1204:. If such data are processed to produce a 95% confidence interval for the mean mileage of the model, it is, for example, possible to use it to project the mean or total gasoline consumption for the manufactured fleet of such autos over their first 5,000 miles of use. Such an interval, would however, not be of much help to a person renting one of these cars and wondering whether the (full) 10-gallon tank of gas will suffice to carry him the 350 miles to his destination. For that job, a prediction interval would be much more useful. (Consider the differing implications of being "95% sure" that
4807:
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2136:
interval cannot answer this question, since the confidence interval is only for the median lead level, and the prediction interval is only for a single lead level. What is required is a tolerance interval; more specifically, an upper tolerance limit. The upper tolerance limit is to be computed subject to the condition that at least 95% of the population lead levels is below the limit, with a certain confidence level, say 99%.
98:
4831:
4819:
2135:
only. A prediction interval has a similar interpretation, and is meant to provide information concerning a single lead level only. Now suppose we want to use the sample to conclude whether or not at least 95% of the population lead levels are below a threshold. The confidence interval and prediction
1289:
nor a prediction interval for a single additional mileage is exactly what is needed by a design engineer charged with determining how large a gas tank the model really needs to guarantee that 99% of the autos produced will have a 400-mile cruising range. What the engineer really needs is a tolerance
1111:
in that both put bounds on variation in future samples. However, the prediction interval only bounds a single future sample, whereas a tolerance interval bounds the entire population (equivalently, an arbitrary sequence of future samples). In other words, a prediction interval covers a specified
1104:, and will approach a zero-width interval at the true population parameter as sample size increases, a tolerance interval's size is due partly to sampling error and partly to actual variance in the population, and will approach the population's probability interval as sample size increases.
586:
2182:
Krishnamoorthy, K. and Lian, Xiaodong(2011) 'Closed-form approximate tolerance intervals for some general linear models and comparison studies', Journal of
Statistical Computation and Simulation, First published on: 13 June 2011
792:
1936:
446:
2024:
1100:, for example) with some confidence, while the tolerance interval bounds the range of data values that includes a specific proportion of the population. Whereas a confidence interval's size is entirely due to
2093:
1668:
1471:
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1849:
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are the same." If we knew a population's exact parameters, we would be able to compute a range within which a certain proportion of the population falls. For example, if we know a population is
260:
200:
441:
1046:, which is the confidence with which this interval actually includes the specified proportion of the population. For a normally distributed population, a z-score can be transformed into a "
2515:
ISO 16269-6, Statistical interpretation of data, Part 6: Determination of statistical tolerance intervals, Technical
Committee ISO/TC 69, Applications of statistical methods. Available at
1202:
909:
977:
1707:
1267:
1938:. Now suppose we want to predict the air lead level at a particular area within the laboratory. A 95% upper prediction limit for the log-transformed lead level is given by
948:
2315:
De Gryze, S.; Langhans, I.; Vandebroek, M. (2007). "Using the correct intervals for prediction: A tutorial on tolerance intervals for ordinary least-squares regression".
1399:
1228:
363:
287:
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1503:
1733:
2026:. A two-sided prediction interval can be similarly computed. The meaning and interpretation of these intervals are well known. For example, if the confidence interval
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1314:
1026:
will not necessarily include 95% of the population, due to variance in these estimates. A tolerance interval bounds this variance by introducing a confidence level
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336:
2170:
D. S. Young (2010), Book
Reviews: "Statistical Tolerance Regions: Theory, Applications, and Computation", TECHNOMETRICS, FEBRUARY 2010, VOL. 52, NO. 1, pp.143-144.
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via lookup tables or several approximation formulas. "As the degrees of freedom approach infinity, the prediction and tolerance intervals become equal."
1350:
different areas within the facility. It was noted that the log-transformed lead levels fitted a normal distribution well (that is, the data are from a
675:
3928:
1854:
581:{\displaystyle \inf _{\theta }\{{\Pr }_{\theta }\left(F_{\theta }(U(\mathbf {X} ))-F_{\theta }(L(\mathbf {X} )\right)\geq p)\}=100(1-\alpha )}
4433:
1133:
1085:, a situation some educators have lamented, as it can lead to misuse of the other intervals where a tolerance interval is more appropriate.
1941:
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4207:
2848:
1762:
degrees of freedom. It may also be of interest to derive a 95% upper confidence bound for the median air lead level. Such a bound for
69:
of the sampled population with confidence 1âα; such a TI is usually referred to as p-content â (1âα) coverage TI." "A (p, 1âα) upper
3981:
4420:
1581:
denote the sample mean and standard deviation of the log-transformed data for a sample of size n, a 95% confidence interval for
2029:
1604:
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2420:
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1424:
2843:
2543:
982:
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802:
One-sided normal tolerance intervals have an exact solution in terms of the sample mean and sample variance based on the
205:
145:
392:
1139:
test scenario, in which several nominally identical autos of a particular model are tested to produce mileage figures
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4122:
1120:, making the tolerance interval more appropriate if a single interval is intended to bound multiple future samples.
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4282:
118:
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4127:
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2095:
is computed repeatedly from independent samples, 95% of the intervals so computed will include the true value of
4862:
4517:
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65:, 1âα) tolerance interval (TI) based on a sample is constructed so that it would include at least a proportion
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4857:
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2115:, in the long run. In other words, the interval is meant to provide information concerning the parameter
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885:
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953:
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1233:
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4035:
3999:
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811:
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3792:
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3130:
1377:
1207:
341:
265:
1535:
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4702:
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4117:
4004:
3001:
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2684:
2583:
2277:"Statistical interpretation of data â Part 6: Determination of statistical tolerance intervals"
1712:
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20:
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35:
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8:
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1401:, respectively, denote the population mean and variance for the log-transformed data. If
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112:
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2800:
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2216:
1532:; this in turn will provide a confidence interval for the median air lead level. If
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1851:. Consequently, a 95% upper confidence bound for the median air lead is given by
1092:
in that the confidence interval bounds a single-valued population parameter (the
4149:
4608:
4603:
3066:
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2642:
1101:
57:
tolerance interval provides limits within which at least a certain proportion (
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4367:
4336:
3800:
3754:
3359:
3061:
2888:
2652:
2647:
2501:
2220:
787:{\displaystyle \inf _{\theta }\{{\Pr }_{\theta }(X_{0}\in )\}=100(1-\alpha )}
4707:
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4617:
4532:
3862:
3158:
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2662:
919:
1931:{\displaystyle \exp {\left({\bar {X}}+t_{n-1,0.95}S/{\sqrt {n}}\right)}}
918:
However, if we have only a sample from the population, we know only the
111:
Definition needs to be contrasted and discussed against definition of a
3596:
3076:
2776:
2707:
2657:
2632:
2552:
2368:
81:
61:) of the population falls with a given level of confidence (1âα)." "A (
2479:
http://media.wiley.com/product_data/excerpt/68/04703802/0470380268.pdf
3749:
3601:
3221:
3016:
2928:
2913:
2908:
2873:
2463:
Statistical
Tolerance Regions: Theory, Applications, and Computation
2413:
Statistical
Tolerance Regions: Theory, Applications, and Computation
2360:
2019:{\displaystyle {\bar {X}}+t_{n-1,0.95}S{\sqrt {\left(1+1/n\right)}}}
3265:
2883:
2760:
2755:
2750:
2485:
2204:
1097:
810:. Two-sided normal tolerance intervals can be estimated using the
828:"In the parameters-known case, a 95% tolerance interval and a 95%
4770:
4471:
979:, which are only estimates of the true parameters. In that case,
912:
2442:
Statistical
Intervals: A Guide for Practitioners and Researchers
4692:
3673:
3647:
3627:
2878:
2669:
2347:
Stephen B. Vardeman (1992). "What about the Other
Intervals?".
