1612:, in a single experiment, and is defined by the Fisherian p-value. Conversely, the epidemiological view, conducted with Neyman-Pearson hypothesis testing, is designed to minimize the Type II false acceptance errors in the long-run by providing error minimizations that work in the long-run. The difference between the two is critical because the epistemic view stresses the conditions under which we might find one value to be statistically significant; meanwhile, the epidemiological view defines the conditions under which long-run results present valid results. These are extremely different inferences, because one-time, epistemic conclusions do not inform long-run errors, and long-run errors cannot be used to certify whether one-time experiments are sensical. The assumption of one-time experiments to long-run occurrences is a misattribution, and the assumption of long run trends to individuals experiments is an example of the ecological fallacy.
1553:; in this approach, the value of the statistic is fixed but our understanding of that statistic is incomplete. For concreteness, imagine trying to measure the stock market quote versus evaluating an asset's price. The stock market fluctuates so greatly that trying to find exactly where a stock price is going to be is not useful: the stock market is better understood using the epistemic approach, where we can try to quantify its fickle movements. Conversely, the price of an asset might not change that much from day to day: it is better to locate the true value of the asset rather than find a range of prices and thus the epidemiological approach is better. The difference between these approaches is non-trivial for the purposes of inference.
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1561:. In frequentist statistics, the cutoff for understanding the frequency occurrence is derived from the family distribution used in the experiment design. For example, a binomial distribution and a negative binomial distribution can be used to analyze exactly the same data, but because their tail ends are different the frequentist analysis will realize different levels of statistical significance for the same data that assumes different probability distributions. This difference does not occur in Bayesian inference. For more, see the
283:. Ronald Fisher contributed to frequentist statistics by developing the frequentist concept of "significance testing", which is the study of the significance of a measure of a statistic when compared to the hypothesis. Neyman-Pearson extended Fisher's ideas to multiple hypotheses by conjecturing that the ratio of probabilities of hypotheses when maximizing the difference between the two hypotheses leads to a maximization of exceeding a given p-value, and also provides the basis of
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authors, the likelihood that the true value of the statistic will occur within a given range of outcomes assuming a number of repetitions of our sampling method. This allows for inference where, in the long-run, we can define that the combined results of multiple frequentist inferences to mean that a 95% confidence interval literally means the true mean lies in the confidence interval 95% of the time, but
1666:, which treats âprobabilityâ as equivalent with âcertaintyâ, and thus that the essential difference between the frequentist inference and the Bayesian inference is the same as the difference between the two interpretations of what a âprobabilityâ means. However, where appropriate, Bayesian inferences (meaning in this case an application of
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probability relates to a yet to occur set of random events and hence does not rely on the frequency interpretation of probability. This formulation has been discussed by Neyman, among others. This is especially pertinent because the significance of a frequentist test can vary under model selection, a violation of the likelihood principle.
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the range of the true mean of a statistic can be inferred. This leads to the
Fisherian reduction and the Neyman-Pearson operational criteria, discussed above. When we define the Fisherian reduction and the Neyman-Pearson operational criteria for any statistic, we are assessing, according to these
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For the epistemic approach, we formulate the problem as if we want to attribute probability to a hypothesis. This can only be done with
Bayesian statistics, where the interpretation of probability is straightforward because Bayesian statistics is conditional on the entire sample space, whereas
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Frequentism is the study of probability with the assumption that results occur with a given frequency over some period of time or with repeated sampling. As such, frequentist analysis must be formulated with consideration to the assumptions of the problem frequentism attempts to analyze. This
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should include, before undertaking the experiment, decisions about exactly what steps will be taken to reach a conclusion from the data yet to be obtained. These steps can be specified by the scientist so that there is a high probability of reaching a correct decision where, in this case, the
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Very commonly the epistemic view and the epidemiological view are regarded as interconvertible. This is demonstrably false. First, the epistemic view is centered around
Fisherian significance tests that are designed to provide inductive evidence against the null hypothesis,
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implausible, then the Neyman-Pearson reduction's evaluation of that distribution can be used to infer where looking purely at the
Fisherian reduction's distributions can give us inaccurate results. Thus, the Neyman-Pearson reduction is used to find the probability of
1421:, can be said to occur in the long run. The Neyman-Pearson operational criteria defines the likelihood of that range actually being adequate or of the range being inadequate. The Neyman-Pearson criteria defines the range of the probability distribution that, if
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results. In this view, the frequentist inference approach to drawing conclusions from data is effectively to require that the correct conclusion should be drawn with a given (high) probability, among this notional set of repetitions.
1141:
Two complementary concepts in frequentist inference are the
Fisherian reduction and the Neyman-Pearson operational criteria. Together these concepts illustrate a way of constructing frequentist intervals that define the limits for
251:, which treats âprobabilityâ in equivalent terms to âfrequencyâ and draws conclusions from sample-data by means of emphasizing the frequency or proportion of findings in the data. Frequentist inference underlies
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and interpretation, and specifically with the view that any given experiment can be considered one of an infinite sequence of possible repetitions of the same experiment, each capable of producing
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1996:
Wagenmakers, Eric-Jan; Lee, Michael; Lodewyckx, Tom; Iverson, Geoffrey J. (2008), Hoijtink, Herbert; Klugkist, Irene; Boelen, Paul A. (eds.), "Bayesian Versus
Frequentist Inference",
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The primary formulation of frequentism stems from the presumption that statistics could be perceived to have been a probabilistic frequency. This view was primarily developed by
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However, exactly the same procedures can be developed under a subtly different formulation. This is one where a pre-experiment point of view is taken. It can be argued that the
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There are two major differences in the frequentist and
Bayesian approaches to inference that are not included in the above consideration of the interpretation of probability:
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exists in this range, is still below the true population statistic. For example, if the distribution from the
Fisherian reduction exceeds a threshold that we consider to be
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For the epidemiological approach, the central idea behind frequentist statistics must be discussed. Frequentist statistics is designed so that, in the
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for what is known about the parameters given the results of the experiment or study. The result of a frequentist approach is either a decision from a
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requires looking into whether the question at hand is concerned with understanding variety of a statistic or locating the true value of a statistic.
