22:
154:, removed from the data set, and a new mean and standard deviation based on the remaining values and new sample size can be calculated. This identification of the outliers will be achieved by finding the number of standard deviations that correspond to the bounds of the probability band around the mean (
2080:
Deletion of outlier data is a controversial practice frowned on by many scientists and science instructors; while
Chauvenet's criterion provides an objective and quantitative method for data rejection, it does not make the practice more scientifically or methodologically sound, especially in small
1609:
that a given data point will be at the value of the suspect data point. Multiply this probability by the number of data points taken. If the result is less than 0.5, the suspicious data point may be discarded, i.e., a reading may be rejected if the probability of obtaining the particular deviation
1785:
2004:
274:
2085:
cannot be assumed. Rejection of outliers is more acceptable in areas of practice where the underlying model of the process being measured and the usual distribution of measurement error are confidently known.
897:
1915:
1224:
1086:
1579:
1544:
1482:
1400:
328:
187:
2062:. It was developed a few years before Chauvenet's criterion was published, and it is a more rigorous approach to the rational deletion of outlier data. Other methods such as
796:
643:
562:
501:
1642:
996:
2201:
Aicha Zerbet, Mikhail
Nikulin. A new statistics for detecting outliers in exponential case, Communications in Statistics: Theory and Methods, 2003, v.32, pp. 573–584.
2046:
413:
1361:
360:
1821:
1687:
1333:
1848:
1680:
1509:
1427:
1132:
442:
741:
695:
669:
588:
527:
1447:
1305:
1283:
1263:
1178:
1154:
1036:
1016:
958:
936:
816:
761:
715:
608:
466:
382:
189:) and comparing that value to the absolute value of the difference between the suspected outliers and the mean divided by the sample standard deviation (Eq.1).
1925:
2116:
Fratta, M; Scaringi, S; Drew, J E; Monguió, M; Knigge, C; Maccarone, T J; Court, J M C; Iłkiewicz, K A; Pala, A F; Gandhi, P; Gänsicke, B (21 July 2021).
1652:
For instance, suppose a value is measured experimentally in several trials as 9, 10, 10, 10, 11, and 50, and we want to find out if 50 is an outlier.
39:
197:
998:
corresponds to the combined probability represented by the two tails of the normal distribution that fall outside of the probability band
826:
86:
2195:
105:
58:
65:
43:
529:
then only 2.5 of the samples must be accounted for in the probability band). In reality we cannot have partial samples so
2219:
2063:
126:) is a means of assessing whether one piece of experimental data from a set of observations is likely to be spurious – an
72:
1038:, only the probability of one of the tails of the normal distribution needs to be analyzed due to its symmetry (Eq.3).
1859:
54:
2214:
1188:
2190:
Barnett, Vic and Lewis, Toby. "Outliers in
Statistical Data". 3rd edition. Chichester: J.Wiley and Sons, 1994.
32:
2166:
Ross, PhD, Stephen (2003). University of New Haven article. J. Engr. Technology, Fall 2003. Retrieved from
1046:
1549:
1514:
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967:
79:
2082:
1602:
143:
2012:
1598:
389:
1780:{\displaystyle P_{z}=1-{\frac {1}{4n}}=1-{\frac {1}{4\times 6}}=1-{\frac {1}{24}}\approx .9583}
1340:
2191:
2149:
1851:
468:
observations in the sample, the probability band (centered on the mean) must only account for
335:
123:
1793:
2139:
2129:
2118:"Population-based identification of H α-excess sources in the Gaia DR2 and IPHAS catalogues"
2117:
1312:
138:
The idea behind
Chauvenet's criterion finds a probability band that reasonably contains all
1826:
1658:
1487:
1405:
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420:
1601:
of the observed data. Based on how much the suspect datum differs from the mean, use the
720:
674:
648:
567:
506:
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1290:
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1139:
1021:
1001:
943:
921:
801:
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700:
593:
451:
367:
2167:
1999:{\displaystyle z={\frac {50-{\bar {x}}}{s_{x}}}={\frac {50-16.67}{16.34}}\approx 2.04}
2208:
2187:. 2nd edition. Sausalito, California: University Science Books, 1997. pp 166–8.