2440:
Hahn, Gerald J.; Meeker, William Q.; Escobar, Luis A. (2017).
2521:
2486:"tolerance: An R Package for Estimating Tolerance Intervals"
2205:"tolerance: An R Package for Estimating Tolerance Intervals"
618:
This is in contrast to a prediction interval with endpoints
2612:
1093:
837:
2314:
2088:{\displaystyle {\bar {X}}\pm t_{n-1,0.975}S/{\sqrt {n}}}
1663:{\displaystyle {\bar {X}}\pm t_{n-1,0.975}S/{\sqrt {n}}}
1505:
is the median air lead level. A confidence interval for
1421:
denotes the corresponding random variable, we thus have
915:
for 95% coverage of a normally distributed population).
2517:
http://standardsproposals.bsigroup.com/home/getpdf/458
1466:{\displaystyle X\sim {\mathcal {N}}(\mu ,\sigma ^{2})}
202:
which are realization of independent random variables
2444:(2nd ed.). John Wiley & Sons, Incorporated.
2121:
2101:
2032:
1944:
1857:
1788:
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1607:
1587:
1567:
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1511:
1479:
1427:
1407:
1380:
1360:
1330:
1296:
1275:
1236:
1210:
1145:
1077:
The tolerance interval is less widely known than the
1060:
1032:
1019:{\displaystyle {\hat {\mu }}\pm 1.96{\hat {\sigma }}}
985:
956:
927:
888:
868:
845:
678:
624:
594:
449:
395:
371:
344:
317:
295:
268:
208:
148:
4434:
Autoregressive conditional heteroskedasticity (ARCH)
2178:
2176:
1844:{\displaystyle {\bar {X}}+t_{n-1,0.95}S/{\sqrt {n}}}
2346:
3896:
2127:
2107:
2087:
2018:
1930:
1843:
1774:
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942:
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874:
851:
786:
664:
607:
580:
435:
377:
357:
330:
301:
281:
255:{\displaystyle \mathbf {X} =(X_{1},\ldots ,X_{n})}
254:
195:{\displaystyle \mathbf {x} =(x_{1},\ldots ,x_{n})}
194:
2460:
2439:
2410:
2406:
2404:
2173:
436:{\displaystyle (L(\mathbf {x} ),U(\mathbf {x} )]}
4849:
694:
680:
465:
451:
3982:Multivariate adaptive regression splines (MARS)
2317:Chemometrics and Intelligent Laboratory Systems
2291:"Tolerance intervals for a normal distribution"
1525:can be constructed the usual way, based on the
2483:
2401:
2386:
2241:
2202:
817:
2537:
2477:; Chap. 1, "Preliminaries", is available at
911:includes 95% of the population (1.96 is the
760:
689:
554:
460:
107:needs attention from an expert in Statistics
2582:
2544:
2530:
2342:
2340:
2338:
2308:
3195:
1269:.) But neither a confidence interval for
1116:, whereas a tolerance interval covers it
389:Then a tolerance interval with endpoints
2382:
2380:
2378:
2248:. John Wiley & Sons. pp. 222â.
1324:The air lead levels were collected from
2335:
2235:
2198:
2196:
1107:The tolerance interval is related to a
4850:
4508:KaplanâMeier estimator (product limit)
1088:The tolerance interval differs from a
121:may be able to help recruit an expert.
4581:
4148:
3895:
3194:
2964:
2581:
2525:
2415:. John Wiley and Sons. pp. 1â6.
2389:"You might want a tolerance interval"
2375:
1197:{\displaystyle y_{1},y_{2},...,y_{n}}
4818:
4518:Accelerated failure time (AFT) model
2193:
1230:as opposed to being "95% sure" that
1132:So consider once again a proverbial
91:
4830:
4113:Analysis of variance (ANOVA, anova)
2965:
904:{\displaystyle \mu \pm 1.96\sigma }
13:
4208:CochranâMantelâHaenszel statistics
2834:Pearson product-moment correlation
2433:
1436:
14:
4884:
443:which has the defining property:
262:which have a common distribution
4829:
4817:
4805:
4792:
4791:
4582:
972:{\displaystyle {\hat {\sigma }}}
747:
730:
652:
635:
588:, without referring to a sample
533:
500:
423:
406:
210:
150:
96:
4467:Least-squares spectral analysis
2490:Journal of Statistical Software
2295:Engineering Statistics Handbook
2279:. ISO 16269-6. 2014. p. 2.
2242:Thomas P. Ryan (22 June 2007).
2209:Journal of Statistical Software
1702:{\displaystyle t_{m,1-\alpha }}
1118:with a certain confidence level
16:Type of statistical probability
3448:Mean-unbiased minimum-variance
2551:
2484:Derek S. Young (August 2010).
2329:10.1016/j.chemolab.2007.03.002
2283:
2269:
2203:Derek S. Young (August 2010).
2164:
2039:
1951:
1876:
1795:
1614:
1545:
1492:
1486:
1460:
1441:
1262:{\displaystyle y_{n+1}\geq 35}
1010:
992:
963:
950:and sample standard deviation
934:
797:
781:
769:
757:
754:
751:
743:
734:
726:
720:
704:
659:
656:
648:
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507:
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430:
427:
419:
410:
402:
396:
249:
217:
189:
157:
1:
4761:Geographic information system
3977:Simultaneous equations models
2387:Mark J. Nelson (2011-08-14).
2245:Modern Engineering Statistics
2157:
1320:Another example is given by:
1128:gives the following example:
943:{\displaystyle {\hat {\mu }}}
365:and independent of the first
87:
49:falls. "More specifically, a
3944:Coefficient of determination
3555:Uniformly most powerful test
2189:10.1080/00949655.2010.545061
7:
4513:Proportional hazards models
4457:Spectral density estimation
4439:Vector autoregression (VAR)
3873:Maximum posterior estimator
3105:Randomized controlled trial
2140:
1394:{\displaystyle \sigma ^{2}}
1223:{\displaystyle \mu \geq 35}
1123:
1112:proportion of a population
818:Relation to other intervals
358:{\displaystyle F_{\theta }}
338:from the same distribution
282:{\displaystyle F_{\theta }}
109:. The specific problem is:
73:(TL) is simply a 1âα upper
10:
4889:
4273:Multivariate distributions
2693:Average absolute deviation
2461:K. Krishnamoorthy (2009).
2411:K. Krishnamoorthy (2009).
1554:{\displaystyle {\bar {X}}}
1498:{\displaystyle \exp(\mu )}
1316:of mileages of such autos.
