |
172 | </p> | |
173 | </th> | |
174 | <th> | |
175 | <p> | |
176 | λ=20 | |
177 | </p> | |
178 | </th> | |
179 | </tr></thead> | |
180 | <tbody> | |
181 | <tr> | |
182 | <td> | |
183 | <p> | |
184 | 2 | |
185 | </p> | |
186 | </td> | |
187 | <td> | |
188 | <p> | |
189 | 0.226 | |
190 | </p> | |
191 | </td> | |
192 | <td> | |
193 | <p> | |
194 | 0.415 | |
195 | </p> | |
196 | </td> | |
197 | <td> | |
198 | <p> | |
199 | 0.584 | |
200 | </p> | |
201 | </td> | |
202 | <td> | |
203 | <p> | |
204 | 0.718 | |
205 | </p> | |
206 | </td> | |
207 | <td> | |
208 | <p> | |
209 | 0.815 | |
210 | </p> | |
211 | </td> | |
212 | <td> | |
213 | <p> | |
214 | 0.883 | |
215 | </p> | |
216 | </td> | |
217 | <td> | |
218 | <p> | |
219 | 0.928 | |
220 | </p> | |
221 | </td> | |
222 | <td> | |
223 | <p> | |
224 | 0.957 | |
225 | </p> | |
226 | </td> | |
227 | <td> | |
228 | <p> | |
229 | 0.974 | |
230 | </p> | |
231 | </td> | |
232 | <td> | |
233 | <p> | |
234 | 0.985 | |
235 | </p> | |
236 | </td> | |
237 | </tr> | |
238 | <tr> | |
239 | <td> | |
240 | <p> | |
241 | 3 | |
242 | </p> | |
243 | </td> | |
244 | <td> | |
245 | <p> | |
246 | 0.192 | |
247 | </p> | |
248 | </td> | |
249 | <td> | |
250 | <p> | |
251 | 0.359 | |
252 | </p> | |
253 | </td> | |
254 | <td> | |
255 | <p> | |
256 | 0.518 | |
257 | </p> | |
258 | </td> | |
259 | <td> | |
260 | <p> | |
261 | 0.654 | |
262 | </p> | |
263 | </td> | |
264 | <td> | |
265 | <p> | |
266 | 0.761 | |
267 | </p> | |
268 | </td> | |
269 | <td> | |
270 | <p> | |
271 | 0.84 | |
272 | </p> | |
273 | </td> | |
274 | <td> | |
275 | <p> | |
276 | 0.896 | |
277 | </p> | |
278 | </td> | |
279 | <td> | |
280 | <p> | |
281 | 0.934 | |
282 | </p> | |
283 | </td> | |
284 | <td> | |
285 | <p> | |
286 | 0.959 | |
287 | </p> | |
288 | </td> | |
289 | <td> | |
290 | <p> | |
291 | 0.975 | |
292 | </p> | |
293 | </td> | |
294 | </tr> | |
295 | <tr> | |
296 | <td> | |
297 | <p> | |
298 | 4 | |
299 | </p> | |
300 | </td> | |
301 | <td> | |
302 | <p> | |
303 | 0.171 | |
304 | </p> | |
305 | </td> | |
306 | <td> | |
307 | <p> | |
308 | 0.32 | |
309 | </p> | |
310 | </td> | |
311 | <td> | |
312 | <p> | |
313 | 0.47 | |
314 | </p> | |
315 | </td> | |
316 | <td> | |
317 | <p> | |
318 | 0.605 | |
319 | </p> | |
320 | </td> | |
321 | <td> | |
322 | <p> | |
323 | 0.716 | |
324 | </p> | |
325 | </td> | |
326 | <td> | |
327 | <p> | |
328 | 0.802 | |
329 | </p> | |
330 | </td> | |
331 | <td> | |
332 | <p> | |
333 | 0.866 | |
334 | </p> | |
335 | </td> | |
336 | <td> | |
337 | <p> | |
338 | 0.912 | |
339 | </p> | |
340 | </td> | |