1606:
21:
697:) and is not valid because we want to find the probability band that contains
2153:
2134:
2048:
and can conclude that 50 is an outlier according to
Chauvenet's Criterion.
2144:
2068:
151:
127:
269:{\displaystyle D_{\mathrm {max} }\geq {\frac {|x-{\bar {x}}|}{s_{x}}}}
2106:
V. II. 1863. Reprint of 1891. 5th ed. Dover, N.Y.: 1960. pp. 474–566.
1134:
is probability represented by one tail of the normal distribution and
150:
samples that lies outside this probability band can be considered an
892:{\displaystyle P={\frac {n-{\tfrac {1}{2}}}{n}}=1-{\tfrac {1}{2n}}}
1018:. In order to find the standard deviation level associated with
1594:
1581:
can be found with the following formula: =ABS(NORM.S.INV(1/(4
15:
1363:
is the standard deviation of standard normal distribution.
743:
samples. In short, we are looking for the probability,
2056:
Another method for eliminating spurious data is called
938:
is the probability band centered on the sample mean and
1618:
972:
873:
846:
777:
624:
543:
482:
2015:
1928:
1862:
1829:
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1690:
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1616:
1552:
1517:
1490:
1455:
1435:
1408:
1373:
1343:
1315:
1293:
1271:
1251:
1191:
1166:
1142:
1113:
1049:
1024:
1004:
970:
946:
924:
829:
804:
769:
749:
723:
703:
677:
651:
616:
596:
570:
535:
509:
474:
454:
423:
392:
370:
338:
301:
200:
160:
1593:
To apply
Chauvenet's criterion, first calculate the
2168:
https://www.researchgate.net/profile/Stephen-Ross-9
46:. Unsourced material may be challenged and removed.
2040:
1998:
1909:
1842:
1815:
1779:
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1573:
1546:can be determined for any sample size. In Excel,
1538:
1503:
1476:
1441:
1421:
1394:
1355:
1327:
1299:
1277:
1257:
1218:
1172:
1148:
1126:
1080:
1030:
1010:
990:
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930:
891:
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790:
755:
735:
709:
689:
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602:
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181:
2122:Monthly Notices of the Royal Astronomical Society
1335:is the mean of standard normal distribution, and
142:samples of a data set, centred on the mean of a
1605:function (or a table thereof) to determine the
1910:{\displaystyle D_{max}=Q(P_{z})\approx 1.7317}
2104:A Manual of Spherical and Practical Astronomy
8:
1219:{\displaystyle Z={\frac {x-\mu }{\sigma }}}
448:In order to be considered as including all
146:. By doing this, any data point from the
2143:
2133:
2026:
2014:
1972:
1961:
1945:
1944:
1935:
1927:
1892:
1867:
1861:
1834:
1828:
1801:
1795:
1761:
1734:
1710:
1695:
1689:
1666:
1660:
1617:
1615:
1558:
1557:
1551:
1523:
1522:
1516:
1495:
1489:
1461:
1460:
1454:
1434:
1413:
1407:
1402:(Eq.1) find the z-score corresponding to
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1378:
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1342:
1314:
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1270:
1250:
1198:
1190:
1165:
1141:
1118:
1112:
1063:
1054:
1048:
1023:
1003:
971:
969:
945:
923:
872:
845:
836:
828:
803:
776:
768:
748:
722:
702:
676:
650:
623:
615:
595:
569:
542:
534:
508:
481:
473:
453:
428:
422:
394:
393:
391:
369:
347:
339:
337:
307:
306:
300:
258:
248:
237:
236:
225:
222:
206:
205:
199:
166:
165:
159:
106:Learn how and when to remove this message
2095:
1081:{\displaystyle P_{z}={\frac {1}{4n}}}
7:
2066:are mentioned under the listing for
1182:
1040:
820:
191:
44:adding citations to reliable sources
330:is the maximum allowable deviation,
1574:{\displaystyle D_{\mathrm {max} }}
1565:
1562:
1559:
1539:{\displaystyle D_{\mathrm {max} }}
1530:
1527:
1524:
1477:{\displaystyle D_{\mathrm {max} }}
1468:
1465:
1462:
1395:{\displaystyle D_{\mathrm {max} }}
1386:
1383:
1380:
384:is the value of suspected outlier,
323:{\displaystyle D_{\mathrm {max} }}
314:
311:
308:
213:
210:
207:
182:{\displaystyle D_{\mathrm {max} }}
173:
170:
167:
14:
2185:An Introduction to Error Analysis
791:{\displaystyle n-{\tfrac {1}{2}}}
638:{\displaystyle n-{\tfrac {1}{2}}}
557:{\displaystyle n-{\tfrac {1}{2}}}
496:{\displaystyle n-{\tfrac {1}{2}}}
1920:Then we find the z-score of 50.