821:
672:has the defining property
47:proportion of a population
18:
4787:
4741:
4678:
4631:
4594:
4590:
4577:
4549:
4531:
4498:
4489:
4447:
4394:
4355:
4304:
4295:
4261:Structural equation model
4216:
4173:
4169:
4144:
4103:
4069:
4023:
3990:
3952:
3919:
3915:
3891:
3831:
3740:
3659:
3623:
3614:
3597:Score/Lagrange multiplier
3582:
3535:
3480:
3406:
3397:
3207:
3203:
3190:
3149:
3123:
3075:
3030:
3012:Sample size determination
2977:
2973:
2960:
2864:
2819:
2793:
2775:
2731:
2683:
2603:
2594:
2590:
2577:
2559:
2349:The American Statistician
1728:{\displaystyle 1-\alpha }
289:, with unknown parameter
4756:Environmental statistics
4278:Elliptical distributions
4071:Generalized linear model
4000:Simple linear regression
3770:HodgesâLehmann estimator
3227:Probability distribution
3136:Stochastic approximation
2698:Coefficient of variation
1290:interval for a fraction
812:chi-squared distribution
38:within which, with some
19:Not to be confused with
4868:Statistical forecasting
4416:Cross-correlation (XCF)
4024:Non-standard predictors
3458:LehmannâScheffĂ© theorem
3131:Adaptive clinical trial
2465:. John Wiley and Sons.
1067:{\displaystyle \gamma }
1039:{\displaystyle \gamma }
875:{\displaystyle \sigma }
302:{\displaystyle \theta }
4812:Mathematics portal
4633:Engineering statistics
4541:NelsonâAalen estimator
4118:Analysis of covariance
4005:Ordinary least squares
3929:Pearson product-moment
3333:Statistical functional
3244:Empirical distribution
3077:Controlled experiments
2806:Frequency distribution
2584:Descriptive statistics
2138:
2129:
2109:
2089:
2020:
1932:
1845:
1776:
1756:
1729:
1703:
1664:
1595:
1575:
1555:
1519:
1499:
1467:
1415:
1395:
1368:
1352:lognormal distribution
1344:
1318:
1310:
1283:
1263:
1224:
1198:
1068:
1040:
1020:
973:
944:
905:
876:
853:
788:
666:
609:
582:
437:
379:
359:
332:
303:
283:
256:
196:
119:WikiProject Statistics
4863:Statistical intervals
4728:Population statistics
4670:System identification
4404:Autocorrelation (ACF)
4332:Exponential smoothing
4246:Discriminant analysis
4241:Canonical correlation
4105:Partition of variance
3967:Regression validation
3811:(JonckheereâTerpstra)
3710:Likelihood-ratio test
3399:Frequentist inference
3311:Locationâscale family
3232:Sampling distribution
3197:Statistical inference
3164:Cross-sectional study
3151:Observational studies
3110:Randomized experiment
2939:Stem-and-leaf display
2741:Central limit theorem
2297:. NIST/Sematech. 2010
2147:Engineering tolerance
2130:
2110:
2090:
2021:
1933:
1846:
1777:
1757:
1730:
1704:
1665:
1596:
1576:
1556:
1520:
1500:
1468:
1416:
1396:
1369:
1345:
1322:
1311:
1309:{\displaystyle p=.99}
1284:
1264:
1225:
1199:
1130:
1069:
1041:
1021:
974:
945:
906:
877:
854:
822:Further information:
789:
667:
610:
608:{\displaystyle X_{0}}
583:
438:
380:
360:
333:
331:{\displaystyle X_{0}}
304:
284:
257:
197:
21:Engineering tolerance
4858:Engineering concepts
4651:Probabilistic design
4236:Principal components
4079:Exponential families
4031:Nonlinear regression
4010:General linear model
3972:Mixed effects models
3962:Errors and residuals
3939:Confounding variable
3841:Bayesian probability
3819:Van der Waerden test
3809:Ordered alternative
3574:Multiple comparisons
3453:RaoâBlackwellization
3416:Estimating equations
3372:Statistical distance
3090:Factorial experiment
2623:Arithmetic-Geometric
2128:{\displaystyle \mu }
2119:
2108:{\displaystyle \mu }
2099:
2030:
1942:
1855:
1786:
1775:{\displaystyle \mu }
1766:
1746:
1713:
1674:
1605:
1594:{\displaystyle \mu }
1585:
1565:
1536:
1518:{\displaystyle \mu }
1509:
1477:
1425:
1405:
1378:
1367:{\displaystyle \mu }
1358:
1343:{\displaystyle n=15}
1328:
1294:
1282:{\displaystyle \mu }
1273:
1234:
1208:
1143:
1058:
1030:
983:
954:
925:
886:
882:, then the interval
866:
852:{\displaystyle \mu }
843:
834:normally distributed
676:
622:
592:
447:
393:
369:
342:
315:
293:
266:
206:
146:
84:of the population."
36:statistical interval
4723:Official statistics
4646:Methods engineering
4327:Seasonal adjustment
4095:Poisson regressions
4015:Bayesian regression
3954:Regression analysis
3934:Partial correlation
3906:Regression analysis
3505:Prediction interval
3500:Likelihood interval
3490:Confidence interval
3482:Interval estimation
3443:Unbiased estimators
3261:Model specification
3141:Up-and-down designs
2829:Partial correlation
2785:Index of dispersion
2703:Interquartile range
1109:prediction interval
1090:confidence interval
1083:prediction interval
1079:confidence interval
830:prediction interval
824:Interval estimation
113:prediction interval
4743:Spatial statistics
4623:Medical statistics
4523:First hitting time
4477:Whittle likelihood
4128:Degrees of freedom
4123:Multivariate ANOVA
4056:Heteroscedasticity
3868:Bayesian estimator
3833:Bayesian inference
3682:KolmogorovâSmirnov
3567:Randomization test
3537:Testing hypotheses
3510:Tolerance interval
3421:Maximum likelihood
3316:Exponential family
3249:Density estimation
3209:Statistical theory
3169:Natural experiment
3115:Scientific control
3032:Survey methodology
2718:Standard deviation
2125:
2105:
2085:
2016:
1928:
1841:
1772:
1752:
1725:
1699:
1660:
1591:
1571:
1551:
1515:
1495:
