]> git.proxmox.com Git - ceph.git/blame - ceph/src/boost/libs/math/doc/html/math_toolkit/stat_tut/weg/nccs_eg/nccs_power_eg.html
projects / ceph.git / blame
? search:
summary | shortlog | log | commit | commitdiff | tree
blob | blame (incremental) | history | HEAD
bump version to 12.2.2-pve1
[ceph.git] / ceph / src / boost / libs / math / doc / html / math_toolkit / stat_tut / weg / nccs_eg / nccs_power_eg.html
CommitLineData
7c673cae
FG		 1<html>
2<head>
3<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
4<title>Tables of the power function of the chi2 test.</title>
5<link rel="stylesheet" href="../../../../math.css" type="text/css">
6<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
7<link rel="home" href="../../../../index.html" title="Math Toolkit 2.5.1">
8<link rel="up" href="../nccs_eg.html" title="Non Central Chi Squared Example">
9<link rel="prev" href="../nccs_eg.html" title="Non Central Chi Squared Example">
10<link rel="next" href="../error_eg.html" title="Error Handling Example">
11</head>
12<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
13<table cellpadding="2" width="100%"><tr>
14<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../../boost.png"></td>
15<td align="center"><a href="../../../../../../../../index.html">Home</a></td>
16<td align="center"><a href="../../../../../../../../libs/libraries.htm">Libraries</a></td>
17<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
18<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
19<td align="center"><a href="../../../../../../../../more/index.htm">More</a></td>
20</tr></table>
21<hr>
22<div class="spirit-nav">
23<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>
24</div>
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 &#967;<sup>2</sup>
32test 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 &#967;<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">&lt;</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">&gt;</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">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</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 &#967;<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">&lt;&lt;</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">&lt;=</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">&lt;&lt;</span> <span class="string">"[[lambda]="</span> <span class="special">&lt;&lt;</span> <span class="identifier">lam</span> <span class="special">&lt;&lt;</span> <span class="string">"]"</span><span class="special">;</span>
61<span class="special">}</span>
62<span class="identifier">cout</span> <span class="special">&lt;&lt;</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">&lt;=</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">&lt;&lt;</span> <span class="string">"[["</span> <span class="special">&lt;&lt;</span> <span class="identifier">n</span> <span class="special">&lt;&lt;</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">&lt;=</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 &#967;<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 &#967;<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">&lt;&lt;</span> <span class="string">"["</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">beta</span> <span class="special">&lt;&lt;</span> <span class="string">"]"</span><span class="special">;</span>
92 <span class="special">}</span>
93 <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"]"</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
94 <span class="special">}</span>
95 <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"]"</span> <span class="special">&lt;&lt;</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 &#957;=10 and &#955;=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 &#957;
127 </p>
128 </th>
129<th>
130 <p>
131 &#955;=2
132 </p>
133 </th>
134<th>
135 <p>
136 &#955;=4
137 </p>
138 </th>
139<th>
140 <p>
141 &#955;=6
142 </p>
143 </th>
144<th>
145 <p>
146 &#955;=8
147 </p>
148 </th>
149<th>
150 <p>
151 &#955;=10
152 </p>
153 </th>
154<th>
155 <p>
156 &#955;=12
157 </p>
158 </th>
159<th>
160 <p>
161 &#955;=14
162 </p>
163 </th>
164<th>
165 <p>
166 &#955;=16
167 </p>
168 </th>
169<th>
170 <p>
171 &#955;=18
172 </p>
173 </th>
174<th>
175 <p>
176 &#955;=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 &#169; 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 R&#229;de, 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>
1285</div>
1286</body>
1287</html>
Ceph