341 | <td> | |
342 | <p> | |
343 | 0.943 | |
344 | </p> | |
345 | </td> | |
346 | <td> | |
347 | <p> | |
348 | 0.964 | |
349 | </p> | |
350 | </td> | |
351 | </tr> | |
352 | <tr> | |
353 | <td> | |
354 | <p> | |
355 | 5 | |
356 | </p> | |
357 | </td> | |
358 | <td> | |
359 | <p> | |
360 | 0.157 | |
361 | </p> | |
362 | </td> | |
363 | <td> | |
364 | <p> | |
365 | 0.292 | |
366 | </p> | |
367 | </td> | |
368 | <td> | |
369 | <p> | |
370 | 0.433 | |
371 | </p> | |
372 | </td> | |
373 | <td> | |
374 | <p> | |
375 | 0.564 | |
376 | </p> | |
377 | </td> | |
378 | <td> | |
379 | <p> | |
380 | 0.677 | |
381 | </p> | |
382 | </td> | |
383 | <td> | |
384 | <p> | |
385 | 0.769 | |
386 | </p> | |
387 | </td> | |
388 | <td> | |
389 | <p> | |
390 | 0.839 | |
391 | </p> | |
392 | </td> | |
393 | <td> | |
394 | <p> | |
395 | 0.89 | |
396 | </p> | |
397 | </td> | |
398 | <td> | |
399 | <p> | |
400 | 0.927 | |
401 | </p> | |
402 | </td> | |
403 | <td> | |
404 | <p> | |
405 | 0.952 | |
406 | </p> | |
407 | </td> | |
408 | </tr> | |
409 | <tr> | |
410 | <td> | |
411 | <p> | |
412 | 6 | |
413 | </p> | |
414 | </td> | |
415 | <td> | |
416 | <p> | |
417 | 0.146 | |
418 | </p> | |
419 | </td> | |
420 | <td> | |
421 | <p> | |
422 | 0.27 | |
423 | </p> | |
424 | </td> | |
425 | <td> | |
426 | <p> | |
427 | 0.403 | |
428 | </p> | |
429 | </td> | |
430 | <td> | |
431 | <p> | |
432 | 0.531 | |
433 | </p> | |
434 | </td> | |
435 | <td> | |
436 | <p> | |
437 | 0.644 | |
438 | </p> | |
439 | </td> | |
440 | <td> | |
441 | <p> | |
442 | 0.738 | |
443 | </p> | |
444 | </td> | |
445 | <td> | |
446 | <p> | |
447 | 0.813 | |
448 | </p> | |
449 | </td> | |
450 | <td> | |
451 | <p> | |
452 | 0.869 | |
453 | </p> | |
454 | </td> | |
455 | <td> | |
456 | <p> | |
457 | 0.911 | |
458 | </p> | |
459 | </td> | |
460 | <td> | |
461 | <p> | |
462 | 0.94 | |
463 | </p> | |
464 | </td> | |
465 | </tr> | |
466 | <tr> | |
467 | <td> | |
468 | <p> | |
469 | 7 | |
470 | </p> | |
471 | </td> | |
472 | <td> | |
473 | <p> | |
474 | 0.138 | |
475 | </p> | |
476 | </td> | |
477 | <td> | |
478 | <p> | |
479 | 0.252 | |
480 | </p> | |
481 | </td> | |
482 | <td> | |
483 | <p> | |
484 | 0.378 | |
485 | </p> | |
486 | </td> | |
487 | <td> | |
488 | <p> | |
489 | 0.502 | |
490 | </p> | |
491 | </td> | |
492 | <td> | |
493 | <p> | |
494 | 0.614 | |
495 | </p> | |
496 | </td> | |
497 | <td> | |
498 | <p> | |
499 | 0.71 | |
500 | </p> | |
501 | </td> | |
502 | <td> | |
503 | <p> | |
504 | 0.788 | |
505 | </p> | |
506 | </td> | |
507 | <td> | |
508 | <p> | |
509 | 0.849 | |
510 | </p> | |
