391:
428:. Where extreme accuracy is not necessary, computer calculations for some ranges of parameters may still rely on using continuity corrections to improve accuracy while retaining simplicity.
149:
442:
224:
281:
A continuity correction can also be applied when other discrete distributions supported on the integers are approximated by the normal distribution. For example, if
412:
having the ability to evaluate probability distribution functions accurately, continuity corrections played an important role in the practical application of
416:
in which the test statistic has a discrete distribution: it had a special importance for manual calculations. A particular example of this is the
478:
299:
437:
483:
46:
425:
92:
413:
174:) are large (sometimes taken as both ≥ 5), then the probability above is fairly well approximated by
180:
421:
59:
409:
286:
25:
8:
234:
29:
79:
52:
238:
472:
417:
465:, The Annals of Mathematical Statistics, Vol. 16 No. 4, Page 319–329, 1945.
17:
242:
400:
is normally distributed with expectation and variance both λ.
386:{\displaystyle P(X\leq x)=P(X<x+1)\approx P(Y\leq x+1/2)}
456:
Probability and
Statistics for Engineering and the Sciences
463:
On the normal approximation to the binomial distribution
302:
183:
95:
385:
218:
143:
47:Binomial distribution § Normal approximation
470:
443:Wilson score interval with continuity correction
74:is distributed as the number of "successes" in
289:with expected value λ then the variance of
458:, Fourth Edition, Duxbury Press, 1995.
471:
144:{\displaystyle P(X\leq x)=P(X<x+1)}
479:Theory of probability distributions
13:
14:
495:
438:Yates's correction for continuity
408:Before the ready availability of
426:checking whether a coin is fair
403:
86:of success on each trial, then
380:
354:
345:
327:
318:
306:
237:random variable with the same
219:{\displaystyle P(Y\leq x+1/2)}
213:
187:
138:
120:
111:
99:
1:
448:
24:is an adjustment made when a
273:is a continuity correction.
269:). This addition of 1/2 to
7:
431:
40:
35:
10:
500:
276:
44:
484:Computational statistics
28:is approximated using a
387:
220:
145:
422:binomial distribution
388:
221:
146:
60:binomial distribution
22:continuity correction
410:statistical software
300:
287:Poisson distribution
235:normally distributed
181:
93:
383:
216:
141:
414:statistical tests
82:with probability
30:continuous object
491:
454:Devore, Jay L.,
420:, involving the
392:
390:
389:
384:
376:
225:
223:
222:
217:
209:
158:∈ {0, 1, 2, ...
150:
148:
147:
142:
80:Bernoulli trials
62:with parameters
499:
498:
494:
493:
492:
490:
489:
488:
469:
468:
451:
434:
406:
372:
301:
298:
297:
293:is also λ, and
279:
205:
182:
179:
178:
94:
91:
90:
53:random variable
49:
43:
38:
26:discrete object
12:
11:
5:
497:
487:
486:
481:
467:
466:
459:
450:
447:
446:
445:
440:
433:
430:
405:
402:
394:
393:
382:
379:
375:
371:
368:
365:
362:
359:
356:
353:
350:
347:
344:
341:
338:
335:
332:
329:
326:
323:
320:
317:
314:
311:
308:
305:
278:
275:
239:expected value
227:
226:
215:
212:
208:
204:
201:
198:
195:
192:
189:
186:
152:
151:
140:
137:
134:
131:
128:
125:
122:
119:
116:
113:
110:
107:
104:
101:
98:
42:
39:
37:
34:
9:
6:
4:
3:
2:
496:
485:
482:
480:
477:
476:
474:
464:
460:
457:
453:
452:
444:
441:
439:
436:
435:
429:
427:
423:
419:
418:binomial test
415:
411:
401:
399:
377:
373:
369:
366:
363:
360:
357:
351:
348:
342:
339:
336:
333:
330:
324:
321:
315:
312:
309:
303:
296:
295:
294:
292:
288:
284:
274:
272:
268:
264:
260:
256:
252:
248:
244:
241:and the same
240:
236:
232:
210:
206:
202:
199:
196:
193:
190:
184:
177:
176:
175:
173:
169:
165:
161:
157:
135:
132:
129:
126:
123:
117:
114:
108:
105:
102:
96:
89:
88:
87:
85:
81:
77:
73:
69:
65:
61:
57:
54:
48:
33:
31:
27:
23:
19:
462:
461:Feller, W.,
455:
407:
404:Applications
397:
395:
290:
282:
280:
270:
266:
262:
258:
254:
250:
246:
230:
228:
171:
167:
163:
159:
155:
153:
83:
78:independent
75:
71:
67:
63:
55:
50:
21:
15:
265:(1 −
170:(1 −
18:mathematics
473:Categories
449:References
249:, i.e., E(
45:See also:
361:≤
349:≈
313:≤
194:≤
106:≤
432:See also
424:, as in
257:and var(
243:variance
154:for any
70:, i.e.,
41:Binomial
36:Examples
277:Poisson
162:}. If
285:has a
229:where
58:has a
233:is a
51:If a
334:<
261:) =
253:) =
166:and
127:<
66:and
20:, a
396:if
245:as
16:In
475::
263:np
255:np
168:np
164:np
32:.
398:Y
381:)
378:2
374:/
370:1
367:+
364:x
358:Y
355:(
352:P
346:)
343:1
340:+
337:x
331:X
328:(
325:P
322:=
319:)
316:x
310:X
307:(
304:P
291:X
283:X
271:x
267:p
259:Y
251:Y
247:X
231:Y
214:)
211:2
207:/
203:1
200:+
197:x
191:Y
188:(
185:P
172:p
160:n
156:x
139:)
136:1
133:+
130:x
124:X
121:(
118:P
115:=
112:)
109:x
103:X
100:(
97:P
84:p
76:n
72:X
68:p
64:n
56:X
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.