1637:{\displaystyle {\tfrac {1}{2n}}}
991:{\displaystyle {\tfrac {1}{2n}}}
20:
31:needs additional citations for
1950:
1898:
1885:
399:
348:
340:
249:
242:
226:
1:
444:is sample standard deviation.
2041:{\displaystyle z>D_{max}}
1610:from the mean is less than
1367:Based on Eq.4, to find the
2236:
2064:Grubbs's test for outliers
1484:is equal to the score for
408:{\displaystyle {\bar {x}}}
2051:
1356:{\displaystyle \sigma =1}
1160:Eq.1 is analogous to the
1180:-score equation (Eq.4).
355:{\displaystyle |\cdot |}
2009:From there we see that
1816:{\displaystyle D_{max}}
118:In statistical theory,
55:"Chauvenet's criterion"
2135:10.1093/mnras/stab1258
2042:
2000:
1911:
1844:
1817:
1781:
1676:
1638:
1575:
1540:
1505:
1478:
1443:
1423:
1396:
1357:
1329:
1328:{\displaystyle \mu =0}
1301:
1279:
1259:
1220:
1174:
1150:
1128:
1082:
1032:
1012:
992:
954:
932:
893:
812:
792:
757:
737:
711:
691:
665:
639:
610:. Anything less than
604:
584:
558:
523:
497:
462:
438:
409:
378:
362:is the absolute value,
356:
324:
270:
183:
2043:
2001:
1912:
1845:
1843:{\displaystyle P_{z}}
1818:
1782:
1677:
1675:{\displaystyle P_{z}}
1639:
1576:
1541:
1511:. Using this method
1506:
1504:{\displaystyle P_{z}}
1479:
1444:
1424:
1422:{\displaystyle P_{z}}
1397:
1358:
1330:
1302:
1280:
1260:
1221:
1175:
1151:
1129:
1127:{\displaystyle P_{z}}
1083:
1033:
1013:
993:
955:
933:
894:
813:
793:
758:
738:
712:
692:
666:
640:
605:
585:
559:
524:
498:
463:
439:
437:{\displaystyle s_{x}}
410:
379:
357:
325:
271:
184:
120:Chauvenet's criterion
2220:Statistical outliers
2102:Chauvenet, William.
2013:
1926:
1860:
1827:
1794:
1688:
1659:
1614:
1550:
1515:
1488:
1453:
1433:
1406:
1371:
1341:
1313:
1307:is the sample value,
1291:
1269:
1249:
1189:
1164:
1140:
1111:
1047:
1022:
1002:
968:
944:
922:
827:
802:
767:
747:
721:
701:
675:
649:
614:
594:
568:
533:
507:
472:
452:
421:
390:
368:
336:
299:
198:
158:
40:improve this article
2083:normal distribution
1603:normal distribution
960:is the sample size.