511 | </td> | |
512 | <td> | |
513 | <p> | |
514 | 0.895 | |
515 | </p> | |
516 | </td> | |
517 | <td> | |
518 | <p> | |
519 | 0.928 | |
520 | </p> | |
521 | </td> | |
522 | </tr> | |
523 | <tr> | |
524 | <td> | |
525 | <p> | |
526 | 8 | |
527 | </p> | |
528 | </td> | |
529 | <td> | |
530 | <p> | |
531 | 0.131 | |
532 | </p> | |
533 | </td> | |
534 | <td> | |
535 | <p> | |
536 | 0.238 | |
537 | </p> | |
538 | </td> | |
539 | <td> | |
540 | <p> | |
541 | 0.357 | |
542 | </p> | |
543 | </td> | |
544 | <td> | |
545 | <p> | |
546 | 0.477 | |
547 | </p> | |
548 | </td> | |
549 | <td> | |
550 | <p> | |
551 | 0.588 | |
552 | </p> | |
553 | </td> | |
554 | <td> | |
555 | <p> | |
556 | 0.685 | |
557 | </p> | |
558 | </td> | |
559 | <td> | |
560 | <p> | |
561 | 0.765 | |
562 | </p> | |
563 | </td> | |
564 | <td> | |
565 | <p> | |
566 | 0.829 | |
567 | </p> | |
568 | </td> | |
569 | <td> | |
570 | <p> | |
571 | 0.879 | |
572 | </p> | |
573 | </td> | |
574 | <td> | |
575 | <p> | |
576 | 0.915 | |
577 | </p> | |
578 | </td> | |
579 | </tr> | |
580 | <tr> | |
581 | <td> | |
582 | <p> | |
583 | 9 | |
584 | </p> | |
585 | </td> | |
586 | <td> | |
587 | <p> | |
588 | 0.125 | |
589 | </p> | |
590 | </td> | |
591 | <td> | |
592 | <p> | |
593 | 0.225 | |
594 | </p> | |
595 | </td> | |
596 | <td> | |
597 | <p> | |
598 | 0.339 | |
599 | </p> | |
600 | </td> | |
601 | <td> | |
602 | <p> | |
603 | 0.454 | |
604 | </p> | |
605 | </td> | |
606 | <td> | |
607 | <p> | |
608 | 0.564 | |
609 | </p> | |
610 | </td> | |
611 | <td> | |
612 | <p> | |
613 | 0.661 | |
614 | </p> | |
615 | </td> | |
616 | <td> | |
617 | <p> | |
618 | 0.744 | |
619 | </p> | |
620 | </td> | |
621 | <td> | |
622 | <p> | |
623 | 0.811 | |
624 | </p> | |
625 | </td> | |
626 | <td> | |
627 | <p> | |
628 | 0.863 | |
629 | </p> | |
630 | </td> | |
631 | <td> | |
632 | <p> | |
633 | 0.903 | |
634 | </p> | |
635 | </td> | |
636 | </tr> | |
637 | <tr> | |
638 | <td> | |
639 | <p> | |
640 | 10 | |
641 | </p> | |
642 | </td> | |
643 | <td> | |
644 | <p> | |
645 | 0.121 | |
646 | </p> | |
647 | </td> | |
648 | <td> | |
649 | <p> | |
650 | 0.215 | |
651 | </p> | |
652 | </td> | |
653 | <td> | |
654 | <p> | |
655 | 0.323 | |
656 | </p> | |
657 | </td> | |
658 | <td> | |
659 | <p> | |
660 | 0.435 | |
661 | </p> | |
662 | </td> | |
663 | <td> | |
664 | <p> | |
665 | 0.542 | |
666 | </p> | |
667 | </td> | |
668 | <td> | |
669 | <p> | |
670 | 0.64 | |
671 | </p> | |
672 | </td> | |
673 | <td> | |
674 | <p> | |
675 | 0.723 | |
676 | </p> | |
677 | </td> | |
678 | <td> | |
679 | <p> | |
680 | 0.793 | |