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frequentist testing is concerned with the whole experimental design. Frequentist statistics is conditioned not on solely the data but also on the
1689:. In contrast, a Bayesian approach allows probabilities to be associated with unknown parameters, where these probabilities can sometimes have a
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Essentially, the
Fisherian reduction is design to find where the sufficient statistic can be used to determine the range of outcomes where
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The Neyman-Pearon operational criteria is an even more specific understanding of the range of outcomes where the relevant statistic,
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that can be used to provide an interval to estimate uncertainty. The pivot is a probability such that for a pivot,
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is likely to occur, the Neyman-Pearson approach is only possible where a
Fisherian reduction can be achieved.
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that the mean is in a particular confidence interval with 95% certainty. This is a popular misconception.
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1162:. The Fisherian reduction is a method of determining the interval within which the true value of
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1895:"Confusion over measures of evidence (p's) versus errors (α's) in classical statistical testing"
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1971:"Outline of a Theory of Statistical Estimation Based on the Classical Theory of Probability"
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2000:, Statistics for Social and Behavioral Sciences, New York, NY: Springer, pp. 181â207,
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Bayesian probability - Personal probabilities and objective methods for constructing priors
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Frequentist inferences stand in contrast to other types of statistical inferences, such as
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The difference between these assumptions is critical for interpreting a hypothesis test
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may lie, while the Neyman-Pearson operational criteria is a decision rule about making
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For statistical inference, the statistic about which we want to make inferences is
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may occur on a probability distribution that defines all the potential values of
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2005:
1457:. As a point of reference, the complement to this in Bayesian statistics is the
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Thus, statistical inference is concerned with the expectation of random vector
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Determine the likelihood function (this is usually just gathering the data);
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Bayesian inference § In frequentist statistics and decision theory
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1988:
1970:
1843:(Spring 2017 ed.), Metaphysics Research Lab, Stanford University
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1644:" is sometimes held to include the approach to inferences leading to
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informally or formally as to assess the adequacy of the formulation.
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are typically considered as being fixed, rather than as being
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To construct areas of uncertainty in frequentist inference, a
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1572:, the frequency of a statistic may be understood, and in the
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2113:
1976:
Philosophical Transactions of the Royal Society of London A
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Frequentist inferences are associated with the application
1137:
Fisherian reduction and Neyman-Pearson operational criteria
1529:
There are broadly two camps of statistical inference, the
649:{\displaystyle E(Y)=E(Y;\theta )=\int yf_{Y}(y;\theta )dy}
1040:
is a range of outcomes that define a one-sided limit for
1648:, a more restricted view is taken here for simplicity.
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is a random vector. This allows that, for some 0 <
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1109:, when we want to estimate a range of outcomes where
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Autoregressive conditional heteroskedasticity (ARCH)
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Statistical inference § Paradigms for inference
1565:, which frequentist statistics inherently violates.
266:
1308:Use the conditional distribution of the data given
60:. Unsourced material may be challenged and removed.
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255:, in which the well-established methodologies of
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1792:
1681:In a frequentist approach to inference, unknown
3483:Multivariate adaptive regression splines (MARS)
1189:The Fisherian reduction is defined as follows:
523:the standard deviation of the population mean,
1892:
2038:
1998:Bayesian Evaluation of Informative Hypotheses
861:{\displaystyle P\{p(T,\psi )\leq p_{c}^{*}\}}
221:
905:
878:
855:
816:
1704:The result of a Bayesian approach can be a
2083:
2045:
2031:
1305:at an arbitrary set of probability levels;
1262:that has a distribution depending only on
228:
214:
142:
2696:
1526:. The next paragraph elaborates on this.
1517:The statistical philosophy of frequentism
923:{\displaystyle P\{\psi \leq q(T,c)\}=1-c}
120:Learn how and when to remove this message
1942:
1841:The Stanford Encyclopedia of Philosophy
1834:
1810:
1129:may occur. This rigorously defines the
349:is a function of an unknown parameter,
14:
4351:
4009:KaplanâMeier estimator (product limit)
1945:The Cambridge Dictionary of Statistics
665:is used which defines the area around
4082:
3649:
3396:
2695:
2465:
2082:
2026:
1965:
1874:
1822:
1651:
4319:
4019:Accelerated failure time (AFT) model
1398:is likely to occur in the long-run.
58:adding citations to reliable sources
29:
4331:
3614:Analysis of variance (ANOVA, anova)
2466:
1926:Principles of Statistical Inference
1923:
1893:Hubbard, R.; Bayarri, M.J. (2003).