763:, that is equal to
736:{\displaystyle n-1}
690:{\displaystyle n=3}
664:{\displaystyle n-1}
590:) is approximately
583:{\displaystyle n=3}
522:{\displaystyle n=3}
415:is sample mean, and
144:normal distribution
2059:Peirce's criterion
2052:Peirce's criterion
2038:
1996:
1907:
1840:
1813:
1777:
1672:
1634:
1632:
1599:standard deviation
1571:
1536:
1501:
1474:
1439:
1419:
1392:
1353:
1325:
1297:
1275:
1255:
1216:
1170:
1146:
1124:
1078:
1028:
1008:
988:
986:
950:
928:
889:
887:
855:
808:
788:
786:
753:
733:
717:observations, not
707:
687:
661:
635:
633:
600:
580:
554:
552:
519:
493:
491:
458:
434:
405:
374:
352:
320:
266:
179:
2215:Statistical tests
2183:Taylor, John R.
1988:
1967:
1953:
1852:Quantile Function
1769:
1750:
1723:
1631:
1442:{\displaystyle Z}
1300:{\displaystyle x}
1278:{\displaystyle Z}
1258:{\displaystyle Z}
1240:
1239:
1214:
1173:{\displaystyle Z}
1149:{\displaystyle n}
1102:
1101:
1076:
1031:{\displaystyle P}
1011:{\displaystyle P}
985:
953:{\displaystyle n}
931:{\displaystyle P}
913:
912:
886:
861:
854:
811:{\displaystyle n}
785:
756:{\displaystyle P}
710:{\displaystyle n}
645:is approximately
632:
603:{\displaystyle n}
551:
490:
461:{\displaystyle n}
402:
377:{\displaystyle x}
290:
289:
264:
245:
124:William Chauvenet
116:
115:
108:
90:
2227:
2171:
2164:
2158:
2157:
2147:
2137:
2128:(1): 1135–1152.
2113:
2107:
2100:
2081:sets or where a
2047:
2045:
2044:
2039:
2037:
2036:
2005:
2003:
2002:
1997:
1989:
1984:
1973:
1968:
1966:
1965:
1956:
1955:
1954:
1946:
1936:
1916:
1914:
1913:
1908:
1897:
1896:
1878:
1877:
1849:
1847:
1846:
1841:
1839:
1838:
1822:
1820:
1819:
1814:
1812:
1811:
1786:
1784:
1783:
1778:
1770:
1762:
1751:
1749:
1735:
1724:
1722:
1711:
1700:
1699:
1681:
1679:
1678:
1673:
1671:
1670:
1643:
1641:
1640:
1635:
1633:
1630:
1619:
1580:
1578:
1577:
1572:
1570:
1569:
1568:
1545:
1543:
1542:
1537:
1535:
1534:
1533:
1510:
1508:
1507:
1502:
1500:
1499:
1483:
1481:
1480:
1475:
1473:
1472:
1471:
1448:
1446:
1445:
1440:
1428:
1426:
1425:
1420:
1418:
1417:
1401:
1399:
1398:
1393:
1391:
1390:
1389:
1362:
1360:
1359:
1354:
1334:
1332:
1331:
1326:
1306:
1304:
1303:
1298:
1284:
1282:
1281:
1276:
1264:
1262:
1261:
1256:
1234:
1225:
1223:
1222:
1217:
1215:
1210:
1199:
1183:
1179:
1177:
1176:
1171:
1155:
1153:
1152:
1147:
1133:
1131:
1130:
1125:
1123:
1122:
1096:
1087:
1085:
1084:
1079:
1077:
1075:
1064:
1059:
1058:
1041:
1037:
1035:
1034:
1029:
1017:
1015:
1014:
1009:
997:
995:
994:
989:
987:
984:
973:
959:
957:
956:
951:
937:
935:
934:
929:
907:
898:
896:
895:
890:
888:
885:
874:
862:
857:
856:
847:
837:
821:
818:samples (Eq.2).