681 | </p> | |
682 | </td> | |
683 | <td> | |
684 | <p> | |
685 | 0.848 | |
686 | </p> | |
687 | </td> | |
688 | <td> | |
689 | <p> | |
690 | 0.891 | |
691 | </p> | |
692 | </td> | |
693 | </tr> | |
694 | <tr> | |
695 | <td> | |
696 | <p> | |
697 | 11 | |
698 | </p> | |
699 | </td> | |
700 | <td> | |
701 | <p> | |
702 | 0.117 | |
703 | </p> | |
704 | </td> | |
705 | <td> | |
706 | <p> | |
707 | 0.206 | |
708 | </p> | |
709 | </td> | |
710 | <td> | |
711 | <p> | |
712 | 0.309 | |
713 | </p> | |
714 | </td> | |
715 | <td> | |
716 | <p> | |
717 | 0.417 | |
718 | </p> | |
719 | </td> | |
720 | <td> | |
721 | <p> | |
722 | 0.523 | |
723 | </p> | |
724 | </td> | |
725 | <td> | |
726 | <p> | |
727 | 0.62 | |
728 | </p> | |
729 | </td> | |
730 | <td> | |
731 | <p> | |
732 | 0.704 | |
733 | </p> | |
734 | </td> | |
735 | <td> | |
736 | <p> | |
737 | 0.775 | |
738 | </p> | |
739 | </td> | |
740 | <td> | |
741 | <p> | |
742 | 0.833 | |
743 | </p> | |
744 | </td> | |
745 | <td> | |
746 | <p> | |
747 | 0.878 | |
748 | </p> | |
749 | </td> | |
750 | </tr> | |
751 | <tr> | |
752 | <td> | |
753 | <p> | |
754 | 12 | |
755 | </p> | |
756 | </td> | |
757 | <td> | |
758 | <p> | |
759 | 0.113 | |
760 | </p> | |
761 | </td> | |
762 | <td> | |
763 | <p> | |
764 | 0.198 | |
765 | </p> | |
766 | </td> | |
767 | <td> | |
768 | <p> | |
769 | 0.297 | |
770 | </p> | |
771 | </td> | |
772 | <td> | |
773 | <p> | |
774 | 0.402 | |
775 | </p> | |
776 | </td> | |
777 | <td> | |
778 | <p> | |
779 | 0.505 | |
780 | </p> | |
781 | </td> | |
782 | <td> | |
783 | <p> | |
784 | 0.601 | |
785 | </p> | |
786 | </td> | |
787 | <td> | |
788 | <p> | |
789 | 0.686 | |
790 | </p> | |
791 | </td> | |
792 | <td> | |
793 | <p> | |
794 | 0.759 | |
795 | </p> | |
796 | </td> | |
797 | <td> | |
798 | <p> | |
799 | 0.818 | |
800 | </p> | |
801 | </td> | |
802 | <td> | |
803 | <p> | |
804 | 0.866 | |
805 | </p> | |
806 | </td> | |
807 | </tr> | |
808 | <tr> | |
809 | <td> | |
810 | <p> | |
811 | 13 | |
812 | </p> | |
813 | </td> | |
814 | <td> | |
815 | <p> | |
816 | 0.11 | |
817 | </p> | |
818 | </td> | |
819 | <td> | |
820 | <p> | |
821 | 0.191 | |
822 | </p> | |
823 | </td> | |
824 | <td> | |
825 | <p> | |
826 | 0.286 | |
827 | </p> | |
828 | </td> | |
829 | <td> | |
830 | <p> | |
831 | 0.387 | |
832 | </p> | |
833 | </td> | |
834 | <td> | |
835 | <p> | |
836 | 0.488 | |
837 | </p> | |
838 | </td> | |
839 | <td> | |
840 | <p> | |
841 | 0.584 | |
842 | </p> | |
843 | </td> | |
844 | <td> | |
845 | <p> | |
846 | 0.669 | |
847 | </p> | |
848 | </td> | |
849 | <td> | |
850 | <p> | |