1463:
1411:
1391:
1364:
1340:
1306:
1279:
1259:
1220:
1194:
1064:
1036:
1016:
969:
940:
901:
872:
861:standard deviation
849:
784:
688:
662:
605:
578:
459:
433:
375:
355:
328:
311:a random variable
299:
279:
252:
192:
28:tolerance interval
4845:
4844:
4783:
4782:
4779:
4778:
4718:National accounts
4688:Actuarial science
4680:Social statistics
4573:
4572:
4569:
4568:
4565:
4564:
4500:Survival function
4485:
4484:
4347:Granger causality
4188:Contingency table
4163:Survival analysis
4140:
4139:
4136:
4135:
3992:Linear regression
3887:
3886:
3883:
3882:
3858:Credible interval
3827:
3826:
3610:
3609:
3426:Method of moments
3295:Parametric family
3256:Statistical model
3186:
3185:
3182:
3181:
3100:Random assignment
3022:Statistical power
2956:
2955:
2952:
2951:
2801:Contingency table
2771:
2770:
2638:Generalized/power
2472:978-0-470-38026-0
2451:978-0-471-68717-7
2422:978-0-470-38026-0
2255:978-0-470-12843-5
2083:
2042:
2014:
1954:
1920:
1879:
1839:
1798:
1755:{\displaystyle m}
1658:
1617:
1574:{\displaystyle S}
1548:
1414:{\displaystyle X}
1013:
995:
966:
937:
679:
450:
378:{\displaystyle n}
136:
135:
4880:
4833:
4832:
4821:
4820:
4810:
4809:
4795:
4794:
4698:Crime statistics
4592:
4591:
4579:
4578:
4496:
4495:
4462:Fourier analysis
4449:Frequency domain
4429:
4376:
4342:Structural break
4302:
4301:
4251:Cluster analysis
4198:Log-linear model
4171:
4170:
4146:
4145:
4087:
4061:Homoscedasticity
3917:
3916:
3893:
3892:
3812:
3804:
3796:
3795:(KruskalâWallis)
3780:
3765:
3720:Cross validation
3705:
3687:AndersonâDarling
3634:
3621:
3620:
3592:Likelihood-ratio
3584:Parametric tests
3562:Permutation test
3545:1- & 2-tails
3436:Minimum distance
3408:Point estimation
3404:
3403:
3355:Optimal decision
3306:
3205:
3204:
3192:
3191:
3174:Quasi-experiment
3124:Adaptive designs
2975:
2974:
2962:
2961:
2839:Rank correlation
2601:
2600:
2592:
2591:
2579:
2578:
2546:
2539:
2532:
2523:
2522:
2512:
2510:
2508:
2476:
2455:
2427:
2426:
2408:
2399:
2398:
2396:
2395:
2384:
2373:
2372:
2344:
2333:
2332:
2312:
2306:
2305:
2303:
2302:
2287:
2281:
2280:
2273:
2267:
2266:
2264:
2262:
2239:
2233:
2231:
2229:
2227:
2200:
2191:
2180:
2171:
2168:
2152:Factor of safety
2134:
2132:
2131:
2126:
2114:
2112:
2111:
2106:
2094:
2092:
2091:
2086:
2084:
2079:
2077:
2069:
2068:
2044:
2043:
2035:
2025:
2023:
2022:
2017:
2015:
2013:
2009:
2005:
1986:
1981:
1980:
1956:
1955:
1947:
1937:
1935:
1934:
1929:
1927:
1926:
1922:
1921:
1916:
1914:
1906:
1905:
1881:
1880:
1872:
1850:
1848:
1847:
1842:
1840:
1835:
1833:
1825:
1824:
1800:
1799:
1791:
1781:
1779:
1778:
1773:
1761:
1759:
1758:
1753:
1734:
1732:
1731:
1726:
1708:
1706:
1705:
1700:
1698:
1697:
1669:
1667:
1666:
1661:
1659:
1654:
1652:
1644:
1643:
1619:
1618:
1610:
1600:
1598:
1597:
1592:
1580:
1578:
1577:
1572:
1560:
1558:
1557:
1552:
1550:
1549:
1541:
1524:
1522:
1521:
1516:
1504:
1502:
1501:
1496:
1472:
1470:
1469:
1464:
1459:
1458:
1440:
1439:
1420:
1418:
1417:
1412:
1400:
1398:
1397:
1392:
1390:
1389:
1373:
1371:
1370:
1365:
1349:
1347:
1346:
1341:
1315:
1313:
1312:
1307:
1288:
1286:
1285:
1280:
1268:
1266:
1265:
1260:
1252:
1251:
1229:
1227:
1226:
1221:
1203:
1201:
1200:
1195:
1193:
1192:
1168:
1167:
1155:
1154:
1073:
1071:
1070:
1065:
1052:tolerance factor
1045:
1043:
1042:
1037:
1025:
1023:
1022:
1017:
1015:
1014:
1006:
997:
996:
988:
978:
976:
975:
970:
968:
967:
959:
949:
947:
946:
941:
939:
938:
930:
910:
908:
907:
902:
881:
879:
878:
873:
858:
856:
855:
850:
793:
791:
790:
785:
750:
733:
716:
715:
703:
702:
697:
687:
671:
669:
668:
665:{\displaystyle }
663:
655:
638:
614:
612:
611:
606:
604:
603:
587:
585:
584:
579:
544:
540:
536:
522:
521:
503:
489:
488:
474:
473:
468:
458:
442:
440:
439:
434:
426:
409:
384:
382:
381:
376:
364:
362:
361:
356:
354:
353:
337:
335:
334:
329:
327:
326:
308:
306:
305:
300:
288:
286:
285:
280:
278:
277:
261:
259:
258:
253:
248:
247:
229:
228:
213:
201:
199:
198:
193:
188:
187:
169:
168:
153:
131:
128:
122:
100:
99:
92:
75:confidence limit
56:
40:confidence level
4888:
4887:
4883:
4882:
4881:
4879:
4878:
4877:
4848:
4847:
4846:
4841:
4804:
4775:
4737:
4674:
4660:quality control
4627:
4609:Clinical trials
4586:
4561:
4545:
4533:Hazard function
4527:
4481:
4443:
4427:
4390:
4386:BreuschâGodfrey
4374:
4351:
4291:
4266:Factor analysis
4212:
4193:Graphical model
4165:
4132:
4099:
4085:
4065:
4019:
3986:
3948:
3911:
3910:
3879:
3823:
3810:
3802:
3794:
3778:
3763:
3742:Rank statistics
3736:
3715:Model selection
3703:
3661:Goodness of fit
3655:
3632:
3606:
3578:
3531:
3476:
3465:Median unbiased
3393:
3304:
3237:Order statistic
3199:
3178:
3145:
3119:
3071:
3026:
2969:
2967:Data collection
2948:
2860:
2815:
2789:
2767:
2727:
2679:
2596:Continuous data
2586:
2573:
2555:
2550:
2506:
2504:
2473:
2452:
2436:
2434:Further reading
2431:
2430:
2423:
2409:
2402:
2393:
2391:
2385:
2376:
2361:10.2307/2685212
2345:
2336:
2313:
2309:
2300:
2298:
2289:
2288:
2284:
2275:
2274:
2270:
2260:
2258:
2256:
2240:
2236:
2225:
2223:
2201:
2194:
2181:
2174:
2169:
2165:
2160:
2143:
2120:
2117:
2116:
2100:
2097:
2096:
2078:
2073:
2052:
2048:
2034:
2033:
2031:
2028:
2027:
2001:
1991:
1987:
1985:
1964:
1960:
1946:
1945:
1943:
1940:
1939:
1915:
1910:
1889:
1885:
1871:
1870:
1869:
1865:
1864:
1856:
1853:
1852:
1834:
1829:
1808:
1804:
1790:
1789:
1787:
1784:
1783:
1767:
1764:
1763:
1747:
1744:
1743:
1714:
1711:
1710:
1681:
1677:
1675:
1672:
1671:
1653:
1648:
1627:
1623:
1609:
1608:
1606:
1603:
1602:
1586:
1583:
1582:
1566:
1563:
1562:
1540:
1539:
1537:
1534:
1533:
1510:
1507:
1506:
1478:
1475:
1474:
1473:. We note that
1454:
1450:
1435:
1434:
1426:
1423:
1422:
1406:
1403:
1402:
1385:
1381:
1379:
1376:
1375:
1359:
1356:
1355:
1329:
1326:
1325:
1295:
1292:
1291:
1274:
1271:
1270:
1241:
1237:
1235:
1232:
1231:
1209:
1206:
1205:
1188:
1184:
1163:
1159:
1150:
1146:
1144:
1141:
1140:
1126:
1059:
1056:
1055:
1031:
1028:
1027:
1005:
1004:
987:
986:
984:
981:
980:
958:
957:
955:
952:
951:
929:
928:
926:
923:
922:
887:
884:
883:
867:
864:
863:
844:
841:
840:
826:
820:
800:
746:
729:
711:
707:
698:
693:
692:
683:
677:
674:
673:
651:
634:
623:
620:
619:
599:
595:
593:
590:
589:
532:
517:
513:
499:
484:
480:
479:
475:
469:
464:
463:
454:
448:
445:
444:
422:
405:
394:
391:
390:
370:
367:
366:
349:
345:
343:
340:
339:
322:
318:
316:
313:
312:
294:
291:
290:
273:
269:
267:
264:
263:
243:
239:
224:
220:
209:
207:
204:
203:
183:
179:
164:
160:
149:
147:
144:
143:
132:
126:
123:
117:
101:
97:
90:
71:tolerance limit
50:
24:
17:
12:
11:
5:
4886:
4876:
4875:
4873:Approximations
4870:
4865:
4860:
4843:
4842:
4840:
4839:
4827:
4815:
4801:
4788:
4785:
4784:
4781:
4780:
4777:
4776:
4774:
4773:
4768:
4763:
4758:
4753:
4747:
4745:
4739:
4738:
4736:
4735:
4730:
4725:
4720:
4715:
4710:
4705:
4700:
4695:
4690:
4684:
4682:
4676:
4675:
4673:
4672:
4667:
4662:
4653:
4648:
4643:
4637:
4635:
4629:
4628:
4626:
4625:
4620:
4615:
4606:
4604:Bioinformatics
4600:
4598:
4588:
4587:
4575:
4574:
4571:
4570:
4567:
4566:
4563:
4562:
4560:
4559:
4553:
4551:
4547:
4546:
4544:
4543:
4537:
4535:
4529:
4528:
4526:
4525:
4520:
4515:
4510:
4504:
4502:
4493:
4487:
4486:
4483:
4482:
4480:
4479:
4474:
4469:
4464:
4459:
4453:
4451:
4445:
4444:
4442:
4441:
4436:
4431:
4423:
4418:
4413:
4412:
4411:
4409:partial (PACF)
4400:
4398:
4392:
4391:
4389:
4388:
4383:
4378:
4370:
4365:
4359:
4357:
4356:Specific tests
4353:
4352:
4350:
4349:
4344:
4339:
4334:
4329:
4324:
4319:
4314:
4308:
4306:
4299:
4293:
4292:
4290:
4289:
4288:
4287:
4286:
4285:
4270:
4269:
4268:
4258:
4256:Classification
4253:
4248:
4243:
4238:
4233:
4228:
4222:
4220:
4214:
4213:
4211:
4210:
4205:
4203:McNemar's test
4200:
4195:
4190:
4185:
4179:
4177:
4167:
4166:
4142:
4141:
4138:
4137:
4134:
4133:
4131:
4130:
4125:
4120:
4115:
4109:
4107:
4101:
4100:
4098:
4097:
4081:
4075:
4073:
4067:
4066:
4064:
4063:
4058:
4053:
4048:
4043:
4041:Semiparametric
4038:
4033:
4027:
4025:
4021:
4020:
4018:
4017:
4012:
4007:
4002:
3996:
3994:
3988:
3987:
3985:
3984:
3979:
3974:
3969:
3964:
3958:
3956:
3950:
3949:
3947:
3946:
3941:
3936:
3931:
3925:
3923:
3913:
3912:
3909:
3908:
3903:
3897:
3889:
3888:
3885:
3884:
3881:
3880:
3878:
3877:
3876:
3875:
3865:
3860:
3855:
3854:
3853:
3848:
3837:
3835:
3829:
3828:
3825:
3824:
3822:
3821:
3816:
3815:
3814:
3806:
3798:
3782:
3779:(MannâWhitney)
3774:
3773:
3772:
3759:
3758:
3757:
3746:
3744:
3738:
3737:
3735:
3734:
3733:
3732:
3727:
3722:
3712:
3707:
3704:(ShapiroâWilk)
3699:
3694:
3689:
3684:
3679:
3671:
3665:
3663:
3657:
3656:
3654:
3653:
3645:
3636:
3624:
3618:
3616:Specific tests
3612:
3611:
3608:
3607:
3605:
3604:
3599:
3594:
3588:
3586:
3580:
3579:
3577:
3576:
3571:
3570:
3569:
3559:
3558:
3557:
3547:
3541:
3539:
3533:
3532:
3530:
3529:
3528:
3527:
3522:
3512:
3507:
3502:
3497:
3492:
3486:
3484:
3478:
3477:
3475:
3474:
3469:
3468:
3467:
3462:
3461:
3460:
3455:
3440:
3439:
3438:
3433:
3428:
3423:
3412:
3410:
3401:
3395:
3394:
3392:
3391:
3386:
3381:
3380:
3379:
3369:
3364:
3363:
3362:
3352:
3351:
3350:
3345:
3340:
3330:
3325:
3320:
3319:
3318:
3313:
3308:
3292:
3291:
3290:
3285:
3280:
3270:
3269:
3268:
3263:
3253:
3252:
3251:
3241:
3240:
3239:
3229:
3224:
3219:
3213:
3211:
3201:
3200:
3188:
3187:
3184:
3183:
3180:
3179:
3177:
3176:
3171:
3166:
3161:
3155:
3153:
3147:
3146:
3144:
3143:
3138:
3133:
3127:
3125:
3121:
3120:
3118:
3117:
3112:
3107:
3102:
3097:
3092:
3087:
3081:
3079:
3073:
3072:
3070:
3069:
3067:Standard error
3064:
3059:
3054:
3053:
3052:
3047:
3036:
3034:
3028:
3027:
3025:
3024:
3019:
3014:
3009:
3004:
2999:
2997:Optimal design
2994:
2989:
2983:
2981:
2971:
2970:
2958:
2957:
2954:
2953:
2950:
2949:
2947:
2946:
2941:
2936:
2931:
2926:
2921:
2916:
2911:
2906:
2901:
2896:
2891:
2886:
2881:
2876:
2870:
2868:
2862:
2861:
2859:
2858:
2853:
2852:
2851:
2846:
2836:
2831:
2825:
2823:
2817:
2816:
2814:
2813:
2808:
2803:
2797:
2795:
2794:Summary tables
2791:
2790:
2788:
2787:
2781:
2779:
2773:
2772:
2769:
2768:
2766:
2765:
2764:
2763:
2758:
2753:
2743:
2737:
2735:
2729:
2728:
2726:
2725:
2720:
2715:
2710:
2705:
2700:
2695:
2689:
2687:
2681:
2680:
2678:
2677:
2672:
2667:
2666:
2665:
2660:
2655:
2650:
2645:
2640:
2635:
2630:
2628:Contraharmonic
2625:
2620:
2609:
2607:
2598:
2588:
2587:
2575:
2574:
2572:
2571:
2566:
2560:
2557:
2556:
2549:
2548:
2541:
2534:
2526:
2520:
2519:
2513:
2481:
2471:
2457:
2456:
2450:
2435:
2432:
2429:
2428:
2421:
2400:
2374:
2355:(3): 193â197.
