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Blocking (statistics)

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338: 25: 7747: 5436: 4948: 1662: 350: 254: 198:: An experiment is designed to test the effects of a new pesticide on a specific patch of grass. The grass area contains a major elevation change and thus consists of two distinct regions – 'high elevation' and 'low elevation'. A treatment group (the new pesticide) and a placebo group are applied to both the high elevation and low elevation areas of grass. In this instance the researcher is blocking the elevation factor which may account for variability in the pesticide's application. 310: 7733: 4934: 224:. Both groups are then asked to use their shoes for a period of time, and then measure the degree of wear of the soles. This is a workable experimental design, but purely from the point of view of statistical accuracy (ignoring any other factors), a better design would be to give each person one regular sole and one new sole, randomly assigning the two types to the left and right shoe of each volunteer. Such a design is called a "randomized complete 246: 7771: 4972: 7759: 4960: 792:
the different dosages. The blocked way to run this experiment, assuming you can convince manufacturing to let you put four experimental wafers in a furnace run, would be to put four wafers with different dosages in each of three furnace runs. The only randomization would be choosing which of the three wafers with dosage 1 would go into furnace run 1, and similarly for the wafers with dosages 2, 3 and 4.
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In the first example provided above, the sex of the patient would be a nuisance variable. For example, consider if the drug was a diet pill and the researchers wanted to test the effect of the diet pills on weight loss. The explanatory variable is the diet pill and the response variable is the amount
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are usually of the least importance (think of the fact that temperature of a reactor or the batch of raw materials is more important than the combination of the two – this is especially true when more (3, 4, ...) factors are present); thus it is preferable to confound this variability with the higher
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that are similar to one another in groups (blocks) based on one or more variables. These variables are chosen carefully to minimize the impact of their variability on the observed outcomes. There are different ways that blocking can be implemented, resulting in different confounding effects. However,
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A non-blocked way to run this experiment would be to run each of the twelve experimental wafers, in random order, one per furnace run. That would increase the experimental error of each resistivity measurement by the run-to-run furnace variability and make it more difficult to study the effects of
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An ideal way to run this experiment would be to run all the 4x3=12 wafers in the same furnace run. That would eliminate the nuisance furnace factor completely. However, regular production wafers have furnace priority, and only a few experimental wafers are allowed into any furnace run at the same
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Blocking is used to remove the effects of a few of the most important nuisance variables. Randomization is then used to reduce the contaminating effects of the remaining nuisance variables. For important nuisance variables, blocking will yield higher significance in the variables of interest than
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In our previous diet pills example, a blocking factor could be the sex of a patient. We could put individuals into one of two blocks (male or female). And within each of the two blocks, we can randomly assign the patients to either the diet pill (treatment) or placebo pill (control).  By
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In the examples listed above, a nuisance variable is a variable that is not the primary focus of the study but can affect the outcomes of the experiment. They are considered potential sources of variability that, if not controlled or accounted for, may confound the interpretation between the
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You may choose to randomly assign experimental units to treatment conditions within each block which may help ensure that any unaccounted for variability is spread evenly across treatment groups. However, depending on how you assign treatments to blocks, you may obtain a different number of
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Suppose engineers at a semiconductor manufacturing facility want to test whether different wafer implant material dosages have a significant effect on resistivity measurements after a diffusion process taking place in a furnace. They have four different dosages they want to try and enough
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A nuisance factor is used as a blocking factor if every level of the primary factor occurs the same number of times with each level of the nuisance factor. The analysis of the experiment will focus on the effect of varying levels of the primary factor within each block of the experiment.
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When studying probability theory the blocks method consists of splitting a sample into blocks (groups) separated by smaller subblocks so that the blocks can be considered almost independent. The blocks method helps proving limit theorems in the case of dependent random variables.
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By using one of these methods to account for nuisance variables, researchers can enhance the internal validity of their experiments, ensuring that the effects observed are more likely attributable to the manipulated variables rather than extraneous influences.
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designs. Today, blocking still plays a pivotal role in experimental design, and in recent years, advancements in statistical software and computational capabilities have allowed researchers to explore more intricate blocking designs.