851 | 0.743 | |
852 | </p> | |
853 | </td> | |
854 | <td> | |
855 | <p> | |
856 | 0.804 | |
857 | </p> | |
858 | </td> | |
859 | <td> | |
860 | <p> | |
861 | 0.854 | |
862 | </p> | |
863 | </td> | |
864 | </tr> | |
865 | <tr> | |
866 | <td> | |
867 | <p> | |
868 | 14 | |
869 | </p> | |
870 | </td> | |
871 | <td> | |
872 | <p> | |
873 | 0.108 | |
874 | </p> | |
875 | </td> | |
876 | <td> | |
877 | <p> | |
878 | 0.185 | |
879 | </p> | |
880 | </td> | |
881 | <td> | |
882 | <p> | |
883 | 0.276 | |
884 | </p> | |
885 | </td> | |
886 | <td> | |
887 | <p> | |
888 | 0.374 | |
889 | </p> | |
890 | </td> | |
891 | <td> | |
892 | <p> | |
893 | 0.473 | |
894 | </p> | |
895 | </td> | |
896 | <td> | |
897 | <p> | |
898 | 0.567 | |
899 | </p> | |
900 | </td> | |
901 | <td> | |
902 | <p> | |
903 | 0.653 | |
904 | </p> | |
905 | </td> | |
906 | <td> | |
907 | <p> | |
908 | 0.728 | |
909 | </p> | |
910 | </td> | |
911 | <td> | |
912 | <p> | |
913 | 0.791 | |
914 | </p> | |
915 | </td> | |
916 | <td> | |
917 | <p> | |
918 | 0.842 | |
919 | </p> | |
920 | </td> | |
921 | </tr> | |
922 | <tr> | |
923 | <td> | |
924 | <p> | |
925 | 15 | |
926 | </p> | |
927 | </td> | |
928 | <td> | |
929 | <p> | |
930 | 0.105 | |
931 | </p> | |
932 | </td> | |
933 | <td> | |
934 | <p> | |
935 | 0.179 | |
936 | </p> | |
937 | </td> | |
938 | <td> | |
939 | <p> | |
940 | 0.267 | |
941 | </p> | |
942 | </td> | |
943 | <td> | |
944 | <p> | |
945 | 0.362 | |
946 | </p> | |
947 | </td> | |
948 | <td> | |
949 | <p> | |
950 | 0.459 | |
951 | </p> | |
952 | </td> | |
953 | <td> | |
954 | <p> | |
955 | 0.552 | |
956 | </p> | |
957 | </td> | |
958 | <td> | |
959 | <p> | |
960 | 0.638 | |
961 | </p> | |
962 | </td> | |
963 | <td> | |
964 | <p> | |
965 | 0.713 | |
966 | </p> | |
967 | </td> | |
968 | <td> | |
969 | <p> | |
970 | 0.777 | |
971 | </p> | |
972 | </td> | |
973 | <td> | |
974 | <p> | |
975 | 0.83 | |
976 | </p> | |
977 | </td> | |
978 | </tr> | |
979 | <tr> | |
980 | <td> | |
981 | <p> | |
982 | 16 | |
983 | </p> | |
984 | </td> | |
985 | <td> | |
986 | <p> | |
987 | 0.103 | |
988 | </p> | |
989 | </td> | |
990 | <td> | |
991 | <p> | |
992 | 0.174 | |
993 | </p> | |
994 | </td> | |
995 | <td> | |
996 | <p> | |
997 | 0.259 | |
998 | </p> | |
999 | </td> | |
1000 | <td> | |
1001 | <p> | |
1002 | 0.351 | |
1003 | </p> | |
1004 | </td> | |
1005 | <td> | |
1006 | <p> | |
1007 | 0.446 | |
1008 | </p> | |
1009 | </td> | |
1010 | <td> | |
1011 | <p> | |
1012 | 0.538 | |
1013 | </p> | |
1014 | </td> | |
1015 | <td> | |
1016 | <p> | |
1017 | 0.623 | |
1018 | </p> | |