2334:
2307:
2282:
2268:
2254:
2234:
2192:
2172:
2162:
2161:
2159:
2156:
2155:
2154:
2149:
2142:
2139:
2124:
2104:
2082:
2076:
2072:
2067:
2064:
2061:
2058:
2055:
2051:
2047:
2041:
2038:
2012:
2008:
2004:
2000:
1997:
1994:
1990:
1984:
1979:
1976:
1973:
1970:
1967:
1963:
1959:
1953:
1950:
1925:
1919:
1913:
1909:
1904:
1901:
1898:
1895:
1892:
1888:
1884:
1878:
1875:
1868:
1863:
1860:
1838:
1832:
1828:
1823:
1820:
1817:
1814:
1811:
1807:
1803:
1797:
1794:
1771:
1751:
1735:quantile of a
1724:
1721:
1718:
1696:
1693:
1690:
1687:
1684:
1680:
1657:
1651:
1647:
1642:
1639:
1636:
1633:
1630:
1626:
1622:
1616:
1613:
1590:
1570:
1547:
1544:
1514:
1494:
1491:
1488:
1485:
1482:
1462:
1457:
1453:
1449:
1446:
1443:
1438:
1433:
1430:
1410:
1388:
1384:
1363:
1339:
1336:
1333:
1305:
1302:
1299:
1278:
1258:
1255:
1250:
1247:
1244:
1240:
1219:
1216:
1213:
1191:
1187:
1183:
1180:
1177:
1174:
1171:
1166:
1162:
1158:
1153:
1149:
1125:
1122:
1102:sampling error
1063:
1035:
1012:
1009:
1003:
1000:
994:
991:
965:
962:
936:
933:
900:
897:
894:
891:
871:
848:
819:
816:
799:
796:
783:
780:
777:
774:
771:
768:
765:
762:
759:
756:
753:
749:
745:
742:
739:
736:
732:
728:
725:
722:
719:
714:
710:
706:
701:
696:
691:
686:
682:
661:
658:
654:
650:
647:
644:
641:
637:
633:
630:
627:
602:
598:
577:
574:
571:
568:
565:
562:
559:
556:
553:
550:
547:
543:
539:
535:
531:
528:
525:
520:
516:
512:
509:
506:
502:
498:
495:
492:
487:
483:
478:
472:
467:
462:
457:
453:
432:
429:
425:
421:
418:
415:
412:
408:
404:
401:
398:
387:
386:
374:
352:
348:
325:
321:
309:
298:
276:
272:
251:
246:
242:
238:
235:
232:
227:
223:
219:
216:
212:
191:
186:
182:
178:
175:
172:
167:
163:
159:
156:
152:
134:
133:
104:
102:
95:
89:
86:
42:, a specified
15:
9:
6:
4:
3:
2:
4885:
4874:
4871:
4869:
4866:
4864:
4861:
4859:
4856:
4855:
4853:
4838:
4837:
4828:
4826:
4825:
4816:
4814:
4813:
4808:
4802:
4800:
4799:
4790:
4789:
4786:
4772:
4769:
4767:
4766:Geostatistics
4764:
4762:
4759:
4757:
4754:
4752:
4749:
4748:
4746:
4744:
4740:
4734:
4733:Psychometrics
4731:
4729:
4726:
4724:
4721:
4719:
4716:
4714:
4711:
4709:
4706:
4704:
4701:
4699:
4696:
4694:
4691:
4689:
4686:
4685:
4683:
4681:
4677:
4671:
4668:
4666:
4663:
4661:
4657:
4654:
4652:
4649:
4647:
4644:
4642:
4639:
4638:
4636:
4634:
4630:
4624:
4621:
4619:
4616:
4614:
4610:
4607:
4605:
4602:
4601:
4599:
4597:
4596:Biostatistics
4593:
4589:
4585:
4580:
4576:
4558:
4557:Log-rank test
4555:
4554:
4552:
4548:
4542:
4539:
4538:
4536:
4534:
4530:
4524:
4521:
4519:
4516:
4514:
4511:
4509:
4506:
4505:
4503:
4501:
4497:
4494:
4492:
4488:
4478:
4475:
4473:
4470:
4468:
4465:
4463:
4460:
4458:
4455:
4454:
4452:
4450:
4446:
4440:
4437:
4435:
4432:
4430:
4428:(BoxâJenkins)
4424:
4422:
4419:
4417:
4414:
4410:
4407:
4406:
4405:
4402:
4401:
4399:
4397:
4393:
4387:
4384:
4382:
4381:DurbinâWatson
4379:
4377:
4371:
4369:
4366:
4364:
4363:DickeyâFuller
4361:
4360:
4358:
4354:
4348:
4345:
4343:
4340:
4338:
4337:Cointegration
4335:
4333:
4330:
4328:
4325:
4323:
4320:
4318:
4315:
4313:
4312:Decomposition
4310:
4309:
4307:
4303:
4300:
4298:
4294:
4284:
4281:
4280:
4279:
4276:
4275:
4274:
4271:
4267:
4264:
4263:
4262:
4259:
4257:
4254:
4252:
4249:
4247:
4244:
4242:
4239:
4237:
4234:
4232:
4229:
4227:
4224:
4223:
4221:
4219:
4215:
4209:
4206:
4204:
4201:
4199:
4196:
4194:
4191:
4189:
4186:
4184:
4183:Cohen's kappa
4181:
4180:
4178:
4176:
4172:
4168:
4164:
4160:
4156:
4152:
4147:
4143:
4129:
4126:
4124:
4121:
4119:
4116:
4114:
4111:
4110:
4108:
4106:
4102:
4096:
4092:
4088:
4082:
4080:
4077:
4076:
4074:
4072:
4068:
4062:
4059:
4057:
4054:
4052:
4049:
4047:
4044:
4042:
4039:
4037:
4036:Nonparametric
4034:
4032:
4029:
4028:
4026:
4022:
4016:
4013:
4011:
4008:
4006:
4003:
4001:
3998:
3997:
3995:
3993:
3989:
3983:
3980:
3978:
3975:
3973:
3970:
3968:
3965:
3963:
3960:
3959:
3957:
3955:
3951:
3945:
3942:
3940:
3937:
3935:
3932:
3930:
3927:
3926:
3924:
3922:
3918:
3914:
3907:
3904:
3902:
3899:
3898:
3894:
3890:
3874:
3871:
3870:
3869:
3866:
3864:
3861:
3859:
3856:
3852:
3849:
3847:
3844:
3843:
3842:
3839:
3838:
3836:
3834:
3830:
3820:
3817:
3813:
3807:
3805:
3799:
3797:
3791:
3790:
3789:
3786:
3785:Nonparametric
3783:
3781:
3775:
3771:
3768:
3767:
3766:
3760:
3756:
3755:Sample median
3753:
3752:
3751:
3748:
3747:
3745:
3743:
3739:
3731:
3728:
3726:
3723:
3721:
3718:
3717:
3716:
3713:
3711:
3708:
3706:
3700:
3698:
3695:
3693:
3690:
3688:
3685:
3683:
3680:
3678:
3676:
3672:
3670:
3667:
3666:
3664:
3662:
3658:
3652:
3650:
3646:
3644:
3642:
3637:
3635:
3630:
3626:
3625:
3622:
3619:
3617:
3613:
3603:
3600:
3598:
3595:
3593:
3590:
3589:
3587:
3585:
3581:
3575:
3572:
3568:
3565:
3564:
3563:
3560:
3556:
3553:
3552:
3551:
3548:
3546:
3543:
3542:
3540:
3538:
3534:
3526:
3523:
3521:
3518:
3517:
3516:
3513:
3511:
3508:
3506:
3503:
3501:
3498:
3496:
3493:
3491:
3488:
3487:
3485:
3483:
3479:
3473:
3470:
3466:
3463:
3459:
3456:
3454:
3451:
3450:
3449:
3446:
3445:
3444:
3441:
3437:
3434:
3432:
3429:
3427:
3424:
3422:
3419:
3418:
3417:
3414:
3413:
3411:
3409:
3405:
3402:
3400:
3396:
3390:
3387:
3385:
3382:
3378:
3375:
3374:
3373:
3370:
3368:
3365:
3361:
3360:loss function
3358:
3357:
3356:
3353:
3349:
3346:
3344:
3341:
3339:
3336:
3335:
3334:
3331:
3329:
3326:
3324:
3321:
3317:
3314:
3312:
3309:
3307:
3301:
3298:
3297:
3296:
3293:
3289:
3286:
3284:
3281:
3279:
3276:
3275:
3274:
3271:
3267:
3264:
3262:
3259:
3258:
3257:
3254:
3250:
3247:
3246:
3245:
3242:
3238:
3235:
3234:
3233:
3230:
3228:
3225:
3223:
3220:
3218:
3215:
3214:
3212:
3210:
3206:
3202:
3198:
3193:
3189:
3175:
3172:
3170:
3167:
3165:
3162:
3160:
3157:
3156:
3154:
3152:
3148:
3142:
3139:
3137:
3134:
3132:
3129:
3128:
3126:
3122:
3116:
3113:
3111:
3108:
3106:
3103:
3101:
3098:
3096:
3093:
3091:
3088:
3086:
3083:
3082:
3080:
3078:
3074:
3068:
3065:
3063:
3062:Questionnaire
3060:
3058:
3055:
3051:
3048:
3046:
3043:
3042:
3041:
3038:
3037:
3035:
3033:
3029:
3023:
3020:
3018:
3015:
3013:
3010:
3008:
3005:
3003:
3000:
2998:
2995:
2993:
2990:
2988:
2985:
2984:
2982:
2980:
2976:
2972:
2968:
2963:
2959:
2945:
2942:
2940:
2937:
2935:
2932:
2930:
2927:
2925:
2922:
2920:
2917:
2915:
2912:
2910:
2907:
2905:
2902:
2900:
2897:
2895:
2892:
2890:
2889:Control chart
2887:
2885:
2882:
2880:
2877:
2875:
2872:
2871:
2869:
2867:
2863:
2857:
2854:
2850:
2847:
2845:
2842:
2841:
2840:
2837:
2835:
2832:
2830:
2827:
2826:
2824:
2822:
2818:
2812:
2809:
2807:
2804:
2802:
2799:
2798:
2796:
2792:
2786:
2783:
2782:
2780:
2778:
2774:
2762:
2759:
2757:
2754:
2752:
2749:
2748:
2747:
2744:
2742:
2739:
2738:
2736:
2734:
2730:
2724:
2721:
2719:
2716:
2714:
2711:
2709:
2706:
2704:
2701:
2699:
2696:
2694:
2691:
2690:
2688:
2686:
2682:
2676:
2673:
2671:
2668:
2664:
2661:
2659:
2656:
2654:
2651:
2649:
2646:
2644:
2641:
2639:
2636:
2634:
2631:
2629:
2626:
2624:
2621:
2619:
2616:
2615:
2614:
2611:
2610:
2608:
2606:
2602:
2599:
2597:
2593:
2589:
2585:
2580:
2576:
2570:
2567:
2565:
2562:
2561:
2558:
2554:
2547:
2542:
2540:
2535:
2533:
2528:
2527:
2524:
2518:
2514:
2503:
2499:
2495:
2491:
2487:
2482:
2480:
2474:
2468:
2464:
2459:
2458:
2453:
2447:
2443:
2438:
2437:
2424:
2418:
2414:
2407:
2405:
2390:
2383:
2381:
2379:
2370:
2366:
2362:
2358:
2354:
2350:
2343:
2341:
2339:
2330:
2326:
2322:
2318:
2311:
2296:
2292:
2286:
2278:
2272:
2257:
2251:
2247:
2246:
2238:
2222:
2218:
2214:
2210:
2206:
2199:
2197:
2190:
2186:
2179:
2177:
2167:
2163:
2153:
2150:
2148:
2145:
2144:
2137:
2122:
2102:
2080:
2074:
2070:
2065:
2062:
2059:
2056:
2053:
2049:
2045:
2036:
2010:
2006:
2002:
1998:
1995:
1992:
1988:
1982:
1977:
1974:
1971:
1968:
1965:
1961:
1957:
1948:
1923:
1917:
1911:
1907:
1902:
1899:
1896:
1893:
1890:
1886:
1882:
1873:
1866:
1861:
1858:
1836:
1830:
1826:
1821:
1818:
1815:
1812:
1809:
1805:
1801:
1792:
1769:
1749:
1741:
1740:-distribution
1739:
1722:
1719:
1716:
1694:
1691:
1688:
1685:
1682:
1678:
1655:
1649:
1645:
1640:
1637:
1634:
1631:
1628:
1624:
1620:
1611:
1588:
1568:
1542:
1531:
1530:-distribution
1529:
1512:
1489:
1483:
1480:
1455:
1451:
1447:
1444:
1431:
1428:
1408:
1386:
1382:
1361:
1353:
1337:
1334:
1331:
1321:
1317:
1303:
1300:
1297:
1276:
1256:
1253:
1248:
1245:
1242:
1238:
1217:
1214:
1211:
1189:
1185:
1181:
1178:
1175:
1172:
1169:
1164:
1160:
1156:
1151:
1147:
1138:
1135:
1129:
1121:
1119:
1115:
1110:
1105:
1103:
1099:
1095:
1091:
1086:
1084:
1080:
1075:
1061:
1053:
1049:
1033:
1007:
1001:
998:
989:
960:
931:
921:
916:
914:
898:
895:
892:
889:
869:
862:
846:
839:
835:
831:
825:
815:
813:
809:
808:-distribution
807:
795:
778:
775:
772:
766:
763:
740:
737:
723:
717:
712:
708:
699:
684:
645:
642:
628:
616:
600:
596:
572:
569:
566:
560:
557:
548:
545:
541:
526:
518:
514:
510:
493:
485:
481:
476:
470:
455:
416:
413:
399:
372:
350:
346:
323:
319:
310:
296:
274:
270:
244:
240:
236:
233:
230:
225:
221:
214:
184:
180:
176:
173:
170:
165:
161:
154:
142:observations
141:
140:
139:
130:
120:
116:
114:
108:
105:This article
103:
94:
93:
85:
83:
80:
76:
72:
68:
64:
60:
54:
48:
45:
41:
37:
33:
29:
22:
4834:
4822:
4803:
4796:
4708:Econometrics
4658: /
4641:Chemometrics
4618:Epidemiology
4611: /
4584:Applications
4426:ARIMA model
4373:Q-statistic
4322:Stationarity
4218:Multivariate
4161: /
4157: /
4155:Multivariate
4153: /
4093: /
4089: /
3863:Bayes factor
3762:Signed rank
3674:
3648:
3640:
3628:
3509:
3323:Completeness
3159:Cohort study
3057:Opinion poll
2992:Missing data
2979:Study design
2934:Scatter plot
2856:Scatter plot
2849:Spearman's Ï
2811:Grouped data
2505:. Retrieved
2493:
2489:
2462:
2441:
2412:
2392:. Retrieved
2352:
2348:
2320:
2316:
2310:
2299:. Retrieved
2294:
2285:
2271:
2259:. Retrieved
2244:
2237:
2224:. Retrieved
2212:
2208:
2166:
1782:is given by
1737:
1709:denotes the
1601:is given by
1527:
1323:
1319:
1131:
1127:
1117:
1113:
1106:
1087:
1076:
1054:for a given
1051:
1047:
917:
827:
805:
801:
617:
388:
137:
124:
110:
106:
78:
77:for the 100
70:
66:
62:
58:
52:
31:
27:
25:
4836:WikiProject
4751:Cartography
4713:Jurimetrics
4665:Reliability
4396:Time domain
4375:(LjungâBox)
4297:Time-series
4175:Categorical
4159:Time-series
4151:Categorical
4086:(Bernoulli)
3921:Correlation
3901:Correlation
3697:JarqueâBera
3669:Chi-squared
3431:M-estimator
3384:Asymptotics
3328:Sufficiency
3095:Interaction
3007:Replication
2987:Effect size
2944:Violin plot
2924:Radar chart
2904:Forest plot
2894:Correlogram
2844:Kendall's Ï
2507:19 February
2496:(5): 1â39.