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To address nuisance variables, researchers can employ different methods such as blocking or randomization. Blocking involves grouping experimental units based on levels of the nuisance variable to control for its influence.
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the different methods share the same purpose: to control variability introduced by specific factors that could influence the outcome of an experiment. The roots of blocking originated from the statistician,
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of weight loss. Although the sex of the patient is not the main focus of the experiment—the effect of the drug is—it is possible that the sex of the individual will affect the amount of weight lost.
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Blocking reduces unexplained variability. Its principle lies in the fact that variability which cannot be overcome (e.g. needing two batches of raw material to produce 1 container of a chemical) is
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The use of blocking in experimental design has an evolving history that spans multiple disciplines. The foundational concepts of blocking date back to the early 20th century with statisticians like
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confounded effects. Therefore, the number of as well as which specific effects get confounded can be chosen which means that assigning treatments to blocks is superior over
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The nuisance factor they are concerned with is "furnace run" since it is known that each furnace run differs from the last and impacts many process parameters.
2279: 8001: 2139: 204:: Suppose a process is invented that intends to make the soles of shoes last longer, and a plan is formed to conduct a field trial. Given a group of 1927:
Bernstein S.N. (1926) Sur l'extension du thĂ©orĂšme limite du calcul des probabilitĂ©s aux sommes de quantitĂ©s dĂ©pendantes. Math. Annalen, v. 97, 1–59.
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There are consequences to partitioning a certain sized experiment into a certain number of blocks as the number of blocks determines the number of
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blocking on sex, this source of variability is controlled, therefore, leading to greater interpretation of how the diet pills affect weight loss.
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Carefully choose blocking factors based on their relevance to the study as well as their potential to confound the primary factors of interest.
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involves a series of steps to effectively control for extraneous variables and enhance the precision of treatment effect estimates.
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Ibragimov I.A. and Linnik Yu.V. (1971) Independent and stationary sequences of random variables. Wolters-Noordhoff, Groningen.
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An alternate way of summarizing the design trials would be to use a 4x3 matrix whose 4 rows are the levels of the treatment
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Addelman, S. (1970). "Variability of Treatments and Experimental Units in the Design and Analysis of Experiments".
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or aliased with a(n) (higher/highest order) interaction to eliminate its influence on the end product. High order
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By extension, note that the trials for any K-factor randomized block design are simply the cell indices of a
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Novak S.Y. (2011) Extreme Value Methods with Applications to Finance. Chapman & Hall/CRC Press, London.
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Identify potential factors that are not the primary focus of the study but could introduce variability.
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in groups (blocks) that are similar to one another. Typically, a blocking factor is a source of
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One useful way to look at a randomized block experiment is to consider it as a collection of
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Wilk, M. B. (1955). "The Randomization Analysis of a Generalized Randomized Block Design".
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be the blocking factor furnace run. Then the experiment can be described as follows:
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Lentner, Marvin; Thomas Bishop (1993). "The Generalized RCB Design (Chapter 6.13)".
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helps distribute the effects of nuisance variables evenly across treatment groups.
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experimental wafers from the same lot to run three wafers at each of the dosages.
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Gates, C.E. (Nov 1995). "What Really Is Experimental Error in Block Designs?".
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experiments, each run within one of the blocks of the total experiment.
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the assignment of the two kinds of soles. This type of experiment is a
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The model for a randomized block design with one nuisance variable is
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Constructions and Combinatorial Problems in Design of Experiments
2399:(Corrected reprint of (1952) Wiley ed.). Robert E. Krieger. 257:
Nuisance variable (sex) effect on response variable (weight loss)
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Berger, Paul D.; Maurer, Robert E.; Celli, Giovana B. (2018).
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and whose columns are the 3 levels of the blocking variable
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No blocking (left) vs blocking (right) experimental design
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Design of experiments to collect similar contexts together
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Blocking used for nuisance factors that can be controlled
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Block Designs: Analysis, Combinatorics and Applications
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Pashley, Nicole E.; Miratrix, Luke W. (July 7, 2021).