1019 | </td> | |
1020 | <td> | |
1021 | <p> | |
1022 | 0.699 | |
1023 | </p> | |
1024 | </td> | |
1025 | <td> | |
1026 | <p> | |
1027 | 0.764 | |
1028 | </p> | |
1029 | </td> | |
1030 | <td> | |
1031 | <p> | |
1032 | 0.819 | |
1033 | </p> | |
1034 | </td> | |
1035 | </tr> | |
1036 | <tr> | |
1037 | <td> | |
1038 | <p> | |
1039 | 17 | |
1040 | </p> | |
1041 | </td> | |
1042 | <td> | |
1043 | <p> | |
1044 | 0.101 | |
1045 | </p> | |
1046 | </td> | |
1047 | <td> | |
1048 | <p> | |
1049 | 0.169 | |
1050 | </p> | |
1051 | </td> | |
1052 | <td> | |
1053 | <p> | |
1054 | 0.251 | |
1055 | </p> | |
1056 | </td> | |
1057 | <td> | |
1058 | <p> | |
1059 | 0.341 | |
1060 | </p> | |
1061 | </td> | |
1062 | <td> | |
1063 | <p> | |
1064 | 0.434 | |
1065 | </p> | |
1066 | </td> | |
1067 | <td> | |
1068 | <p> | |
1069 | 0.525 | |
1070 | </p> | |
1071 | </td> | |
1072 | <td> | |
1073 | <p> | |
1074 | 0.609 | |
1075 | </p> | |
1076 | </td> | |
1077 | <td> | |
1078 | <p> | |
1079 | 0.686 | |
1080 | </p> | |
1081 | </td> | |
1082 | <td> | |
1083 | <p> | |
1084 | 0.752 | |
1085 | </p> | |
1086 | </td> | |
1087 | <td> | |
1088 | <p> | |
1089 | 0.807 | |
1090 | </p> | |
1091 | </td> | |
1092 | </tr> | |
1093 | <tr> | |
1094 | <td> | |
1095 | <p> | |
1096 | 18 | |
1097 | </p> | |
1098 | </td> | |
1099 | <td> | |
1100 | <p> | |
1101 | 0.0992 | |
1102 | </p> | |
1103 | </td> | |
1104 | <td> | |
1105 | <p> | |
1106 | 0.165 | |
1107 | </p> | |
1108 | </td> | |
1109 | <td> | |
1110 | <p> | |
1111 | 0.244 | |
1112 | </p> | |
1113 | </td> | |
1114 | <td> | |
1115 | <p> | |
1116 | 0.332 | |
1117 | </p> | |
1118 | </td> | |
1119 | <td> | |
1120 | <p> | |
1121 | 0.423 | |
1122 | </p> | |
1123 | </td> | |
1124 | <td> | |
1125 | <p> | |
1126 | 0.512 | |
1127 | </p> | |
1128 | </td> | |
1129 | <td> | |
1130 | <p> | |
1131 | 0.596 | |
1132 | </p> | |
1133 | </td> | |
1134 | <td> | |
1135 | <p> | |
1136 | 0.673 | |
1137 | </p> | |
1138 | </td> | |
1139 | <td> | |
1140 | <p> | |
1141 | 0.74 | |
1142 | </p> | |
1143 | </td> | |
1144 | <td> | |
1145 | <p> | |
1146 | 0.796 | |
1147 | </p> | |
1148 | </td> | |
1149 | </tr> | |
1150 | <tr> | |
1151 | <td> | |
1152 | <p> | |
1153 | 19 | |
1154 | </p> | |
1155 | </td> | |
1156 | <td> | |
1157 | <p> | |
1158 | 0.0976 | |
1159 | </p> | |
1160 | </td> | |
1161 | <td> | |
1162 | <p> | |
1163 | 0.161 | |
1164 | </p> | |
1165 | </td> | |
1166 | <td> | |
1167 | <p> | |
1168 | 0.238 | |
1169 | </p> | |
1170 | </td> | |
1171 | <td> | |
1172 | <p> | |
1173 | 0.323 | |
1174 | </p> | |
1175 | </td> | |
1176 | <td> | |
1177 | <p> | |
