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absolute deviation about the median and the population absolute deviation about the mean are 2/3. The average of all the sample absolute deviations about the mean of size 3 that can be drawn from the population is 44/81, while the average of all the sample absolute deviations about the median is 4/9. Therefore, the absolute deviation is a biased estimator.
760:(MAD), also referred to as the "mean deviation" or sometimes "average absolute deviation", is the mean of the data's absolute deviations around the data's mean: the average (absolute) distance from the mean. "Average absolute deviation" can refer to either this usage, or to the general form with respect to a specified central point (see above).
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that can be used as well. Thus, to uniquely identify the absolute deviation it is necessary to specify both the measure of deviation and the measure of central tendency. The statistical literature has not yet adopted a standard notation, as both the mean absolute deviation around the mean and the
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of the mean absolute deviation of the population. In order for the absolute deviation to be an unbiased estimator, the expected value (average) of all the sample absolute deviations must equal the population absolute deviation. However, it does not. For the population 1,2,3 both the population
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For the example {2, 2, 3, 4, 14}: 3 is the median, so the absolute deviations from the median are {1, 1, 0, 1, 11} (reordered as {0, 1, 1, 1, 11}) with a median of 1, in this case unaffected by the value of the outlier 14, so the median absolute deviation is 1.
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around an arbitrary point is the maximum of the absolute deviations of a sample from that point. While not strictly a measure of central tendency, the maximum absolute deviation can be found using the formula for the average absolute deviation as above with
1502:. The mean absolute deviation from the median is less than or equal to the mean absolute deviation from the mean. In fact, the mean absolute deviation from the median is always less than or equal to the mean absolute deviation from any other fixed number.
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See also Geary's 1936 and 1946 papers: Geary, R. C. (1936). Moments of the ratio of the mean deviation to the standard deviation for normal samples. Biometrika, 28(3/4), 295â307 and Geary, R. C. (1947). Testing for normality. Biometrika, 34(3/4),
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In other words, for a normal distribution, mean absolute deviation is about 0.8 times the standard deviation. However, in-sample measurements deliver values of the ratio of mean average deviation / standard deviation for a given
Gaussian sample
778:(MSE) method which is just the average squared error of the forecasts. Although these methods are very closely related, MAD is more commonly used because it is both easier to compute (avoiding the need for squaring) and easier to understand.
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median absolute deviation around the median have been denoted by their initials "MAD" in the literature, which may lead to confusion, since they generally have values considerably different from each other.
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dispersion: The median is the measure of central tendency most associated with the absolute deviation. Some location parameters can be compared as follows:
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is the point about which the mean deviation is minimized. The MAD median offers a direct measure of the scale of a random variable around its median
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While in principle the mean or any other central point could be taken as the central point for the median absolute deviation, most often the
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However, this argument is based on the notion of mean-unbiasedness. Each measure of location has its own form of unbiasedness (see entry on
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Geary, R. C. (1935). The ratio of the mean deviation to the standard deviation as a test of normality. Biometrika, 27(3/4), 310â332.
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1674:{\displaystyle \mathbf {I} _{O}:={\begin{cases}1&{\text{if }}x>{\text{median}},\\0&{\text{otherwise}}.\end{cases}}}
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The measures of statistical dispersion derived from absolute deviation characterize various measures of central tendency as
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MAD is often the preferred method of measuring the forecast error because it does not require squaring.
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since it corresponds better to real life. Because the MAD is a simpler measure of variability than the
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1195:{\displaystyle \left(\mathbb {E} |X-\mu \right|)^{2}\leq \mathbb {E} \left(|X-\mu |^{2}\right)}
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Management and Advanced Planning: Concepts, Models, Software, and Case Studies
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absolute deviation of the distribution after the top and bottom 25% have been trimmed off.
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is a normally distributed random variable with expected value 0 then, see Geary (1935):
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By using the general dispersion function, Habib (2011) defined MAD about median as
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1586:{\displaystyle D_{\text{med}}=E|X-{\text{median}}|=2\operatorname {Cov} (X,I_{O})}
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For a symmetric distribution, the median absolute deviation is equal to half the
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This representation allows for obtaining MAD median correlation coefficients.
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The mean absolute deviation from the mean is less than or equal to the
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For paired differences (also known as mean absolute deviation), see
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Stadtler, Hartmut; Kilger, Christoph; Meyr, Herbert, eds. (2014),
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Since the median minimizes the average absolute distance, we have
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Guidelines for
Assessment and Instruction in Statistics Education
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absolute deviation of the whole distribution, also minimizes the
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or variability. In the general form, the central point can be a
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Franklin, Christine, Gary Kader, Denise
Mewborn, Jerry Moreno,
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This method's forecast accuracy is very closely related to the
739:{\displaystyle {\frac {|2-2|+|2-2|+|3-2|+|4-2|+|14-2|}{5}}=3.0}
594:{\displaystyle {\frac {|2-3|+|2-3|+|3-3|+|4-3|+|14-3|}{5}}=2.8}
449:{\displaystyle {\frac {|2-5|+|2-5|+|3-5|+|4-5|+|14-5|}{5}}=3.6}
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For arbitrary differences (not around a central point), see
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232:{\displaystyle {\frac {1}{n}}\sum _{i=1}^{n}|x_{i}-m(X)|.}
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1422:{\displaystyle D_{\text{med}}=E|X-{\text{median}}|}
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1687:Median absolute deviation around a central point
3760:Multivariate adaptive regression splines (MARS)
2072:"What scientific idea is ready for retirement?"