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Without blocking: diet pills vs placebo on weight loss
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that is not of primary interest to the experimenter.
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Autoregressive conditional heteroskedasticity (ARCH)
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Autoregressive conditional heteroskedasticity (ARCH)
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factor accounting for treatment variability between
2340:. Vol. II: Design. New York: Springer-Verlag. 2203:(1948). "The Validity of Comparative Experiments". 2142:(1969). "The Generalized Randomized Block Design". 2061:Ledolter, Johannes; Kardon, Randy H. (2020-07-09). 895:Before randomization, the design trials look like: 353:
With blocking: diet pills vs placebo on weight loss
6836: 4037: 2508: 2333: 2310: 1974:Journal of the Royal Statistical Society, Series B 1894:, New York, NY: Springer, 2008, pp. 447–448, 1592: 1555: 1480: 1443: 1383: 1310:is the general location parameter (i.e., the mean) 1244: 750: 679: 631: 610: 589: 367:Block a few of the most important nuisance factors 2391: 1851: 1783: 1781: 357: 208:volunteers, one possible design would be to give 8050: 2278:: CS1 maint: bot: original URL status unknown ( 2067:Investigative Ophthalmology & Visual Science 2015:Journal of Educational and Behavioral Statistics 795: 375:"Block what you can; randomize what you cannot." 6922:Multivariate adaptive regression splines (MARS) 4123:Multivariate adaptive regression splines (MARS) 2422:. Vol. I and II (Second ed.). Wiley. 2284:Pre-publication chapters are available on-line. 2173:Journal of the American Statistical Association 2011:"Block What You Can, Except When You Shouldn't" 2008: 1816: 1814: 1812: 1810: 1808: 1789:"5.3.3.3.3. Blocking of full factorial designs" 2127:National Institute of Standards and Technology 2060: 1778: 423: 395: 7803: 5477: 5004: 2678: 249:Nuisance variable effect on response variable 2570: 2287: 1805: 2056: 2054: 7810: 7796: 5522: 5484: 5470: 5011: 4997: 2723: 2685: 2671: 2261:. Archived from the original on 2011-03-06 736:= number of levels (settings) of factor 4 216:/2 of them shoes with the ordinary soles, 6135: 5018: 3336: 2645: 2094: 2026: 1985: 1593:{\displaystyle {\overline {Y}}_{\cdot j}} 1481:{\displaystyle {\overline {Y}}_{i\cdot }} 727:= number of levels (settings) of factor 3 718:= number of levels (settings) of factor 2 709:= number of levels (settings) of factor 1 69:Learn how and when to remove this message 7817: 2552:Shah, Kirti R.; Sinha, Bikas K. (1989). 2206:Journal of the Royal Statistical Society 2199: 2170: 2138: 2051: 1967: 1847: 1845: 1843: 1841: 1016: 768:= number of levels (settings) of factor 348: 336: 308: 252: 244: 212:/2 of them shoes with the new soles and 32:This article includes a list of general 2627: 2336:Block designs: A Randomization approach 2313:Block designs: A Randomization approach 441:By running a different design for each 8051: 7448:Kaplan–Meier estimator (product limit) 4649:Kaplan–Meier estimator (product limit) 2397:The Design and Analysis of Experiments 2241: 1892:The Concise Encyclopedia of Statistics 7791: 7521: 7088: 6835: 6134: 5904: 5521: 5465: 4992: 4722: 4289: 4036: 3335: 3105: 2722: 2666: 2634:The Annals of Mathematical Statistics 2362: 1838: 1733: 1731: 1319:is the effect for being in treatment 411: 240: 7758: 7458:Accelerated failure time (AFT) model 4959: 4659:Accelerated failure time (AFT) model 2598: 2581:Combinatorics of Experimental Design 1626:Generalized