817:
815:
814:
809:
797:
795:
794:
789:
787:
778:
762:
760:
759:
754:
742:
740:
739:
734:
716:
714:
713:
708:
696:
694:
693:
688:
670:
668:
667:
662:
644:
642:
641:
636:
634:
625:
609:
607:
606:
601:
589:
587:
586:
581:
563:
561:
560:
555:
553:
544:
528:
526:
525:
520:
502:
500:
499:
494:
492:
483:
467:
465:
464:
459:
443:
441:
440:
435:
433:
432:
414:
412:
411:
406:
404:
403:
395:
383:
381:
380:
375:
361:
359:
358:
353:
351:
343:
329:
327:
326:
321:
319:
318:
317:
284:
275:
273:
272:
267:
265:
263:
262:
253:
252:
247:
246:
238:
229:
223:
218:
217:
216:
192:
188:
186:
185:
180:
178:
177:
176:
111:
104:
100:
97:
91:
89:
48:
24:
16:
2235:
2234:
2230:
2229:
2228:
2226:
2225:
2224:
2205:
2204:
2180:
2175:
2174:
2165:
2161:
2115:
2114:
2110:
2101:
2097:
2092:
2078:
2054:
2022:
2011:
2010:
2008:
1974:
1957:
1937:
1924:
1923:
1919:
1888:
1863:
1858:
1857:
1830:
1825:
1824:
1797:
1792:
1791:
1789:
1739:
1715:
1691:
1686:
1685:
1662:
1657:
1656:
1655:First, we find
1650:
1623:
1612:
1611:
1591:
1553:
1548:
1547:
1518:
1513:
1512:
1491:
1486:
1485:
1456:
1451:
1450:
1449:-score table.
1431:
1430:
1409:
1404:
1403:
1374:
1369:
1368:
1339:
1338:
1311:
1310:
1289:
1288:
1267:
1266:
1247:
1246:
1232:
1200:
1187:
1186:
1162:
1161:
1138:
1137:
1114:
1109:
1108:
1094:
1068:
1050:
1045:
1044:
1020:
1019:
1000:
999:
977:
966:
965:
942:
941:
920:
919:
905:
878:
838:
825:
824:
800:
799:
765:
764:
745:
744:
719:
718:
699:
698:
673:
672:
647:
646:
612:
611:
592:
591:
566:
565:
531:
530:
505:
504:
470:
469:
450:
449:
424:
419:
418:
388:
387:
366:
365:
334:
333:
302:
297:
296:
282:
254:
224:
201:
196:
195:
161:
156:
155:
136:
112:
101:
95:
92:
49:
47:
37:
25:
12:
11:
5:
2233:
2231:
2223:
2222:
2217:
2207:
2206:
2203:
2202:
2199:
2188:
2179:
2176:
2173:
2172:
2159:
2108:
2094:
2093:
2091:
2088:
2077:
2074:
2053:
2050:
2035:
2032:
2029:
2025:
2021:
2018:
1995:
1992:
1987:
1983:
1980:
1977:
1971:
1964:
1960:
1952:
1949:
1943:
1940:
1934:
1931:
1906:
1903:
1900:
1895:
1891:
1887:
1884:
1881:
1876:
1873:
1870:
1866:
1837:
1833:
1810:
1807:
1804:
1800:
1776:
1773:
1768:
1765:
1760:
1757:
1754:
1748:
1745:
1742:
1738:
1733:
1730:
1727:
1721:
1718:
1714:
1709:
1706:
1703:
1698:
1694:
1669:
1665:
1649:
1646:
1629:
1626:
1622:
1590:
1587:
1567:
1564:
1561:
1556:
1532:
1529:
1526:
1521:
1498:
1494:
1470:
1467:
1464:
1459:
1438:
1416:
1412:
1388:
1385:
1382:
1377:
1365:
1364:
1352:
1349:
1346:
1336:
1324:
1321:
1318:
1308:
1296:
1286:
1274:
1254:
1238:
1237:
1228:
1226:
1213:
1209:
1206:
1203:
1197:
1194:
1169:
1158:
1157:
1156:= sample size.