1798:
1762:
1750:
1488:Experimental design and methodology
24:
3709:CochranâMantelâHaenszel statistics
2335:Pearson product-moment correlation
1616:Relationship with other approaches
25:
4370:
267:History of frequentist statistics
4330:
4318:
4306:
4293:
4292:
4083:
195:
34:
3968:Least-squares spectral analysis
1916:
1886:
1662:Bayesian inference is based in
1549:is concerned with the study of
45:needs additional citations for
2949:Mean-unbiased minimum-variance
2052:
1868:
1828:
1768:
1670:) are used by those employing
952:
940:
902:
890:
834:
822:
727:
715:
637:
625:
603:
591:
582:
576:
483:might be the population mean,
408:{\displaystyle \psi ,\lambda }
257:statistical hypothesis testing
13:
1:
4262:Geographic information system
3478:Simultaneous equations models
1839:, in Zalta, Edward N. (ed.),
1737:
503:, and the nuisance parameter
389:is further partitioned into (
298:
3445:Coefficient of determination
3056:Uniformly most powerful test
1835:Romeijn, Jan-Willem (2017),
1693:interpretation as well as a
1459:minimum Bayes risk criterion
705:, which is a function, that
7:
4014:Proportional hazards models
3958:Spectral density estimation
3940:Vector autoregression (VAR)
3374:Maximum posterior estimator
2606:Randomized controlled trial
2006:10.1007/978-0-387-09612-4_9
1720:
1628:Probability interpretations
10:
4375:
3774:Multivariate distributions
2194:Average absolute deviation
1949:Cambridge University Press
1877:"The Likelihood Principle"
1837:"Philosophy of Statistics"
1655:
1625:
1619:
740:is strictly increasing in
733:{\displaystyle p(t,\psi )}
329:, where the random vector
291:errors. For more, see the
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4242:
4179:
4132:
4095:
4091:
4078:
4050:
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3990:
3948:
3895:
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3762:Structural equation model
3717:
3674:
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3645:
3604:
3570:
3524:
3491:
3453:
3420:
3416:
3392:
3332:
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3160:
3124:
3115:
3098:Score/Lagrange multiplier
3083:
3036:
2981:
2907:
2898:
2708:
2704:
2691:
2650:
2624:
2576:
2531:
2513:Sample size determination
2478:
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2461:
2365:
2320:
2294:
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2232:
2184:
2104:
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1924:Cox, D. R. (2006-08-01).
1902:The American Statistician
1863:Wagenmakers et al. (2008)
1502:statistically independent
1219:of the same dimension as
1186:probability assumptions.
1089:is a two-sided limit for
293:foundations of statistics
4257:Environmental statistics
3779:Elliptical distributions
3572:Generalized linear model
3501:Simple linear regression
3271:HodgesâLehmann estimator
2728:Probability distribution
2637:Stochastic approximation
2199:Coefficient of variation
1825:, pp. 236, 333â380.
1706:probability distribution
1547:epidemiological approach
1535:epidemiological approach
516:{\displaystyle \lambda }
452:{\displaystyle \lambda }
3917:Cross-correlation (XCF)
3525:Non-standard predictors
2959:LehmannâScheffĂ© theorem
2632:Adaptive clinical trial
1510:design of an experiment
1494:frequentist probability
1232:{\displaystyle \theta }
536:{\displaystyle \sigma }
382:{\displaystyle \theta }
362:{\displaystyle \theta }
249:frequentist probability
69:"Frequentist inference"
4313:Mathematics portal
4134:Engineering statistics
4042:NelsonâAalen estimator
3619:Analysis of covariance
3506:Ordinary least squares
3430:Pearson product-moment
2834:Statistical functional
2745:Empirical distribution
2578:Controlled experiments
2307:Frequency distribution
2085:Descriptive statistics
1943:Everitt, B.S. (2002).
1606:
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958:{\displaystyle q(t,c)}
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806:< 1, we can define
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779:{\displaystyle t\in T}
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322:{\displaystyle y\in Y}
253:frequentist statistics
202:Mathematics portal
4359:Statistical inference
4229:Population statistics
4171:System identification
3905:Autocorrelation (ACF)
3833:Exponential smoothing
3747:Discriminant analysis
3742:Canonical correlation
3606:Partition of variance
3468:Regression validation
3312:(JonckheereâTerpstra)
3211:Likelihood-ratio test
2900:Frequentist inference
2812:Locationâscale family
2733:Sampling distribution
2698:Statistical inference
2665:Cross-sectional study
2652:Observational studies
2611:Randomized experiment
2440:Stem-and-leaf display
2242:Central limit theorem
1983:(767): 236, 333â380.