randomized block designs 321:The blocks method was introduced by 18: 7770: 7053:Analysis of variance (ANOVA, anova) 5905: 5360:Generalized randomized block design 4971: 4254:Analysis of variance (ANOVA, anova) 3106: 1822:"5.3.3.2. Randomized block designs" 1737: 1711:Dependent and independent variables 1691:Generalized randomized block design 404:Select appropriate blocking factors 264:independent and dependent variables 180:trial. The sex of the patient is a 13: 7148:Cochran–Mantel–Haenszel statistics 5774:Pearson product-moment correlation 4349:Cochran–Mantel–Haenszel statistics 2975:Pearson product-moment correlation 2466:Design and Analysis of Experiments 2443:Design and Analysis of Experiments 2420:Design and Analysis of Experiments 1728: 1619: 1238: 1235: 1232: 1229: 1226: 1220: 1217: 1214: 1211: 1208: 1205: 38:it lacks sufficient corresponding 14: 8070: 5411:Sequential probability ratio test 2332:CaliƄski T.; Kageyama S. (2003). 2309:CaliƄski T.; Kageyama S. (2000). 2248:Design of Comparative Experiments 1945:Leadbetter M.R., Lindgren G. and 1648:Hyper-Graeco-Latin square designs 1339:is the effect for being in block 383: 7769: 7757: 7745: 7732: 7731: 7522: 5434: 5336:Polynomial and rational modeling 4970: 4958: 4946: 4933: 4932: 4723: 2487:Experimental design and analysis 2291:Linear Algebra and Linear Models 2121: This article incorporates 2116: 1660: 23: 7407:Least-squares spectral analysis 4608:Least-squares spectral analysis 2132: 2002: 1961: 1696:Glossary of experimental design 1384:{\displaystyle {\overline {Y}}} 466:Randomized block designs (RBD) 298:, blocking is the arranging of 232:is more closely matched to the 102:, following his development of 7961:Cremona–Richmond configuration 6388:Mean-unbiased minimum-variance 5491: 5103:Replication versus subsampling 3589:Mean-unbiased minimum-variance 2692: 2251:. Cambridge University Press. 1952: 1939: 1930: 1921: 1880: 821:= 2 factors (1 primary factor 436: 358:Definition of blocking factors 1: 7701:Geographic information system 6917:Simultaneous equations models 4902:Geographic information system 4118:Simultaneous equations models 2294:(Second ed.). Springer. 1900:10.1007/978-0-387-32833-1_344 1721: 1391:= the average of all the data 1265:is any observation for which 796:Description of the experiment 8038:Kirkman's schoolgirl problem 7971:GrĂŒnbaum–Rigby configuration 6884:Coefficient of determination 6495:Uniformly most powerful test 5330:Response surface methodology 5238:Analysis of variance (Anova) 4085:Coefficient of determination 3696:Uniformly most powerful test 1576: 1548: 1526: 1464: 1436: 1414: 1376: 1354: 775: 448: 222:completely randomized design 7: 7931:Möbius–Kantor configuration 7453:Proportional hazards models 7397:Spectral density estimation 7379:Vector autoregression (VAR) 6813:Maximum posterior estimator 6045:Randomized controlled trial 5400:Randomized controlled trial 4654:Proportional hazards models 4598:Spectral density estimation 4580:Vector autoregression (VAR) 4014:Maximum posterior estimator 3246:Randomized controlled trial 1653: 424:Assign treatments to blocks 396:Identify nuisance variables 147: 10: 8075: 8017:Bruck–Ryser–Chowla theorem 7213:Multivariate distributions 5633:Average absolute deviation 4414:Multivariate distributions 2834:Average absolute deviation 332: 109: 8025: 8007:SzemerĂ©di–Trotter theorem 7989: 7911: 7846: 7825: 7727: 7681: 7618: 7571: 7534: 7530: 7517: 7489: 7471: 7438: 7429: 7387: 7334: 7295: 7244: 7235: 7201:Structural equation model 7156: 7113: 7109: 7084: 7043: 7009: 6963: 6930: 6892: 6859: 