1145:
1135:
1121:
1117:
1100:
1099:
1090:
1088:
1074:
1071:
1067:
1062:
1057:
1053:
1027:
1007:
983:
980:
976:
962:
961:
949:
939:
927:
911:
910:
901:
899:
884:
881:
877:
871:
868:
865:
860:
853:
850:
844:
841:
835:
832:
807:
784:
781:
775:
772:
752:
732:
729:
726:
706:
686:
683:
680:
660:
657:
654:
631:
628:
622:
619:
599:
579:
576:
573:
550:
547:
541:
538:
518:
515:
512:
489:
486:
480:
477:
457:
446:
445:
431:
427:
416:
401:
398:
385:
373:
363:
350:
346:
342:
331:
316:
313:
310:
305:
288:
287:
278:
276:
261:
257:
251:
244:
241:
235:
232:
228:
221:
215:
212:
209:
204:
175:
172:
169:
164:
135:
132:
114:
113:
28:
26:
19:
13:
10:
9:
6:
4:
3:
2:
2232:
2221:
2218:
2216:
2213:
2212:
2210:
2200:
2197:
2196:0-471-93094-6
2193:
2189:
2186:
2182:
2181:
2177:
2169:
2163:
2160:
2155:
2151:
2146:
2141:
2136:
2131:
2127:
2123:
2119:
2112:
2109:
2105:
2099:
2096:
2089:
2087:
2084:
2075:
2073:
2071:
2070:
2065:
2061:
2060:
2049:
2033:
2030:
2027:
2023:
2019:
2016:
2006:
1993:
1990:
1985:
1981:
1978:
1975:
1969:
1962:
1958:
1947:
1941:
1938:
1932:
1929:
1921:
1917:
1904:
1901:
1893:
1889:
1882:
1879:
1874:
1871:
1868:
1864:
1855:
1853:
1835:
1831:
1808:
1805:
1802:
1798:
1790:Then we find
1787:
1774:
1771:
1766:
1763:
1758:
1755:
1752:
1746:
1743:
1740:
1736:
1731:
1728:
1725:
1719:
1716:
1712:
1707:
1704:
1701:
1696:
1692:
1683:
1667:
1663:
1653:
1647:
1645:
1627:
1624:
1620:
1608:
1604:
1600:
1596:
1588:
1586:
1584:
1554:
1519:
1496:
1492:
1457:
1436:
1414:
1410:
1375:
1350:
1347:
1344:
1337:
1322:
1319:
1316:
1309:
1294:
1287:
1272:
1252:
1245:
1244:
1243:
1236:
1229:
1227:
1211:
1207:
1204:
1201:
1195:
1192:
1185:
1184:
1181:
1167:
1143:
1136:
1119:
1115:
1107:
1106:
1105:
1098:
1091:
1089:
1072:
1069:
1065:
1060:
1055:
1051:
1043:
1042:
1039:
1025:
1005:
981:
978:
974:
964:The quantity
947:
940:
925:
918:
917:
916:
909:
902:
900:
882:
879:
875:
869:
866:
863:
858:
851:
848:
842:
839:
833:
830:
823:
822:
819:
805:
782:
779:
773:
770:
750:
730:
727:
724:
704:
684:
681:
678:
658:
655:
652:
629:
626:
620:
617:
597:
577:
574:
571:
548:
545:
539:
536:
516:
513:
510:
487:
484:
478:
475:
455:
429:
425:
417:
396:
386:
371:
364:
344:
332:
303:
295:
294:
293:
286:
279:
277:
259:
255:
239:
233:
230:
219:
202:
194:
193:
190:
162:
153:
149:
145:
141:
133:
131:
129:
125:
121:
110:
107:
99:
88:
85:
81:
78:
74:
71:
67:
64:
60:
57: –
56:
52:
51:Find sources:
45:
41:
35:
34:
29:This article
27:
23:
18:
17:
2184:
2178:Bibliography
2162:
2125:
2121:
2111:
2103:
2098:
2079:
2067:
2057:
2055:
2007:
1922:
1918:
1856:
1823:by plugging
1788:
1684:
1654:
1651:
1592:
1582:
1366:
1241:
1230:
1159:
1103:
1092:
963:
914:
903:
503:samples (if
447:
291:
280:
147:
139:
137:
119:
117:
102:
93:
83:
76:
69:
62:
50:
38:Please help
33:verification
30:
2145:2117/366137
1607:probability
1589:Calculation
122:(named for
2209:Categories
2090:References
134:Derivation
66:newspapers
2154:0035-8711
2076:Criticism
1991:≈
1979:−
1951:¯
1942:−
1902:≈
1850:into the
1772:≈
1759:−
1744:×
1732:−
1708:−
1345:σ
1317:μ
1212:σ
1208:μ
1205:−
870:−
843:−
774:−
728:−
656:−
621:−
564:(2.5 for
540:−
479:−
400:¯
345:⋅
243:¯
234:−
220:≥
96:July 2013
1265:is the
2069:Outlier
1648:Example
1285:-score,
798:out of
152:outlier
128:outlier
80:scholar
2194:
2152:
1905:1.7317
1242:where
1104:where
915:where
671:(2 if
292:where
82:
75:
68:
61:
53:
1986:16.34
1982:16.67
1775:.9583
1585:))).
1429:in a
87:JSTOR
73:books
2192:ISBN
2150:ISSN
2020:>
1994:2.04
1597:and
1595:mean
59:news
2140:hdl
2130:doi
2126:505
1854:.
42:by
2211::
2148:.
2138:.
2124:.
2120:.
2072:.
1976:50
1939:50
1767:24
1682:.
1644:.
130:.
2198:.
2170:.
2156:.
2142::
2132::
2034:x
2031:a
2028:m
2024:D
2017:z
1970:=
1963:x
1959:s
1948:x
1933:=
1930:z
1899:)
1894:z
1890:P
1886:(
1883:Q
1880:=
1875:x
1872:a
1869:m
1865:D
1836:z
1832:P
1809:x
1806:a
1803:m
1799:D
1764:1
1756:1
1753:=
1747:6
1741:4
1737:1
1729:1
1726:=
1720:n
1717:4
1713:1
1705:1
1702:=
1697:z
1693:P
1668:z
1664:P
1628:n
1625:2
1621:1
1583:n
1566:x
1563:a
1560:m
1555:D
1531:x
1528:a
1525:m
1520:D
1497:z
1493:P
1469:x
1466:a
1463:m
1458:D
1437:Z
1415:z
1411:P
1387:x
1384:a
1381:m
1376:D
1351:1
1348:=
1323:0
1320:=
1295:x
1273:Z
1253:Z
1235:)
1233:4
1231:(
1202:x
1196:=
1193:Z
1168:Z
1144:n
1120:z
1116:P
1097:)
1095:3
1093:(
1073:n
1070:4
1066:1
1061:=
1056:z
1052:P
1026:P
1006:P
982:n
979:2
975:1
948:n
926:P
908:)
906:2
904:(
883:n
880:2
876:1
867:1
864:=
859:n
852:2
849:1
840:n
834:=
831:P
806:n
783:2
780:1
771:n
751:P
731:1
725:n
705:n
685:3
682:=
679:n
659:1
653:n
630:2
627:1
618:n
598:n
578:3
575:=
572:n
549:2
546:1
537:n
517:3
514:=
511:n
488:2
485:1
476:n
456:n
430:x
426:s
397:x
372:x
349:|
341:|
315:x
312:a
309:m
304:D
285:)
283:1
281:(
260:x
256:s
250:|
240:x
231:x
227:|
214:x
211:a
208:m
203:D
174:x
171:a
168:m
163:D
148:n
140:n
109:)
103:(
98:)
94:(
84:·
77:·
70:·
63:·
36:.
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