1691:frequency probability
1672:frequency probability
1626:Further information:
1607:
1605:{\displaystyle H_{0}}
1479:
1477:{\displaystyle \psi }
1436:
1434:{\displaystyle \psi }
1416:
1414:{\displaystyle \psi }
1393:
1391:{\displaystyle \psi }
1373:
1371:{\displaystyle \psi }
1353:
1351:{\displaystyle \psi }
1329:
1300:
1298:{\displaystyle \psi }
1277:
1275:{\displaystyle \psi }
1257:
1242:Find the function of
1234:
1214:
1177:
1175:{\displaystyle \psi }
1157:
1155:{\displaystyle \psi }
1124:
1122:{\displaystyle \psi }
1104:
1102:{\displaystyle \psi }
1084:
1055:
1053:{\displaystyle \psi }
1035:
1009:
1007:{\displaystyle \psi }
986:
960:
925:
863:
801:
781:
755:
753:{\displaystyle \psi }
735:
700:
680:
678:{\displaystyle \psi }
651:
561:
538:
518:
498:
478:
476:{\displaystyle \psi }
454:
437:parameter of interest
430:
428:{\displaystyle \psi }
410:
384:
364:
344:
324:
245:statistical inference
241:Frequentist inference
4152:Probabilistic design
3737:Principal components
3580:Exponential families
3532:Nonlinear regression
3511:General linear model
3473:Mixed effects models
3463:Errors and residuals
3440:Confounding variable
3342:Bayesian probability
3320:Van der Waerden test
3310:Ordered alternative
3075:Multiple comparisons
2954:RaoâBlackwellization
2917:Estimating equations
2873:Statistical distance
2591:Factorial experiment
2124:Arithmetic-Geometric
1727:Intuitive statistics
1664:Bayesian probability
1589:
1563:likelihood principle
1468:
1425:
1405:
1382:
1362:
1342:
1312:
1289:
1266:
1246:
1223:
1203:
1198:sufficient statistic
1166:
1146:
1113:
1093:
1082:{\displaystyle 1-2c}
1064:
1044:
1018:
998:
969:
934:
872:
810:
790:
764:
744:
709:
689:
669:
570:
550:
527:
507:
496:{\displaystyle \mu }
487:
467:
463:. For concreteness,
443:
419:
393:
373:
353:
333:
307:
261:confidence intervals
54:improve this article
4224:Official statistics
4147:Methods engineering
3828:Seasonal adjustment
3596:Poisson regressions
3516:Bayesian regression
3455:Regression analysis
3435:Partial correlation
3407:Regression analysis
3006:Prediction interval
3001:Likelihood interval
2991:Confidence interval
2983:Interval estimation
2944:Unbiased estimators
2762:Model specification
2642:Up-and-down designs
2330:Partial correlation
2286:Index of dispersion
2204:Interquartile range
1732:German tank problem
1714:confidence interval
1638:fiducial inferences
1634:Bayesian inferences
1559:experimental design
1498:experimental design
1327:{\displaystyle S=s}
1131:confidence interval
1033:{\displaystyle 1-c}
984:{\displaystyle 1-c}
854:
4244:Spatial statistics
4124:Medical statistics
4024:First hitting time
3978:Whittle likelihood
3629:Degrees of freedom
3624:Multivariate ANOVA
3557:Heteroscedasticity
3369:Bayesian estimator
3334:Bayesian inference
3183:KolmogorovâSmirnov
3068:Randomization test
3038:Testing hypotheses
3011:Tolerance interval
2922:Maximum likelihood
2817:Exponential family
2750:Density estimation
2710:Statistical theory
2670:Natural experiment
2616:Scientific control
2533:Survey methodology
2219:Standard deviation
1875:Vidakovic, Brani.
1765:, pp. 24, 47.
1652:Bayesian inference
1642:Bayesian inference
1602:
1539:epistemic approach
1531:epistemic approach
1474:
1431:
1411:
1388:
1368:
1348:
1324:
1295:
1272:
1252:
1229:
1209:
1172:
1152:
1119:
1099:
1079:
1050:
1030:
1004:
981:
955:
920:
858:
840:
796:
776:
750:
730:
695:
675:
646:
556:
533:
513:
493:
473:
461:nuisance parameter
449:
425:
405:
379:
359:
339:
319:
27:Probability Theory
4346:
4345:
4284:
4283:
4280:
4279:
4219:National accounts
4189:Actuarial science
4181:Social statistics
4074:
4073:
4070:
4069:
4066:
4065:
4001:Survival function
3986:
3985:
3848:Granger causality
3689:Contingency table
3664:Survival analysis
3641:
3640:
3637:
3636:
3493:Linear regression
3388:
3387:
3384:
3383:
3359:Credible interval
3328:
3327:
3111:
3110:
2927:Method of moments
2796:Parametric family
2757:Statistical model
2687:
2686:
2683:
2682:
2601:Random assignment
2523:Statistical power
2457:
2456:
2453:
2452:
2302:Contingency table
2272:
2271:
2139:Generalized/power
2015:978-0-387-09612-4
1710:significance test
1646:optimal decisions
1255:{\displaystyle S}
1212:{\displaystyle S}
799:{\displaystyle c}
698:{\displaystyle p}
559:{\displaystyle Y}
342:{\displaystyle Y}
238:
237:
130:
129:
122:
104:
16:(Redirected from
4366:
4334:
4333:
4322:
4321:
4311:
4310:
4296:
4295:
4199:Crime statistics
4093:
4092:
4080:
4079:
3997:
3996:
3963:Fourier analysis
3950:Frequency domain
3930:
3877:
3843:Structural break
3803:
3802:
3752:Cluster analysis
3699:Log-linear model
3672:
3671:
3647:
3646:
3588:
3562:Homoscedasticity
3418:
3417:
3394:
3393:
3313:
3305:
3297:
3296:(KruskalâWallis)
3281:
3266:
3221:Cross validation
3206:
3188:AndersonâDarling
3135:
3122:
3121:
3093:Likelihood-ratio
3085:Parametric tests
3063:Permutation test
3046:1- & 2-tails
2937:Minimum distance
2909:Point estimation
2905:
2904:
2856:Optimal decision
2807:
2706:
2705:
2693:
2692:
2675:Quasi-experiment
2625:Adaptive designs
2476:
2475:
2463:
2462:
2340:Rank correlation
2102:
2101:
2093:
2092:
2080:
2079:
2047:
2040:
2033:
2024:
2023:
2018:
1992:
1962:
1939:
1910:
1909:
1899:
1890:
1884:
1883:
1881:
1872:
1866:
1860:
1851:
1850:
1849:
1848:
1832:
1826:
1820:
1814:
1808:
1802:
1796:
1790:
1789:
1787:
1786:
1772:
1766:
1760:
1754:
1748:
1611:
1609:
1608:
1603:
1601:
1600:
1541:is the study of
1483:
1481:
1480:
1475:
1440:
1438:
1437:
1432:
1420:
1418:
1417:
1412:
1397:
1395:
1394:
1389:
1377:
1375:
1374:
1369:
1357:
1355:
1354:
1349:
1333:
1331:
1330:
1325:
1304:
1302:
1301:
1296:
1281:
1279:
1278:
1273:
1261:
1259:
1258:
1253:
1238:
1236:
1235:
1230:
1218:
1216:
1215:
1210:
1181:
1179:
1178:
1173:
1161:
1159:
1158:
1153:
1128:
1126:
1125:
1120:
1108:
1106:
1105:
1100:
1088:
1086:
1085:
1080:
1059:
1057:
1056:
1051:
1039:
1037:
1036:
1031:
1013:
1011:
1010:
1005:
990:
988:
987:
982:
964:
962:
961:
956:
929:
927:
926:
921:
867:
865:
864:
859:
853:
848:
805:
803:
802:
797:
785:
783:
782:
777:
759:
757:
756:
751:
739:
737:
736:
731:
704:
702:
701:
696:
684:
682:
681:
676:
655:
653:
652:
647:
624:
623:
565:
563:
562:
557:
542:
540:
539:
534:
522:
520:
519:
514:
502:
500:
499:
494:
482:
480:
479:
474:
458:
456:
455:
450:
434:
432:
431:
426:
414:
412:
411:
406:
388:
386:
385:
380:
369:. The parameter
368:
366:
365:
360:
348:
346:
345:
340:
328:
326:
325:
320:
275:and the team of
230:
223:
216:
200:
199:
146:
132:
131:
125:
118:
114:
111:
105:
103:
62:
38:
30:
21:
4374:
4373:
4369:
4368:
4367:
4365:
4364:
4363:
4349:
4348:
4347:
4342:
4305:
4276:
4238:
4175:
4161:quality control
4128:
4110:Clinical trials
4087:
4062:
4046:
4034:Hazard function
4028:
3982:
3944:
3928:
3891:
3887:BreuschâGodfrey
3875:
3852:
3792:
3767:Factor analysis
3713:
3694:Graphical model
3666:
3633:
3600:
3586:
3566:
3520:
3487:
3449:
3412:
3411:
3380:
3324:
3311:
3303:
3295:
3279:
3264:
3243:Rank statistics
3237:
3216:Model selection
3204:
3162:Goodness of fit
3156:
3133:
3107:
3079:
3032:
2977:
2966:Median unbiased
2894:
2805:
2738:Order statistic
2700:
2679:
2646:
2620:
2572:
2527:
2470:
2468:Data collection
2449:
2361:
2316:
2290:
2268:
2228:
2180:
2097:Continuous data
2087:
2074:
2056:
2051:
2021:
2016:
1959:
1936:
1919:
1914:
1913:
1897:
1891:
1887:
1879:
1873:
1869:
1861:
1854:
1846:
1844:
1833:
1829:
1821:
1817:
1809:
1805:
1797:
1793:
1784:
1782:
1774:
1773:
1769:
1761:
1757:
1753:, pp. 1â2.
1749:
1745:
1740:
1723:
1687:random variates
1660:
1654:
1630:
1624:
1618:
1596:
1592:
1590:
1587:
1586:
1519:
1490:
1469:
1466:
1465:
1426:
1423:
1422:
1406:
1403:
1402:
1383:
1380:
1379:
1363:
1360:
1359:
1343:
1340:
1339:
1313:
1310:
1309:
1290:
1287:
1286:
1267:
1264:
1263:
1247:
1244:
1243:
1224:
1221:
1220:
1204:
1201:
1200:
1167:
1164:
1163:
1147:
1144:
1143:
1139:
1114:
1111:
1110:
1094:
1091:
1090:
1065:
1062:
1061:
1045:
1042:
1041:
1019:
1016:
1015:
999:
996:
995:
970:
967:
966:
935:
932:
931:
873:
870:
869:
849:
844:
811:
808:
807:
791:
788:
787:
765:
762:
761:
745:
742:
741:
710:
707:
706:
690:
687:
686:
670:
667:
666:
619:
615:
571:
568:
567:
551:
548:
547:
528:
525:
524:
508:
505:
504:
488:
485:
484:
468:
465:
464:
444:
441:
440:
420:
417:
416:
394:
391:
390:
374:
371:
370:
354:
351:
350:
334:
331:
330:
308:
305:
304:
301:
269:
234:
194:
193:
179:Lists of topics
126:
115:
109:
106:
63:
61:
51:
39:
28:
23:
22:
15:
12:
11:
5:
4372:
4362:
4361:
4344:
4343:
4341:
4340:
4328:
4316:
4302:
4289:
4286:
4285:
4282:
4281:
4278:
4277:
4275:
4274:
4269:
4264:
4259:
4254:
4248:
4246:
4240:
4239:
4237:
4236:
4231:
4226:
4221:
4216:
4211:
4206:
4201:
4196:
4191:
4185:
4183:
4177:
4176:
4174:
4173:
4168:
4163:
4154:
4149:
4144:
4138:
4136:
4130:
4129:
4127:
4126:
4121:
4116:
4107:
4105:Bioinformatics
4101:
4099:
4089:
4088:
4076:
4075:
4072:
4071:
4068:
4067:
4064:
4063:
4061:
4060:
4054:
4052:
4048:
4047:
4045:
4044:
4038:
4036:
4030:
4029:
4027:
4026:
4021:
4016:
4011:
4005:
4003:
3994:
3988:
3987:
3984:
3983:
3981:
3980:
3975:
3970:
3965:
3960:
3954:
3952:
3946:
3945:
3943:
3942:
3937:
3932:
3924:
3919:
3914:
3913:
3912:
3910:partial (PACF)
3901:
3899:
3893:
3892:
3890:
3889:
3884:
3879:
3871:
3866:
3860:
3858:
3857:Specific tests
3854:
3853:
3851:
3850:
3845:
3840:
3835:
3830:
3825:
3820:
3815:
3809:
3807:
3800:
3794:
3793:
3791:
3790:
3789:
3788:
3787:
3786:
3771:
3770:
3769:
3759:
3757:Classification
3754:
3749:
3744:
3739:
3734:
3729:
3723:
3721:
3715:
3714:
3712:
3711:
3706:
3704:McNemar's test
3701:
3696:
3691:
3686:
3680:
3678:
3668:
3667:
3643:
3642:
3639:
3638:
3635:
3634:
3632:
3631:
3626:
3621:
3616:
3610:
3608:
3602:
3601:
3599:
3598:
3582:
3576:
3574:
3568:
3567:
3565:
3564:
3559:
3554:
3549:
3544:
3542:Semiparametric
3539:
3534:
3528:
3526:
3522:
3521:
3519:
3518:
3513:
3508:
3503:
3497:
3495:
3489:
3488:
3486:
3485:
3480:
3475:
3470:
3465:
3459:
3457:
3451:
3450:
3448:
3447:
3442:
3437:
3432:
3426:
3424:
3414:
3413:
3410:
3409:
3404:
3398:
3390:
3389:
3386:
3385:
3382:
3381:
3379:
3378:
3377:
3376:
3366:
3361:
3356:
3355:
3354:
3349:
3338:
3336:
3330:
3329:
3326:
3325:
3323:
3322:
3317:
3316:
3315:
3307:
3299:
3283:
3280:(MannâWhitney)
3275:
3274:
3273:
3260:
3259:
3258:
3247:
3245:
3239:
3238:
3236:
3235:
3234:
3233:
3228:
3223:
3213:
3208:
3205:(ShapiroâWilk)
3200:
3195:
3190:
3185:
3180:
3172:
3166:
3164:
3158:
3157:
3155:
3154:
3146:
3137:
3125:
3119:
3117:Specific tests
3113:
3112:
3109:
3108:
3106:
3105:
3100:
3095:
3089:
3087:
3081:
3080:
3078:
3077:
3072:
3071:
3070:
3060:
3059:
3058:
3048:
3042:
3040:
3034:
3033:
3031:
3030:
3029:
3028:
3023:
3013:
3008:
3003:
2998:
2993:
2987:
2985:
2979:
2978:
2976:
2975:
2970:
2969:
2968:
2963:
2962:
2961:
2956:
2941:
2940:
2939:
2934:
2929:
2924:
2913:
2911:
2902:
2896:
2895:
2893:
2892:
2887:
2882:
2881:
2880:
2870:
2865:
2864:
2863:
2853:
2852:
2851:
2846:
2841:
2831:
2826:
2821:
2820:
2819:
2814:
2809:
2793:
2792:
2791:
2786:
2781:
2771:
2770:
2769:
2764:
2754:
2753:
2752:
2742:
2741:
2740:
2730:
2725:
2720:
2714:
2712:
2702:
2701:
2689:
2688:
2685:
2684:
2681:
2680:
2678:
2677:
2672:
2667:
2662:
2656:
2654:
2648:
2647:
2645:
2644:
2639:
2634:
2628:
2626:
2622:
2621:
2619:
2618:
2613:
2608:
2603:
2598:
2593:
2588:
2582:
2580:
2574:
2573:
2571:
2570:
2568:Standard error
2565:
2560:
2555:
2554:
2553:
2548:
2537:
2535:
2529:
2528:
2526:
2525:
2520:
2515:
2510:
2505:
2500:
2498:Optimal design
2495:
2490:
2484:
2482:
2472:
2471:
2459:
2458:
2455:
2454:
2451:
2450:
2448:
2447:
2442:
2437:
2432:
2427:
2422:
2417:
2412:
2407:
2402:
2397:
2392:
2387:
2382:
2377:
2371:
2369:
2363:
2362:
2360:
2359:
2354:
2353:
2352:
2347:
2337:
2332:
2326:
2324:
2318:
2317:
2315:
2314:
2309:
2304:
2298:
2296:
2295:Summary tables
2292:
2291:
2289:
2288:
2282:
2280:
2274:
2273:
2270:
2269:
2267:
2266:
2265:
2264:
2259:
2254:
2244:
2238:
2236:
2230:
2229:
2227:
2226:
2221:
2216:
2211:
2206:
2201:
2196:
2190:
2188:
2182:
2181:
2179:
2178:
2173:
2168:
2167:
2166:
2161:
2156:
2151:
2146:
2141:
2136:
2131:
2129:Contraharmonic
2126:
2121:
2110:
2108:
2099:
2089:
2088:
2076:
2075:
2073:
2072:
2067:
2061:
2058:
2057:
2050:
2049:
2042:
2035:
2027:
2020:
2019:
2014:
1993:
1963:
1957:
1940:
1934:
1920:
1918:
1915:
1912:
1911:
1885:
1867:
1852:
1827:
1815:
1811:Everitt (2002)
1803:
1791:
1776:"OpenStax CNX"
1767:
1755:
1742:
1741:
1739:
1736:
1735:
1734:
1729:
1722:
1719:
1718:
1717:
1702:
1668:Bayes' theorem
1656:Main article:
1653:
1650:
1620:Main article:
1617:
1614:
1599:
1595:
1518:
1515:
1489:
1486:
1473:
1430:
1410:
1387:
1367:
1347:
1336:
1335:
1323:
1320:
1317:
1306:
1294:
1283:
1271:
1251:
1240:
1228:
1208:
1194:
1171:
1151:
1138:
1135:
1118:
1098:
1078:
1075:
1072:
1069:
1049:
1029:
1026:
1023:
1003:
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4314:
4309:
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4301:
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4291:
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4287:
4273:
4270:
4268:
4267:Geostatistics
4265:
4263:
4260:
4258:
4255:
4253:
4250:
4249:
4247:
4245:
4241:
4235:
4234:Psychometrics
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4120:
4117:
4115:
4111:
4108:
4106:
4103:
4102:
4100:
4098:
4097:Biostatistics
4094:
4090:
4086:
4081:
4077:
4059:
4058:Log-rank test
4056:
4055:
4053:
4049:
4043:
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3959:
3956:
3955:
3953:
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3947:
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3929:(BoxâJenkins)
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3911:
3908:
3907:
3906:
3903:
3902:
3900:
3898:
3894:
3888:
3885:
3883:
3882:DurbinâWatson
3880:
3878:
3872:
3870:
3867:
3865:
3864:DickeyâFuller
3862:
3861:
3859:
3855:
3849:
3846:
3844:
3841:
3839:
3838:Cointegration
3836:
3834:
3831:
3829:
3826:
3824:
3821:
3819:
3816:
3814:
3813:Decomposition
3811:
3810:
3808:
3804:
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3799:
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3710:
3707:
3705:
3702:
3700:
3697:
3695:
3692:
3690:
3687:
3685:
3684:Cohen's kappa
3682:
3681:
3679:
3677:
3673:
3669:
3665:
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3563:
3560:
3558:
3555:
3553:
3550:
3548:
3545:
3543:
3540:
3538:
3537:Nonparametric
3535:
3533:
3530:
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3523:
3517:
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3408:
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3335:
3331:
3321:
3318:
3314:
3308:
3306:
3300:
3298:
3292:
3291:
3290:
3287:
3286:Nonparametric
3284:
3282:
3276:
3272:
3269:
3268:
3267:
3261:
3257:
3256:Sample median
3254:
3253:
3252:
3249:
3248:
3246:
3244:
3240:
3232:
3229:
3227:
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2874:
2871:
2869:
2866:
2862:
2861:loss function
2859:
2858:
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2847:
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2569:
2566:
2564:
2563:Questionnaire
2561:
2559:
2556:
2552:
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2547:
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2398:
2396:
2393:
2391:
2390:Control chart
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2368:
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2202:
2200:
2197:
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2189:
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2172:
2169:
2165:
2162:
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2111:
2109:
2107:
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2100:
2098:
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2090:
2086:
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2077:
2071:
2068:
2066:
2063:
2062:
2059:
2055:
2048:
2043:
2041:
2036:
2034:
2029:
2028:
2025:
2017:
2011:
2007:
2003:
1999:
1994:
1990:
1986:
1982:
1978:
1977:
1972:
1968:
1967:Jerzy, Neyman
1964:
1960:
1958:0-521-81099-X
1954:
1950:
1946:
1941:
1937:
1931:
1927:
1922:
1921:
1907:
1903:
1896:
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1871:
1864:
1859:
1857:
1842:
1838:
1831:
1824:
1819:
1812:
1807:
1801:, p. 24.
1800:
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1730:
1728:
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1724:
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1711:
1707:
1703:
1700:
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1684:
1680:
1679:
1678:
1675:
1673:
1669:
1665:
1659:
1649:
1647:
1643:
1640:. While the "
1639:
1635:
1629:
1623:
1613:
1597:
1593:
1582:
1580:
1575:
1571:
1566:
1564:
1560:
1554:
1552:
1548:
1544:
1540:
1536:
1532:
1527:
1525:
1514:
1511:
1506:
1503:
1499:
1495:
1485:
1471:
1462:
1460:
1456:
1454:
1450:
1444:
1428:
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1385:
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1321:
1318:
1315:
1307:
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1269:
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1241:
1226:
1206:
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1192:
1191:
1190:
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1185:
1169:
1149:
1134:
1132:
1116:
1096:
1076:
1073:
1070:
1067:
1047:
1027:
1024:
1021:
1001:
993:
978:
975:
972:
949:
946:
943:
937:
917:
914:
911:
908:
899:
896:
893:
887:
884:
881:
875:
850:
845:
841:
837:
831:
828:
825:
819:
813:
793:
773:
770:
767:
747:
724:
721:
718:
712:
692:
672:
664:
663:
657:
643:
640:
634:
631:
628:
620:
616:
612:
609:
606:
600:
597:
594:
588:
585:
579:
573:
553:
544:
530:
510:
490:
470:
462:
446:
438:
422:
402:
399:
396:
376:
356:
336:
316:
313:
310:
296:
294:
290:
286:
282:
278:
274:
273:Ronald Fisher
264:
263:are founded.