6855: 6831: 6771: 6680: 6599: 6563: 6554: 6537:Score/Lagrange multiplier 6522: 6475: 6420: 6346: 6337: 6147: 6143: 6130: 6089: 6063: 6015: 5970: 5952:Sample size determination 5917: 5913: 5900: 5804: 5759: 5733: 5715: 5671: 5623: 5543: 5534: 5530: 5517: 5499: 5419: 5288: 5183: 5116: 5026: 4928: 4882: 4819: 4772: 4735: 4731: 4718: 4690: 4672: 4639: 4630: 4588: 4535: 4496: 4445: 4436: 4402:Structural equation model 4357: 4314: 4310: 4285: 4244: 4210: 4164: 4131: 4093: 4060: 4056: 4032: 3972: 3881: 3800: 3764: 3755: 3738:Score/Lagrange multiplier 3723: 3676: 3621: 3547: 3538: 3348: 3344: 3331: 3290: 3264: 3216: 3171: 3153:Sample size determination 3118: 3114: 3101: 3005: 2960: 2934: 2916: 2872: 2824: 2744: 2735: 2731: 2718: 2700: 2554:Theory of Optimal Designs 2365:The American Statistician 2144:The American Statistician 2037:10.3102/10769986211027240 1968:Karmakar, Bikram (2022). 1888:"Randomized Block Design" 1864:10.1007/978-3-319-64583-4 1744:The American Statistician 1738:Box, Joan Fisher (1980). 388:Implementing blocking in 118:. His work in developing 7997:Sylvester–Gallai theorem 7696:Environmental statistics 7218:Elliptical distributions 7011:Generalized linear model 6940:Simple linear regression 6710:Hodges–Lehmann estimator 6167:Probability distribution 6076:Stochastic approximation 5638:Coefficient of variation 5386:Repeated measures design 5098:Restricted randomization 4897:Environmental statistics 4419:Elliptical distributions 4212:Generalized linear model 4141:Simple linear regression 3911:Hodges–Lehmann estimator 3368:Probability distribution 3277:Stochastic approximation 2839:Coefficient of variation 2628:Zyskind, George (1963). 2533:; Padgett, L.V. (2005). 1638:Latin hypercube sampling 1141: 871:= 1 replication per cell 453: 8002:De Bruijn–ErdƑs theorem 7946:Desargues configuration 7356:Cross-correlation (XCF) 6964:Non-standard predictors 6398:Lehmann–ScheffĂ© theorem 6071:Adaptive clinical trial 4557:Cross-correlation (XCF) 4165:Non-standard predictors 3599:Lehmann–ScheffĂ© theorem 3272:Adaptive clinical trial 2647:10.1214/aoms/1177703889 751:{\displaystyle \vdots } 680:{\displaystyle \cdots } 632:{\displaystyle \vdots } 611:{\displaystyle \vdots } 590:{\displaystyle \vdots } 53:more precise citations. 7752:Mathematics portal 7573:Engineering statistics 7481:Nelson–Aalen estimator 7058:Analysis of covariance 6945:Ordinary least squares 6869:Pearson product-moment 6273:Statistical functional 6184:Empirical distribution 6017:Controlled experiments 5746:Frequency distribution 5524:Descriptive statistics 5441:Mathematics portal 5203:Ordinary least squares 4953:Mathematics portal 4774:Engineering statistics 4682:Nelson–Aalen estimator 4259:Analysis of covariance 4146:Ordinary least squares 4070:Pearson product-moment 3474:Statistical functional 3385:Empirical distribution 3218:Controlled experiments 2947:Frequency distribution 2725:Descriptive statistics 2123:public domain material 1706:Paired difference test 1594: 1557: 1482: 1445: 1385: 1304:is the blocking factor 1246: 828:and 1 blocking factor 807:be dosage "level" and 752: 681: 633: 612: 591: 354: 342: 314: 258: 250: 130: 8059:Design of experiments 8033:Design of experiments 7668:Population statistics 7610:System identification 7344:Autocorrelation (ACF) 7272:Exponential smoothing 7186:Discriminant analysis 7181:Canonical correlation 7045:Partition of variance 6907:Regression validation 6751:(Jonckheere–Terpstra) 6650:Likelihood-ratio test 6339:Frequentist inference 6251:Location–scale family 6172:Sampling distribution 6137:Statistical inference 