1178 | 0.412 | |
1179 | </p> | |
1180 | </td> | |
1181 | <td> | |
1182 | <p> | |
1183 | 0.5 | |
1184 | </p> | |
1185 | </td> | |
1186 | <td> | |
1187 | <p> | |
1188 | 0.584 | |
1189 | </p> | |
1190 | </td> | |
1191 | <td> | |
1192 | <p> | |
1193 | 0.66 | |
1194 | </p> | |
1195 | </td> | |
1196 | <td> | |
1197 | <p> | |
1198 | 0.728 | |
1199 | </p> | |
1200 | </td> | |
1201 | <td> | |
1202 | <p> | |
1203 | 0.786 | |
1204 | </p> | |
1205 | </td> | |
1206 | </tr> | |
1207 | <tr> | |
1208 | <td> | |
1209 | <p> | |
1210 | 20 | |
1211 | </p> | |
1212 | </td> | |
1213 | <td> | |
1214 | <p> | |
1215 | 0.0961 | |
1216 | </p> | |
1217 | </td> | |
1218 | <td> | |
1219 | <p> | |
1220 | 0.158 | |
1221 | </p> | |
1222 | </td> | |
1223 | <td> | |
1224 | <p> | |
1225 | 0.232 | |
1226 | </p> | |
1227 | </td> | |
1228 | <td> | |
1229 | <p> | |
1230 | 0.315 | |
1231 | </p> | |
1232 | </td> | |
1233 | <td> | |
1234 | <p> | |
1235 | 0.402 | |
1236 | </p> | |
1237 | </td> | |
1238 | <td> | |
1239 | <p> | |
1240 | 0.489 | |
1241 | </p> | |
1242 | </td> | |
1243 | <td> | |
1244 | <p> | |
1245 | 0.572 | |
1246 | </p> | |
1247 | </td> | |
1248 | <td> | |
1249 | <p> | |
1250 | 0.648 | |
1251 | </p> | |
1252 | </td> | |
1253 | <td> | |
1254 | <p> | |
1255 | 0.716 | |
1256 | </p> | |
1257 | </td> | |
1258 | <td> | |
1259 | <p> | |
1260 | 0.775 | |
1261 | </p> | |
1262 | </td> | |
1263 | </tr> | |
1264 | </tbody> | |
1265 | </table></div> | |
1266 | <p> | |
1267 | See <a href="../../../../../../example/nc_chi_sq_example.cpp" target="_top">nc_chi_sq_example.cpp</a> | |
1268 | for the full C++ source code. | |
1269 | </p> | |
1270 | </div> | |
1271 | <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> | |
1272 | <td align="left"></td> | |
1273 | <td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal, | |
1274 | Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert | |
1275 | Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani, | |
1276 | Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p> | |
1277 | Distributed under the Boost Software License, Version 1.0. (See accompanying | |
1278 | file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) | |
1279 | </p> | |
1280 | </div></td> | |
1281 | </tr></table> | |
1282 | <hr> | |
1283 | <div class="spirit-nav"> | |
1284 | <a accesskey="p" href="../nccs_eg.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../nccs_eg.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../error_eg.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> | |
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