223:
Each element of the population may have a different probability of being included in the sample. The inclusion probability is also termed the "first-order inclusion probability" to distinguish it from the "second-order inclusion probability", i.e. the probability of including a pair of elements.
175:
218:
198:
69:
77:
242:
th element of the population that is sampled is included in a sample during the drawing of a single sample is denoted by π
377:
345:
296:
396:
28:
320:
24:
48:
40:
8:
203:
183:
54:
47:
of becoming part of the sample during the drawing of a single sample. For example, in
373:
341:
292:
365:
316:
312:
262:
267:
170:{\displaystyle p_{i}={\frac {\binom {N-1}{n-1}}{\binom {N}{n}}}={\frac {n}{N}}}
390:
257:
234:
and the second-order inclusion probability that a pair consisting of the
44:
20:
368:(1997). "The mathematics of probability sampling designs".
224:
Generally, the first-order inclusion probability of the
228:
th element of the population is denoted by the symbol π
335:
206:
186:
80:
57:
311:
16:
Theory relating to sampling from finite populations
212:
192:
169:
63:
388:
147:
134:
127:
98:
289:The Oxford Dictionary of Statistical Terms
364:
372:. Taylor & Francis. pp. 9–48.
389:
286:
51:the probability of a particular unit
43:or member of the population, is its
13:
358:
336:Sarndal; Swenson; Wretman (1992).
138:
102:
71:to be selected into the sample is
14:
408:
338:Model Assisted Survey Sampling
329:
305:
280:
1:
273:
322:Stereology for Statisticians
23:, in the theory relating to
7:
251:
10:
413:
370:Theory of Sample Surveys
220:is the population size.
200:is the sample size and
214:
194:
171:
65:
49:simple random sampling
397:Sampling (statistics)
215:
195:
172:
66:
37:inclusion probability
317:Vedel Jensen, Eva B.
204:
184:
78:
55:
33:sampling probability
340:. Springer-Verlag.
287:Dodge, Y. (2003).
210:
190:
167:
61:
213:{\displaystyle N}
193:{\displaystyle n}
165:
152:
145:
125:
64:{\displaystyle i}
404:
383:
352:
351:
333:
327:
326:
313:Baddeley, Adrian
309:
303:
302:
284:
219:
217:
216:
211:
199:
197:
196:
191:
176:
174:
173:
168:
166:
158:
153:
151:
150:
137:
131:
130:
124:
113:
101:
95:
90:
89:
70:
68:
67:
62:
412:
411:
407:
406:
405:
403:
402:
401:
387:
386:
380:
366:Thompson, M. E.
361:
359:Further reading
356:
355:
348:
334:
330:
310:
306:
299:
285:
281:
276:
263:Sampling design
254:
247:
233:
205:
202:
201:
185:
182:
181:
157:
146:
133:
132:
126:
114:
103:
97:
96:
94:
85:
81:
79:
76:
75:
56:
53:
52:
35:(also known as
17:
12:
11:
5:
410:
400:
399:
385:
384:
378:
360:
357:
354:
353:
346:
328:
325:. p. 334.
304:
297:
278:
277:
275:
272:
271:
270:
268:Sampling frame
265:
260:
253:
250:
243:
229:
209:
189:
178:
177:
164:
161:
156:
149:
144:
141:
136:
129:
123:
120:
117:
112:
109:
106:
100:
93:
88:
84:
60:
15:
9:
6:
4:
3:
2:
409:
398:
395:
394:
392:
381:
379:0-412-31780-X
375:
371:
367:
363:
362:
349:
347:0-387-40620-4
343:
339:
332:
324:
323:
318:
314:
308:
300:
298:0-19-850994-4
294:
290:
283:
279:
269:
266:
264:
261:
259:
258:Sampling bias
256:
255:
249:
246:
241:
237:
232:
227:
221:
207:
187:
162:
159:
154:
142:
139:
121:
118:
115:
110:
107:
104:
91:
86:
82:
74:
73:
72:
58:
50:
46:
42:
38:
34:
30:
26:
22:
369:
337:
331:
321:
307:
288:
282:
244:
239:
235:
230:
225:
222:
179:
36:
32:
27:from finite
18:
45:probability
29:populations
274:References
21:statistics
119:−
108:−
391:Category
319:(2004).
252:See also
39:) of an
25:sampling
291:. OUP.
238:th and
41:element
376:
344:
295:
180:where
31:, the
374:ISBN
342:ISBN
293:ISBN
19:In
393::
315:;
248:.
245:ij
382:.
350:.
301:.
240:j
236:i
231:i
226:i
208:N
188:n
163:N
160:n
155:=
148:)
143:n
140:N
135:(
128:)
122:1
116:n
111:1
105:N
99:(
92:=
87:i
83:p
59:i
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.