819:{\textstyle {\sqrt {2/\pi }}=0.79788456\ldots }
112:Mean absolute deviation around a central point
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2259:the meaning of the MAD is easier to interpret
1968:The mean absolute deviation of a sample is a
763:MAD has been proposed to be used in place of
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2217:(7th ed.), Waveland Press, p. 62,
2192:: CS1 maint: multiple names: authors list (
2149:, Mike Perry, and Richard Scheaffer (2007).
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2078:. Archived from the original on 2014-01-16
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2295:Advantages of the mean absolute deviation
2116:Mathematics Teaching in the Middle School
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752:Mean absolute deviation around the mean
4286:KaplanâMeier estimator (product limit)
2185:
2088:
130:The mean absolute deviation of a set {
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4636:Statistical deviation and dispersion
4596:
4296:Accelerated failure time (AFT) model
2158:. American Statistical Association.
1095:{\displaystyle Y=\vert X-\mu \vert }
975:; one way of proving this relies on
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3891:Analysis of variance (ANOVA, anova)
1858:statistics: the mean minimizes the
1725:of the absolute deviation from the
3986:CochranâMantelâHaenszel statistics
2612:Pearson product-moment correlation
2214:Production and Operations Analysis
25:
1870:statistics: the median minimizes
1435:estimator of the scale parameter
1283:monotonically increasing function
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1593:where the indicator function is
27:Summary statistic of variability
4245:Least-squares spectral analysis
2175:from the original on 2013-03-07
2126:from the original on 2013-05-18
2070:Taleb, Nassim Nicholas (2014).
3226:Mean-unbiased minimum-variance
2034:Mean absolute percentage error
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3722:Coefficient of determination
3333:Uniformly most powerful test
1905:(average of first and third
1796:{\displaystyle m(X)=\max(X)}
276:Measure of central tendency
4291:Proportional hazards models
4235:Spectral density estimation
4217:Vector autoregression (VAR)
3651:Maximum posterior estimator
2883:Randomized controlled trial
919:with the following bounds:
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4051:Multivariate distributions
2471:Average absolute deviation
2110:Kader, Gary (March 1999).
1756:maximum absolute deviation
1750:Maximum absolute deviation
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2790:Sample size determination
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2019:Least absolute deviations
2009:Median absolute deviation
1717:median absolute deviation
1711:Median absolute deviation
1693:Median absolute deviation
957:{\displaystyle w_{n}\in }
80:median absolute deviation
4534:Environmental statistics
4056:Elliptical distributions
3849:Generalized linear model
3778:Simple linear regression
3548:HodgesâLehmann estimator
3005:Probability distribution
2914:Stochastic approximation
2476:Coefficient of variation
2046:Mean absolute difference
1701:value is taken instead.
1285:in the positive domain:
964:, with a bias for small
307:Mean absolute deviation
118:Mean absolute difference
4194:Cross-correlation (XCF)
3802:Non-standard predictors
3236:LehmannâScheffĂ© theorem
2909:Adaptive clinical trial
2051:Average rectified value
1825:{\displaystyle \max(X)}
986:Jensen's inequality is
758:mean absolute deviation
75:mean absolute deviation
38:) of a data set is the
18:Mean absolute deviation
4590:Mathematics portal
4411:Engineering statistics
4319:NelsonâAalen estimator
3896:Analysis of covariance
3783:Ordinary least squares
3707:Pearson product-moment
3111:Statistical functional
3022:Empirical distribution
2855:Controlled experiments
2584:Frequency distribution
2362:Descriptive statistics
2004:Deviation (statistics)
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97:statistical dispersion
91:Measures of dispersion