262:
258:
254:
250:
246:
243:is a type of
242:
231:
226:
224:
219:
217:
212:
211:
209:
208:
203:
198:
192:
190:
187:
185:
182:
180:
177:
175:
172:
170:
167:
165:
162:
160:
159:Statisticians
157:
155:
152:
151:
150:
149:
145:
141:
140:
137:
134:
133:
124:
121:
113:
102:
99:
95:
92:
88:
85:
81:
78:
74:
71: â
70:
66:
65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
19:
4335:
4323:
4304:
4297:
4209:Econometrics
4159: /
4142:Chemometrics
4119:Epidemiology
4112: /
4085:Applications
3927:ARIMA model
3874:Q-statistic
3823:Stationarity
3719:Multivariate
3662: /
3658: /
3656:Multivariate
3654: /
3594: /
3590: /
3364:Bayes factor
3263:Signed rank
3175:
3149:
3141:
3129:
2899:
2824:Completeness
2660:Cohort study
2558:Opinion poll
2493:Missing data
2480:Study design
2435:Scatter plot
2357:Scatter plot
2350:Spearman's Ï
2312:Grouped data
1997:
1980:
1974:
1944:
1925:
1917:Bibliography
1905:
1901:
1888:
1870:
1845:, retrieved
1840:
1830:
1823:Jerzy (1937)
1818:
1806:
1794:
1783:. Retrieved
1779:
1770:
1758:
1746:
1695:Bayesian one
1676:
1661:
1631:
1583:
1578:
1573:
1569:
1567:
1558:
1555:
1550:
1546:
1542:
1538:
1534:
1530:
1528:
1523:
1520:
1507:
1491:
1463:
1452:
1448:
1442:
1400:
1337:
1196:Reduce to a
1188:
1183:
1140:
1130:
1014:. Note that
991:
660:
658:
545:
460:
436:
302:
288:
284:
281:Egon Pearson
277:Jerzy Neyman
270:
252:
240:
239:
116:
107:
97:
90:
83:
76:
64:
52:Please help
47:verification
44:
4337:WikiProject
4252:Cartography
4214:Jurimetrics
4166:Reliability
3897:Time domain
3876:(LjungâBox)
3798:Time-series
3676:Categorical
3660:Time-series
3652:Categorical
3587:(Bernoulli)
3422:Correlation
3402:Correlation
3198:JarqueâBera
3170:Chi-squared
2932:M-estimator
2885:Asymptotics
2829:Sufficiency
2596:Interaction
2508:Replication
2488:Effect size
2445:Violin plot
2425:Radar chart
2405:Forest plot
2395:Correlogram
2345:Kendall's Ï
1551:uncertainty
1543:variability
1060:, and that
992:upper limit
18:Frequentist
4204:Demography
3922:ARMA model
3727:Regression
3304:(Friedman)
3265:(Wilcoxon)
3203:Normality
3193:Lilliefors
3140:Student's
3016:Resampling
2890:Robustness
2878:divergence
2868:Efficiency
2806:(monotone)
2801:Likelihood
2718:Population
2551:Stratified
2503:Population
2322:Dependence
2278:Count data
2209:Percentile
2186:Dispersion
2119:Arithmetic
2054:Statistics
1935:0521685672
1908:: 171â182.
1847:2021-09-14
1799:Cox (2006)
1785:2021-09-14
1763:Cox (2006)
1751:Cox (2006)
1738:References
1683:parameters
299:Definition
136:Statistics
110:April 2021
80:newspapers
3585:Logistic
3352:posterior
3278:Rank sum
3026:Jackknife
3021:Bootstrap
2839:Bootstrap
2774:Parameter
2723:Statistic
2518:Statistic
2430:Run chart
2415:Pie chart
2410:Histogram
2400:Fan chart
2375:Bar chart
2257:L-moments
2144:Geometric
1472:ψ
1429:ψ
1409:ψ
1386:ψ
1366:ψ
1346:ψ
1293:ψ
1270:ψ
1227:θ
1170:ψ
1150:ψ
1117:ψ
1097:ψ
1071:−
1048:ψ
1025:−
1002:ψ
976:−
915:−
885:≤
882:ψ
851:∗
838:≤
832:ψ
771:∈
748:ψ
725:ψ
673:ψ
635:θ
610:∫
601:θ
531:σ
511:λ
491:μ
471:ψ
447:λ
423:ψ
415:), where
403:λ
397:ψ
377:θ
357:θ
314:∈
247:based in
4353:Category
4299:Category
3992:Survival
3869:Johansen
3592:Binomial
3547:Isotonic
3134:(normal)
2779:location
2586:Blocking
2541:Sampling
2420:QâQ plot
2385:Box plot
2367:Graphics
2262:Skewness
2252:Kurtosis
2224:Variance
2154:Heronian
2149:Harmonic
1969:(1937).
1721:See also
1574:long-run
1570:long-run
1533:and the
1443:a priori
1184:a priori
930:, where
760:, where
189:Category
184:Articles
174:Journals
169:Notation
164:Glossary
4325:Commons
4272:Kriging
4157:Process
4114:studies
3973:Wavelet
3806:General
2973:Plug-in
2767:L space
2546:Cluster
2247:Moments
2065:Outline
1780:cnx.org
1453:type II
459:is the
435:is the
289:type II
154:Outline
94:scholar
4194:Census
3784:Normal
3732:Manova
3552:Robust
3302:2-way
3294:1-way
3132:-test
2803:
2380:Biplot
2171:Median
2164:Lehmer
2106:Center
2012:
1987:
1955:
1932:
1537:. The
1455:errors
1449:type I
439:, and
295:page.
285:type I
96:
89:
82:
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3818:Trend
3347:prior
3289:anova
3178:-test
3152:-test
3144:-test
3051:Power
2996:Pivot
2789:shape
2784:scale
2234:Shape
2214:Range
2159:Heinz
2134:Cubic
2070:Index
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1985:JSTOR
1898:(PDF)
1880:(PDF)
1712:or a
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662:pivot
101:JSTOR
87:books
4051:Test
3251:Sign
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2176:Mode
2114:Mean
2010:ISBN
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1930:ISBN
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