2261:22 February
2226:19 February
2215:(5): 1â39.
1050:factor" or
920:sample mean
804:noncentral
798:Calculation
55:%/100Ă(1âα)
4852:Categories
4703:Demography
4421:ARMA model
4226:Regression
3803:(Friedman)
3764:(Wilcoxon)
3702:Normality
3692:Lilliefors
3639:Student's
3515:Resampling
3389:Robustness
3377:divergence
3367:Efficiency
3305:(monotone)
3300:Likelihood
3217:Population
3050:Stratified
3002:Population
2821:Dependence
2777:Count data
2708:Percentile
2685:Dispersion
2618:Arithmetic
2553:Statistics
2394:2011-08-26
2323:(2): 147.
2301:2011-08-26
2158:References
1114:on average
385:variables.
88:Definition
82:percentile
4084:Logistic
3851:posterior
3777:Rank sum
3525:Jackknife
3520:Bootstrap
3338:Bootstrap
3273:Parameter
3222:Statistic
3017:Statistic
2929:Run chart
2914:Pie chart
2909:Histogram
2899:Fan chart
2874:Bar chart
2756:L-moments
2643:Geometric
2502:1548-7660
2221:1548-7660
2123:μ
2103:μ
2057:−
2046:±
2040:¯
1969:−
1952:¯
1894:−
1877:¯
1862:
1813:−
1796:¯
1770:μ
1723:α
1720:−
1695:α
1692:−
1632:−
1621:±
1615:¯
1589:μ
1546:¯
1513:μ
1490:μ
1484:
1452:σ
1445:μ
1432:∼
1383:σ
1362:μ
1277:μ
1254:≥
1215:≥
1212:μ
1062:γ
1034:γ
1011:^
1008:σ
999:±
993:^
990:μ
964:^
961:σ
935:^
932:μ
899:σ
893:±
890:μ
870:σ
847:μ
779:α
776:−
718:∈
700:θ
685:θ
573:α
570:−
546:≥
519:θ
511:−
486:θ
471:θ
456:θ
351:θ
297:θ
275:θ
234:…
174:…
4798:Category
4491:Survival
4368:Johansen
4091:Binomial
4046:Isotonic
3633:(normal)
3278:location
3085:Blocking
3040:Sampling
2919:QâQ plot
2884:Box plot
2866:Graphics
2761:Skewness
2751:Kurtosis
2723:Variance
2653:Heronian
2648:Harmonic
2141:See also
1670:, where
1124:Examples
1098:variance
127:May 2024
4824:Commons
4771:Kriging
4656:Process
4613:studies
4472:Wavelet
4305:General
3472:Plug-in
3266:L space
3045:Cluster
2746:Moments
2564:Outline
2369:2685212
1137:mileage
1096:or the
913:z-score
138:Given
44:sampled
34:) is a
4693:Census
4283:Normal
4231:Manova
4051:Robust
3801:2-way
3793:1-way
3631:-test
3302:
2879:Biplot
2670:Median
2663:Lehmer
2605:Center
2500:
2469:
2448:
2419:
2367:
2252:
2232:, p.23
2219:
1354:. Let
4317:Trend
3846:prior
3788:anova
3677:-test
3651:-test
3643:-test
3550:Power
3495:Pivot
3288:shape
3283:scale
2733:Shape
2713:Range
2658:Heinz
2633:Cubic
2569:Index
2365:JSTOR
2066:0.975
1742:with
1641:0.975
836:with
4550:Test
3750:Sign
3602:Wald
2675:Mode
2613:Mean
2509:2013
2498:ISSN
2467:ISBN
2446:ISBN
2417:ISBN
2263:2013
2250:ISBN
2228:2013
2217:ISSN
1978:0.95
1903:0.95
1822:0.95
1561:and
1374:and
1094:mean
1081:and
1002:1.96
896:1.96
859:and
838:mean
51:100Ă
3730:BIC
3725:AIC
2357:doi
2325:doi
2185:doi
1859:exp
1481:exp
1304:.99
1134:EPA
767:100
681:inf
561:100
452:inf
4854::
2494:36
2492:.
2488:.
2403:^
2377:^
2363:.
2353:46
2351:.
2337:^
2321:87
2319:.
2293:.
2213:36
2211:.
2207:.
2195:^
2175:^
1338:15
1257:35
1218:35
814:.
794:.
695:Pr
615:.
466:Pr
32:TI
26:A
3675:G
3649:F
3641:t
3629:Z
3348:V
3343:U
2545:e
2538:t
2531:v
2511:.
2475:.
2454:.
2425:.
2397:.
2371:.
2359::
2331:.
2327::
2304:.
2265:.
2230:.
2187::
2081:n
2075:/
2071:S
2063:,
2060:1
2054:n
2050:t
2037:X
2011:)
2007:n
2003:/
1999:1
1996:+
1993:1
1989:(
1983:S
1975:,
1972:1
1966:n
1962:t
1958:+
1949:X
1924:)
1918:n
1912:/
1908:S
1900:,
1897:1
1891:n
1887:t
1883:+
1874:X
1867:(
1837:n
1831:/
1827:S
1819:,
1816:1
1810:n
1806:t
1802:+
1793:X
1750:m
1738:t
1717:1
1689:1
1686:,
1683:m
1679:t
1656:n
1650:/
1646:S
1638:,
1635:1
1629:n
1625:t
1612:X
1569:S
1543:X
1528:t
1493:)
1487:(
1461:)
1456:2
1448:,
1442:(
1437:N
1429:X
1409:X
1387:2
1335:=
1332:n
1301:=
1298:p
1249:1
1246:+
1243:n
1239:y
1190:n
1186:y
1182:,
1179:.
1176:.
1173:.
1170:,
1165:2
1161:y
1157:,
1152:1
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1048:k
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773:1
770:(
764:=
761:}
758:)
755:]
752:)
748:X
744:(
741:u
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735:)
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727:(
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690:{
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555:}
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530:(
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237:,
231:,
226:1
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218:(
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211:X
190:)
185:n
181:x
177:,
171:,
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158:(
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151:x
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125:(
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79:p
67:p
63:p
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