59:statistical dispersion
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4448:System identification
4182:Autocorrelation (ACF)
4110:Exponential smoothing
4024:Discriminant analysis
4019:Canonical correlation
3883:Partition of variance
3745:Regression validation
3589:(JonckheereâTerpstra)
3488:Likelihood-ratio test
3177:Frequentist inference
3089:Locationâscale family
3010:Sampling distribution
2975:Statistical inference
2942:Cross-sectional study
2929:Observational studies
2888:Randomized experiment
2717:Stem-and-leaf display
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3857:Exponential families
3809:Nonlinear regression
3788:General linear model
3750:Mixed effects models
3740:Errors and residuals
3717:Confounding variable
3619:Bayesian probability
3597:Van der Waerden test
3587:Ordered alternative
3352:Multiple comparisons
3231:RaoâBlackwellization
3194:Estimating equations
3150:Statistical distance
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2401:Arithmetic-Geometric
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4424:Methods engineering
4105:Seasonal adjustment
3873:Poisson regressions
3793:Bayesian regression
3732:Regression analysis
3712:Partial correlation
3684:Regression analysis
3283:Prediction interval
3278:Likelihood interval
3268:Confidence interval
3260:Interval estimation
3221:Unbiased estimators
3039:Model specification
2919:Up-and-down designs
2607:Partial correlation
2563:Index of dispersion
2481:Interquartile range
2029:Mean absolute error
1874:absolute deviation,
1744:interquartile range
1360:Hölder's inequality
977:Jensen's inequality
783:normal distribution
125:Mean absolute error
4521:Spatial statistics
4401:Medical statistics
4301:First hitting time
4255:Whittle likelihood
3906:Degrees of freedom
3901:Multivariate ANOVA
3834:Heteroscedasticity
3646:Bayesian estimator
3611:Bayesian inference
3460:KolmogorovâSmirnov
3345:Randomization test
3315:Testing hypotheses
3288:Tolerance interval
3199:Maximum likelihood
3094:Exponential family
3027:Density estimation
2987:Statistical theory
2947:Natural experiment
2893:Scientific control
2810:Survey methodology
2496:Standard deviation
2209:Olsen, Tava Lennon
2014:Squared deviations
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1941:. You can help by
1891:absolute deviation
1860:mean squared error
1822:
1793:
1719:(also MAD) is the
1671:
1666:
1583:
1492:
1445:
1433:maximum likelihood
1419:
1346:
1265:
1192:
1092:
1050:
984:
973:standard deviation
954:
904:
816:
776:mean squared error
769:standard deviation
765:standard deviation
736:
591:
446:
295:
260:
229:
4623:
4622:
4561:
4560:
4557:
4556:
4496:National accounts
4466:Actuarial science
4458:Social statistics
4351:
4350:
4347:
4346:
4343:
4342:
4278:Survival function
4263:
4262:
4125:Granger causality
3966:Contingency table
3941:Survival analysis
3918:
3917:
3914:
3913:
3770:Linear regression
3665:
3664:
3661:
3660:
3636:Credible interval
3605:
3604:
3388:
3387:
3204:Method of moments
3073:Parametric family
3034:Statistical model
2964:
2963:
2960:
2959:
2878:Random assignment
2800:Statistical power
2734:
2733:
2730:
2729:
2579:Contingency table
2549:
2548:
2416:Generalized/power
2207:Nahmias, Steven;
2165:978-0-9791747-1-1
1959:
1958:
1659:
1642:
1631:
1542:
1519:
1489:
1476:
1448:{\displaystyle b}
1412:
1389:
1344:
982:
899:
898:
884:
883:
805:
749:
748:
728:
583:
438:
168:
55:summary statistic
16:(Redirected from
4643:
4611:
4610:
4599:
4598:
4588:
4587:
4573:
4572:
4476:Crime statistics
4370:
4357:
4274:
4240:Fourier analysis
4227:Frequency domain
4207:
4154:
4120:Structural break
4080:
4029:Cluster analysis
3976:Log-linear model
3949:
3924:
3865:
3839:Homoscedasticity
3695:
3671:
3590:
3582:
3574:
3573:(KruskalâWallis)
3558:
3543:
3498:Cross validation
3483:
3465:AndersonâDarling
3412:
3399:
3370:Likelihood-ratio
3362:Parametric tests
3340:Permutation test
3323:1- & 2-tails
3214:Minimum distance
3186:Point estimation
3182:
3133:Optimal decision
3084:
2983:
2970:
2952:Quasi-experiment
2902:Adaptive designs
2753:
2740:
2617:Rank correlation
2379:
2370:
2357:
2324:
2317:
2310:
2301:
2282:
2278:
2272:
2269:
2263:
2261:
2238:
2232:
2231:
2204:
2198:
2197:
2191:
2183:
2181:
2180:
2174:
2157:
2142:
2136:
2135:
2133:
2131:
2112:"Means and MADS"
2107:
2101:
2100:
2094:
2086:
2084:
2083:
2067:
1978:biased estimator
1970:biased estimator
1954:
1951:
1933:
1926:
1883:statistics: the
1831:
1829:
1828:
1823:
1802:
1800:
1799:
1794:
1680:
1678:
1677:
1672:
1670:
1669:
1660:
1657:
1643:
1640:
1632:
1629:
1611:
1610:
1605:
1592:
1590:
1589:
1584:
1579:
1578:
1548:
1543:
1540:
1532:
1521:
1520:
1517:
1501:
1499:
1498:
1493:
1491:
1490:
1487:
1478:
1477:
1474:
1454:
1452:
1451:
1446:
1428:
1426:
1425:
1420:
1418:
1413:
1410:
1402:
1391:
1390:
1387:
1355:
1353:
1352:
1347:
1345:
1328:
1320:
1316:
1306:
1296:
1274:
1272:
1271:
1266:
1246:
1245:
1236:
1232:
1222:
1217:
1201:
1199:
1198:
1193:
1191:
1187:
1186:
1185:
1180:
1165:
1155:
1147:
1146:
1137:
1133:
1123:
1118:
1101:
1099:
1098:
1093:
1059:
1057:
1056:
1051:
1049:
1045:
1027:
1019:
1015:
1005:
963:
961:
960:
955:
935:
934:
913:
911:
910:
905:
900:
891:
890:
885:
879:
878:
863:
862:
861:
853:
844:
825:
823:
822:
817:
806:
801:
793:
745:
743:
742:
737:
729:
724:
723:
709:
701:
687:
679:
665:
657:
643:
635:
621:
615:
600:
598:
597:
592:
584:
579:
578:
564:
556:
542:
534:
520:
512:
498:
490:
476:
470:
455:
453:
452:
447:
439:
434:
433:
419:
411:
397:
389:
375:
367:
353:
345:
331:
325:
304:
302:
301:
296:
273:
269:
267:
266:
261:
238:
236:
235:
230:
225:
205:
204:
195:
189:
184:
169:
161:
105:central tendency
21:
4651:
4650:
4646:
4645:
4644:
4642:
4641:
4640:
4626:
4625:
4624:
4619:
4582:
4553:
4515:
4452:
4438:quality control
4405:
4387:Clinical trials
4364:
4339:
4323:
4311:Hazard function
4305:
4259:
4221:
4205:
4168:
4164:BreuschâGodfrey
4152:
4129:
4069:
4044:Factor analysis
3990:
3971:Graphical model
3943:
3910:
3877:
3863:
3843:
3797:
3764:
3726:
3689:
3688:
3657:
3601:
3588:
3580:
3572:
3556:
3541:
3520:Rank statistics
3514:
3493:Model selection
3481:
3439:Goodness of fit
3433:
3410:
3384:
3356:
3309:
3254:
3243:Median unbiased
3171:
3082:
3015:Order statistic
2977:
2956:
2923:
2897:
2849:
2804:
2747:
2745:Data collection
2726:
2638:
2593:
2567:
2545:
2505:
2457:
2374:Continuous data
2364:
2351:
2333:
2328:
2291:
2286:
2285:
2279:
2275:
2270:
2266:
2255:
2240:
2239:
2235:
2225:
2206:
2205:
2201:
2184:
2178:
2176:
2172:
2166:
2155:
2144:
2143:
2139:
2129:
2127:
2109:
2108:
2104:
2087:
2081:
2079:
2069:
2068:
2064:
2059:
1993:
1955:
1949:
1946:
1939:needs expansion
1924:
1842:
1805:
1804:
1761:
1760:
1752:
1713:
1707:
1695:
1689:
1665:
1664:
1654:
1648:
1647:
1626:
1616:
1600:
1595:
1594:
1570:
1512:
1507:
1506:
1482:
1469:
1464:
1463:
1437:
1436:
1382:
1377:
1376:
1369:
1364:
1301:
1297:
1287:
1286:
1237:
1212:
1208:
1203:
1202:
1175:
1160:
1156:
1138:
1113:
1109:
1104:
1103:
1066:
1065:
1032:
1028:
1000:
996:
988:
987:
926:
921:
920:
870:
845:
832:
831:
787:
786:
754:
616:
609:
608:
471:
464:
463:
326:
319:
318:
313:Arithmetic Mean
278:
277:
243:
242:
196:
155:
154:
152:
143:
136:
128:
121:
114:
93:
28:
23:
22:
15:
12:
11:
5:
4649:
4647:
4639:
4638:
4628:
4627:
4621:
4620:
4618:
4617:
4605:
4593:
4579:
4566:
4563:
4562:
4559:
4558:
4555:
4554:
4552:
4551:
4546:
4541:
4536:
4531:
4525:
4523:
4517:
4516:
4514:
4513:
4508:
4503:
4498:
4493:
4488:
4483:
4478:
4473:
4468:
4462:
4460:
4454:
4453:
4451:
4450:
4445:
4440:
4431:
4426:
4421:
4415:
4413:
4407:
4406:
4404:
4403:
4398:
4393:
4384:
4382:Bioinformatics
4378:
4376:
4366:
4365:
4360:
4353:
4352:
4349:
4348:
4345:
4344:
4341:
4340:
4338:
4337:
4331:
4329:
4325:
4324:
4322:
4321:
4315:
4313:
4307:
4306:
4304:
4303:
4298:
4293:
4288:
4282:
4280:
4271:
4265:
4264:
4261:
4260:
4258:
4257:
4252:
4247:
4242:
4237:
4231:
4229:
4223:
4222:
4220:
4219:
4214:
4209:
4201:
4196:
4191:
4190:
4189:
4187:partial (PACF)
4178:
4176:
4170:
4169:
4167:
4166:
4161:
4156:
4148:
4143:
4137:
4135:
4134:Specific tests
4131:
4130:
4128:
4127:
4122:
4117:
4112:
4107:
4102:
4097:
4092:
4086:
4084:
4077:
4071:
4070:
4068:
4067:
4066:
4065:
4064:
4063:
4048:
4047:
4046:
4036:
4034:Classification
4031:
4026:
4021:
4016:
4011:
4006:
4000:
3998:
3992:
3991:
3989:
3988:
3983:
3981:McNemar's test
3978:
3973:
3968:
3963:
3957:
3955:
3945:
3944:
3927:
3920:
3919:
3916:
3915:
3912:
3911:
3909:
3908:
3903:
3898:
3893:
3887:
3885:
3879:
3878:
3876:
3875:
3859:
3853:
3851:
3845:
3844:
3842:
3841:
3836:
3831:
3826:
3821:
3819:Semiparametric
3816:
3811:
3805:
3803:
3799:
3798:
3796:
3795:
3790:
3785:
3780:
3774:
3772:
3766:
3765:
3763:
3762:
3757:
3752:
3747:
3742:
3736:
3734:
3728:
3727:
3725:
3724:
3719:
3714:
3709:
3703:
3701:
3691:
3690:
3687:
3686:
3681:
3675:
3674:
3667:
3666:
3663:
3662:
3659:
3658:
3656:
3655:
3654:
3653:
3643:
3638:
3633:
3632:
3631:
3626:
3615:
3613:
3607:
3606:
3603:
3602:
3600:
3599:
3594:
3593:
3592:
3584:
3576:
3560:
3557:(MannâWhitney)
3552:
3551:
3550:
3537:
3536:
3535:
3524:
3522:
3516:
3515:
3513:
3512:
3511:
3510:
3505:
3500:
3490:
3485:
3482:(ShapiroâWilk)
3477:
3472:
3467:
3462:
3457:
3449:
3443:
3441:
3435:
3434:
3432:
3431:
3423:
3414:
3402:
3396:
3394:Specific tests
3390:
3389:
3386:
3385:
3383:
3382:
3377:
3372:
3366:
3364:
3358:
3357:
3355:
3354:
3349:
3348:
3347:
3337:
3336:
3335:
3325:
3319:
3317:
3311:
3310:
3308:
3307:
3306:
3305:
3300:
3290:
3285:
3280:
3275:
3270:
3264:
3262:
3256:
3255:
3253:
3252:
3247:
3246:
3245:
3240:
3239:
3238:
3233:
3218:
3217:
3216:
3211:
3206:
3201:
3190:
3188:
3179:
3173:
3172:
3170:
3169:
3164:
3159:
3158:
3157:
3147:
3142:
3141:
3140:
3130:
3129:
3128:
3123:
3118:
3108:
3103:
3098:
3097:
3096:
3091:
3086:
3070:
3069:
3068:
3063:
3058:
3048:
3047:
3046:
3041:
3031:
3030:
3029:
3019:
3018:
3017:
3007:
3002:
2997:
2991:
2989:
2979:
2978:
2973:
2966:
2965:
2962:
2961:
2958:
2957:
2955:
2954:
2949:
2944:
2939:
2933:
2931:
2925:
2924:
2922:
2921:
2916:
2911:
2905:
2903:
2899:
2898:
2896:
2895:
2890:
2885:
2880:
2875:
2870:
2865:
2859:
2857:
2851:
2850:
2848:
2847:
2845:Standard error
2842:
2837:
2832:
2831:
2830:
2825:
2814:
2812:
2806:
2805:
2803:
2802:
2797:
2792:
2787:
2782:
2777:
2775:Optimal design
2772:
2767:
2761:
2759:
2749:
2748:
2743:
2736:
2735:
2732:
2731:
2728:
2727:
2725:
2724:
2719:
2714:
2709:
2704:
2699:
2694:
2689:
2684:
2679:
2674:
2669:
2664:
2659:
2654:
2648:
2646:
2640:
2639:
2637:
2636:
2631:
2630:
2629:
2624:
2614:
2609:
2603:
2601:
2595:
2594:
2592:
2591:
2586:
2581:
2575:
2573:
2572:Summary tables
2569:
2568:
2566:
2565:
2559:
2557:
2551:
2550:
2547:
2546:
2544:
2543:
2542:
2541:
2536:
2531:
2521:
2515:
2513:
2507:
2506:
2504:
2503:
2498:
2493:
2488:
2483:
2478:
2473:
2467:
2465:
2459:
2458:
2456:
2455:
2450:
2445:
2444:
2443:
2438:
2433:
2428:
2423:
2418:
2413:
2408:
2406:Contraharmonic
2403:
2398:
2387:
2385:
2376:
2366:
2365:
2360:
2353:
2352:
2350:
2349:
2344:
2338:
2335:
2334:
2329:
2327:
2326:
2319:
2312:
2304:
2298:
2297:
2290:
2289:External links
2287:
2284:
2283:
2273:
2264:
2253:
2233:
2223:
2199:
2164:
2137:
2122:(6): 398â403.
2102:
2061:
2060:
2058:
2055:
2054:
2053:
2048:
2043:
2042:
2041:
2039:Probable error
2036:
2031:
2023:
2022:
2021:
2016:
2011:
1992:
1989:
1957:
1956:
1936:
1934:
1923:
1920:
1919:
1918:
1892:
1887:minimizes the
1875:
1862:
1841:
1838:
1834:sample maximum
1821:
1818:
1815:
1812:
1792:
1789:
1786:
1783:
1780:
1777:
1774:
1771:
1768:
1751:
1748:
1709:Main article:
1706:
1703:
1691:Main article:
1688:
1685:
1668:
1663:
1655:
1653:
1650:
1649:
1646:
1638:
1635:
1627:
1625:
1622:
1621:
1619:
1614:
1609:
1604:
1582:
1577:
1573:
1569:
1566:
1563:
1560:
1557:
1554:
1551:
1547:
1538:
1535:
1531:
1527:
1524:
1515:
1485:
1481:
1472:
1444:
1417:
1408:
1405:
1401:
1397:
1394:
1385:
1368:
1365:
1343:
1340:
1337:
1334:
1331:
1326:
1323:
1319:
1315:
1312:
1309:
1305:
1300:
1295:
1264:
1261:
1258:
1255:
1252:
1249:
1244:
1240:
1235:
1231:
1228:
1225:
1221:
1216:
1211:
1190:
1184:
1179:
1174:
1171:
1168:
1164:
1159:
1154:
1150:
1145:
1141:
1136:
1132:
1129:
1126:
1122:
1117:
1112:
1091:
1088:
1085:
1082:
1079:
1076:
1073:
1048:
1044:
1041:
1038:
1035:
1031:
1026:
1022:
1018:
1014:
1011:
1008:
1004:
999:
995:
981:
953:
950:
947:
944:
941:
938:
933:
929:
903:
897:
894:
888:
882:
877:
873:
869:
866:
860:
856:
852:
848:
842:
839:
815:
812:
809:
804:
800:
796:
753:
750:
747:
746:
735:
732:
727:
722:
718:
715:
712:
708:
704:
700:
696:
693:
690:
686:
682:
678:
674:
671:
668:
664:
660:
656:
652:
649:
646:
642:
638:
634:
630:
627:
624:
620:
606:
602:
601:
590:
587:
582:
577:
573:
570:
567:
563:
559:
555:
551:
548:
545:
541:
537:
533:
529:
526:
523:
519:
515:
511:
507:
504:
501:
497:
493:
489:
485:
482:
479:
475:
461:
457:
456:
445:
442:
437:
432:
428:
425:
422:
418:
414:
410:
406:
403:
400:
396:
392:
388:
384:
381:
378:
374:
370:
366:
362:
359:
356:
352:
348:
344:
340:
337:
334:
330:
316:
309:
308:
305:
294:
291:
288:
285:
259:
256:
253:
250:
228:
224:
220:
217:
214:
211:
208:
203:
199:
194:
188:
183:
180:
177:
173:
167:
164:
148:
141:
134:
113:
110:
92:
89:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
4648:
4637:
4634:
4633:
4631:
4616:
4615:
4606:
4604:
4603:
4594:
4592:
4591:
4586:
4580:
4578:
4577:
4568:
4567:
4564:
4550:
4547:
4545:
4544:Geostatistics
4542:
4540:
4537:
4535:
4532:
4530:
4527:
4526:
4524:
4522:
4518:
4512:
4511:Psychometrics
4509:
4507:
4504:
4502:
4499:
4497:
4494:
4492:
4489:
4487:
4484:
4482:
4479:
4477:
4474:
4472:
4469:
4467:
4464:
4463:
4461:
4459:
4455:
4449:
4446:
4444:
4441:
4439:
4435:
4432:
4430:
4427:
4425:
4422:
4420:
4417:
4416:
4414:
4412:
4408:
4402:
4399:
4397:
4394:
4392:
4388:
4385:
4383:
4380:
4379:
4377:
4375:
4374:Biostatistics
4371:
4367:
4363:
4358:
4354:
4336:
4335:Log-rank test
4333:
4332:
4330:
4326:
4320:
4317:
4316:
4314:
4312:
4308:
4302:
4299:
4297:
4294:
4292:
4289:
4287:
4284:
4283:
4281:
4279:
4275:
4272:
4270:
4266:
4256:
4253:
4251:
4248:
4246:
4243:
4241:
4238:
4236:
4233:
4232:
4230:
4228:
4224:
4218:
4215:
4213:
4210:
4208:
4206:(BoxâJenkins)
4202:
4200:
4197:
4195:
4192:
4188:
4185:
4184:
4183:
4180:
4179:
4177:
4175:
4171:
4165:
4162:
4160:
4159:DurbinâWatson
4157:
4155:
4149:
4147:
4144:
4142:
4141:DickeyâFuller
4139:
4138:
4136:
4132:
4126:
4123:
4121:
4118:
4116:
4115:Cointegration
4113:
4111:
4108:
4106:
4103:
4101:
4098:
4096:
4093:
4091:
4090:Decomposition
4088:
4087:
4085:
4081:
4078:
4076:
4072:
4062:
4059:
4058:
4057:
4054:
4053:
4052:
4049:
4045:
4042:
4041:
4040:
4037:
4035:
4032:
4030:
4027:
4025:
4022:
4020:
4017:
4015:
4012:
4010:
4007:
4005:
4002:
4001:
3999:
3997:
3993:
3987:
3984:
3982:
3979:
3977:
3974:
3972:
3969:
3967:
3964:
3962:
3961:Cohen's kappa
3959:
3958:
3956:
3954:
3950:
3946:
3942:
3938:
3934:
3930:
3925:
3921:
3907:
3904:
3902:
3899:
3897:
3894:
3892:
3889:
3888:
3886:
3884:
3880:
3874:
3870:
3866:
3860:
3858:
3855:
3854:
3852:
3850:
3846:
3840:
3837:
3835:
3832:
3830:
3827:
3825:
3822:
3820:
3817:
3815:
3814:Nonparametric
3812:
3810:
3807:
3806:
3804:
3800:
3794:
3791:
3789:
3786:
3784:
3781:
3779:
3776:
3775:
3773:
3771:
3767:
3761:
3758:
3756:
3753:
3751:
3748:
3746:
3743:
3741:
3738:
3737:
3735:
3733:
3729:
3723:
3720:
3718:
3715:
3713:
3710:
3708:
3705:
3704:
3702:
3700:
3696:
3692:
3685:
3682:
3680:
3677:
3676:
3672:
3668:
3652:
3649:
3648:
3647:
3644:
3642:
3639:
3637:
3634:
3630:
3627:
3625:
3622:
3621:
3620:
3617:
3616:
3614:
3612:
3608:
3598:
3595:
3591:
3585:
3583:
3577:
3575:
3569:
3568:
3567:
3564:
3563:Nonparametric
3561:
3559:
3553:
3549:
3546:
3545:
3544:
3538:
3534:
3533:Sample median
3531:
3530:
3529:
3526:
3525:
3523:
3521:
3517:
3509:
3506:
3504:
3501:
3499:
3496:
3495:
3494:
3491:
3489:
3486:
3484:
3478:
3476:
3473:
3471:
3468:
3466:
3463:
3461:
3458:
3456:
3454:
3450:
3448:
3445:
3444:
3442:
3440:
3436:
3430:
3428:
3424:
3422:
3420:
3415:
3413:
3408:
3404:
3403:
3400:
3397:
3395:
3391:
3381:
3378:
3376:
3373:
3371:
3368:
3367:
3365:
3363:
3359:
3353:
3350:
3346:
3343:
3342:
3341:
3338:
3334:
3331:
3330:
3329:
3326:
3324:
3321:
3320:
3318:
3316:
3312:
3304:
3301:
3299:
3296:
3295:
3294:
3291:
3289:
3286:
3284:
3281:
3279:
3276:
3274:
3271:
3269:
3266:
3265:
3263:
3261:
3257:
3251:
3248:
3244:
3241:
3237:
3234:
3232:
3229:
3228:
3227:
3224:
3223:
3222:
3219:
3215:
3212:
3210:
3207:
3205:
3202:
3200:
3197:
3196:
3195:
3192:
3191:
3189:
3187:
3183:
3180:
3178:
3174:
3168:
3165:
3163:
3160:
3156:
3153:
3152:
3151:
3148:
3146:
3143:
3139:
3138:loss function
3136:
3135:
3134:
3131:
3127:
3124:
3122:
3119:
3117:
3114:
3113:
3112:
3109:
3107:
3104:
3102:
3099:
3095:
3092:
3090:
3087:
3085:
3079:
3076:
3075:
3074:
3071:
3067:
3064:
3062:
3059:
3057:
3054:
3053:
3052:
3049:
3045:
3042:
3040:
3037:
3036:
3035:
3032:
3028:
3025:
3024:
3023:
3020:
3016:
3013:
3012:
3011:
3008:
3006:
3003:
3001:
2998:
2996:
2993:
2992:
2990:
2988:
2984:
2980:
2976:
2971:
2967:
2953:
2950:
2948:
2945:
2943:
2940:
2938:
2935:
2934:
2932:
2930:
2926:
2920:
2917:
2915:
2912:
2910:
2907:
2906:
2904:
2900:
2894:
2891:
2889:
2886:
2884:
2881:
2879:
2876:
2874:
2871:
2869:
2866:
2864:
2861:
2860:
2858:
2856:
2852:
2846:
2843:
2841:
2840:Questionnaire
2838:
2836:
2833:
2829:
2826:
2824:
2821:
2820:
2819:
2816:
2815:
2813:
2811:
2807:
2801:
2798:
2796:
2793:
2791:
2788:
2786:
2783:
2781:
2778:
2776:
2773:
2771:
2768:
2766:
2763:
2762:
2760:
2758:
2754:
2750:
2746:
2741:
2737:
2723:
2720:
2718:
2715:
2713:
2710:
2708:
2705:
2703:
2700:
2698:
2695:
2693:
2690:
2688:
2685:
2683:
2680:
2678:
2675:
2673:
2670:
2668:
2667:Control chart
2665:
2663:
2660:
2658:
2655:
2653:
2650:
2649:
2647:
2645:
2641:
2635:
2632:
2628:
2625:
2623:
2620:
2619:
2618:
2615:
2613:
2610:
2608:
2605:
2604:
2602:
2600:
2596:
2590:
2587:
2585:
2582:
2580:
2577:
2576:
2574:
2570:
2564:
2561:
2560:
2558:
2556:
2552:
2540:
2537:
2535:
2532:
2530:
2527:
2526:
2525:
2522:
2520:
2517:
2516:
2514:
2512:
2508:
2502:
2499:
2497:
2494:
2492:
2489:
2487:
2484:
2482:
2479:
2477:
2474:
2472:
2469:
2468:
2466:
2464:
2460:
2454:
2451:
2449:
2446:
2442:
2439:
2437:
2434:
2432:
2429:
2427:
2424:
2422:
2419:
2417:
2414:
2412:
2409:
2407:
2404:
2402:
2399:
2397:
2394:
2393:
2392:
2389:
2388:
2386:
2384:
2380:
2377:
2375:
2371:
2367:
2363:
2358:
2354:
2348:
2345:
2343:
2340:
2339:
2336:
2332:
2325:
2320:
2318:
2313:
2311:
2306:
2305:
2302:
2296:
2293:
2292:
2288:
2277:
2274:
2268:
2265:
2260:
2256:
2254:9783642553097
2250:
2246:
2245:
2237:
2234:
2230:
2226:
2224:9781478628248
2220:
2216:
2215:
2210:
2203:
2200:
2195:
2189:
2171:
2167:
2161:
2154:
2153:
2148:
2141:
2138:
2125:
2121:
2117:
2113:
2106:
2103:
2098:
2092:
2077:
2073:
2066:
2063:
2056:
2052:
2049:
2047:
2044:
2040:
2037:
2035:
2032:
2030:
2027:
2026:
2024:
2020:
2017:
2015:
2012:
2010:
2007:
2006:
2005:
2002:
2001:
1997:
1990:
1985:
1981:
1979:
1974:
1971:
1963:
1953:
1944:
1940:
1937:This section
1935:
1932:
1928:
1927:
1921:
1916:
1912:
1908:
1904:
1900:
1898:
1893:
1890:
1886:
1882:
1880:
1876:
1873:
1869:
1867:
1863:
1861:
1857:
1855:
1851:
1850:
1849:
1847:
1839:
1837:
1835:
1816:
1787:
1778:
1772:
1766:
1757:
1749:
1747:
1745:
1740:
1736:
1734:
1730:
1729:
1724:
1723:
1718:
1712:
1704:
1702:
1700:
1694:
1686:
1684:
1681:
1661:
1651:
1644:
1636:
1633:
1623:
1617:
1612:
1607:
1575:
1571:
1567:
1564:
1558:
1555:
1552:
1549:
1536:
1533:
1525:
1522:
1513:
1503:
1483:
1479:
1470:
1460:
1458:
1442:
1434:
1429:
1406:
1403:
1395:
1392:
1383:
1374:
1366:
1363:
1361:
1356:
1338:
1332:
1329:
1324:
1317:
1313:
1310:
1307:
1298:
1284:
1280:
1275:
1259:
1253:
1250:
1247:
1242:
1233:
1229:
1226:
1223:
1209:
1188:
1182:
1172:
1169:
1166:
1157:
1148:
1143:
1134:
1130:
1127:
1124:
1110:
1086:
1083:
1080:
1074:
1071:
1063:
1046:
1039:
1033:
1029:
1020:
1016:
1009:
997:
993:
980:
978:
974:
969:
967:
948:
945:
942:
936:
931:
927:
918:
901:
895:
892:
886:
875:
871:
864:
854:
846:
840:
837:
829:
813:
810:
807:
802:
798:
794:
784:
779:
777:
772:
770:
766:
761:
759:
751:
733:
730:
725:
716:
713:
710:
702:
694:
691:
688:
680:
672:
669:
666:
658:
650:
647:
644:
636:
628:
625:
622:
607:
604:
603:
588:
585:
580:
571:
568:
565:
557:
549:
546:
543:
535:
527:
524:
521:
513:
505:
502:
499:
491:
483:
480:
477:
462:
459:
458:
443:
440:
435:
426:
423:
420:
412:
404:
401:
398:
390:
382:
379:
376:
368:
360:
357:
354:
346:
338:
335:
332:
317:
314:
311:
310:
306:
289:
283:
275:
274:
271:
254:
248:
239:
226:
215:
209:
206:
201:
197:
186:
181:
178:
175:
171:
165:
162:
151:
147:
140:
133:
126:
119:
111:
109:
106:
102:
98:
90:
88:
86:
82:
81:
76:
72:
68:
64:
60:
56:
52:
51:central point
48:
45:
41:
37:
33:
19:
4612:
4600:
4581:
4574:
4486:Econometrics
4436: /
4419:Chemometrics
4396:Epidemiology
4389: /
4362:Applications
4204:ARIMA model
4151:Q-statistic
4100:Stationarity
3996:Multivariate
3939: /
3935: /
3933:Multivariate
3931: /
3871: /
3867: /
3641:Bayes factor
3540:Signed rank
3452:
3426:
3418:
3406:
3101:Completeness
2937:Cohort study
2835:Opinion poll
2770:Missing data
2757:Study design
2712:Scatter plot
2634:Scatter plot
2627:Spearman's Ï
2589:Grouped data
2470:
2276:
2267:
2258:
2243:
2236:
2228:
2213:
2202:
2177:. Retrieved
2151:
2140:
2128:. Retrieved
2119:
2115:
2105:
2080:. Retrieved
2075:
2065:
1975:
1967:
1947:
1943:adding to it
1938:
1914:
1910:
1896:
1888:
1878:
1871:
1865:
1853:
1845:
1843:
1840:Minimization
1755:
1753:
1741:
1737:
1726:
1720:
1716:
1714:
1696:
1682:
1504:
1461:
1431:This is the
1430:
1370:
1357:
1276:
1061:
985:
970:
965:
916:
827:
780:
773:
762:
757:
755:
240:
149:
145:
138:
131:
129:
94:
84:
78:
74:
35:
31:
29:
4614:WikiProject
4529:Cartography
4491:Jurimetrics
4443:Reliability
4174:Time domain
4153:(LjungâBox)
4075:Time-series
3953:Categorical
3937:Time-series
3929:Categorical
3864:(Bernoulli)
3699:Correlation
3679:Correlation
3475:JarqueâBera
3447:Chi-squared
3209:M-estimator
3162:Asymptotics
3106:Sufficiency
2873:Interaction
2785:Replication
2765:Effect size
2722:Violin plot
2702:Radar chart
2682:Forest plot
2672:Correlogram
2622:Kendall's Ï
2130:20 February
1279:square root
460:Median = 3
4481:Demography
4199:ARMA model
4004:Regression
3581:(Friedman)
3542:(Wilcoxon)
3480:Normality
3470:Lilliefors
3417:Student's
3293:Resampling
3167:Robustness
3155:divergence
3145:Efficiency
3083:(monotone)
3078:Likelihood
2995:Population
2828:Stratified
2780:Population
2599:Dependence
2555:Count data
2486:Percentile
2463:Dispersion
2396:Arithmetic
2331:Statistics
2179:2013-02-20
2082:2014-01-16
2057:References
1950:March 2009
1922:Estimation
1846:minimizing
1731:. It is a
826:. Thus if
811:0.79788456
53:. It is a
47:deviations
3862:Logistic
3629:posterior
3555:Rank sum
3303:Jackknife
3298:Bootstrap
3116:Bootstrap
3051:Parameter
3000:Statistic
2795:Statistic
2707:Run chart
2692:Pie chart
2687:Histogram
2677:Fan chart
2652:Bar chart
2534:L-moments
2421:Geometric
2188:cite book
2147:Roxy Peck
1907:quartiles
1885:mid-range
1658:otherwise
1559:
1537:−
1480:≤
1407:−
1333:
1325:≤
1314:μ
1311:−
1254:
1248:≤
1230:μ
1227:−
1173:μ
1170:−
1149:≤
1131:μ
1128:−
1087:μ
1084:−
1034:φ
1021:≤
994:φ
937:∈
896:π
814:…
803:π
714:−
692:−
670:−
648:−
626:−
605:Mode = 2
569:−
547:−
525:−
503:−
481:−
424:−
402:−
380:−
358:−
336:−
207:−
172:∑
4630:Category
4576:Category
4269:Survival
4146:Johansen
3869:Binomial
3824:Isotonic
3411:(normal)
3056:location
2863:Blocking
2818:Sampling
2697:QâQ plot
2662:Box plot
2644:Graphics
2539:Skewness
2529:Kurtosis
2501:Variance
2431:Heronian
2426:Harmonic
2281:209â242.
2211:(2015),
2170:Archived
2124:Archived
2091:cite web
1991:See also
1903:midhinge
1894:trimmed
1803:, where
1630:if
1060:, where
781:For the
77:and the
44:absolute
4602:Commons
4549:Kriging
4434:Process
4391:studies
4250:Wavelet
4083:General
3250:Plug-in
3044:L space
2823:Cluster
2524:Moments
2342:Outline
2025:Errors
1915:maximum
1889:maximum
1872:average
1832:is the
1455:of the
144:, ...,
49:from a
42:of the
40:average
4471:Census
4061:Normal
4009:Manova
3829:Robust
3579:2-way
3571:1-way
3409:-test
3080:
2657:Biplot
2448:Median
2441:Lehmer
2383:Center
2251:
2221:
2162:
1911:median
1728:median
1722:median
1699:median
1641:median
1541:median
1411:median
1373:median
1102:that:
67:median
4095:Trend
3624:prior
3566:anova
3455:-test
3429:-test
3421:-test
3328:Power
3273:Pivot
3066:shape
3061:scale
2511:Shape
2491:Range
2436:Heinz
2411:Cubic
2347:Index
2173:(PDF)
2156:(PDF)
1281:is a
983:Proof
153:} is
4328:Test
3528:Sign
3380:Wald
2453:Mode
2391:Mean
2249:ISBN
2219:ISBN
2194:link
2160:ISBN
2132:2013
2097:link
2076:Edge
1899:norm
1881:norm
1868:norm
1856:norm
1754:The
1735:.
1715:The
1637:>
1488:mean
1371:The
756:The
315:= 5
71:mode
63:mean
30:The
3508:BIC
3503:AIC
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