6104:Cross-sectional study 6091:Observational studies 6050:Randomized experiment 5879:Stem-and-leaf display 5681:Central limit theorem 5038:Scientific experiment 5020:Design of experiments 4869:Population statistics 4811:System identification 4545:Autocorrelation (ACF) 4473:Exponential smoothing 4387:Discriminant analysis 4382:Canonical correlation 4246:Partition of variance 4108:Regression validation 3952:(Jonckheere–Terpstra) 3851:Likelihood-ratio test 3540:Frequentist inference 3452:Location–scale family 3373:Sampling distribution 3338:Statistical inference 3305:Cross-sectional study 3292:Observational studies 3251:Randomized experiment 3080:Stem-and-leaf display 2882:Central limit theorem 2288:Bapat, R. B. (2000). 1595: 1558: 1483: 1446: 1386: 1295:is the primary factor 1247: 1017:Matrix representation 859:= 3 levels of factor 844:= 4 levels of factor 753: 682: 634: 613: 592: 460:completely randomized 371:The general rule is: 352: 340: 312: 296:design of experiments 256: 248: 87:design of experiments 7966:Kummer configuration 7936:Pappus configuration 7819:Incidence structures 7591:Probabilistic design 7176:Principal components 7019:Exponential families 6971:Nonlinear regression 6950:General linear model 6912:Mixed effects models 6902:Errors and residuals 6879:Confounding variable 6781:Bayesian probability 6759:Van der Waerden test 6749:Ordered alternative 6514:Multiple comparisons 6393:Rao–Blackwellization 6356:Estimating equations 6312:Statistical distance 6030:Factorial experiment 5563:Arithmetic-Geometric 5312:Fractional factorial 4792:Probabilistic design 4377:Principal components 4220:Exponential families 4172:Nonlinear regression 4151:General linear model 4113:Mixed effects models 4103:Errors and residuals 4080:Confounding variable 3982:Bayesian probability 3960:Van der Waerden test 3950:Ordered alternative 3715:Multiple comparisons 3594:Rao–Blackwellization 3557:Estimating equations 3513:Statistical distance 3231:Factorial experiment 2764:Arithmetic-Geometric 2572:Street, Anne Penfold 2537:. World Scientific. 2531:Raghavarao, Damaraju 2505:Raghavarao, Damaraju 2079:10.1167/iovs.61.8.11 1686:Combinatorial design 1676:Algebraic statistics 1643:Graeco-Latin squares 1567: 1517: 1455: 1405: 1368: 1153: 1138:dimensional matrix. 1049:combinations above. 742: 671: 623: 602: 581: 327:extreme value theory 120:analysis of variance 93:is the arranging of 7976:Klein configuration 7956:SchlĂ€fli double six 7941:Hesse configuration 7921:Complete quadrangle 7663:Official statistics 7586:Methods engineering 7267:Seasonal adjustment 7035:Poisson regressions 6955:Bayesian regression 6894:Regression analysis 6874:Partial correlation 6846:Regression analysis 6445:Prediction interval 6440:Likelihood interval 6430:Confidence interval 6422:Interval estimation 6383:Unbiased estimators 6201:Model specification 6081:Up-and-down designs 5769:Partial correlation 5725:Index of dispersion 5643:Interquartile range 5446:Statistical outline 5406:Sequential analysis 5371:Graeco-Latin square 5280:Multiple comparison 5227:Hierarchical model: 4864:Official statistics 4787:Methods engineering 4468:Seasonal adjustment 4236:Poisson regressions 4156:Bayesian regression 4095:Regression analysis 4075:Partial correlation 4047:Regression analysis 3646:Prediction interval 3641:Likelihood interval 3631:Confidence interval 3623:Interval estimation 3584:Unbiased estimators 3402:Model specification 3282:Up-and-down designs 2970:Partial correlation 2926:Index of dispersion 2844:Interquartile range 2556:. Springer-Verlag. 2460:Hinkelmann, Klaus; 2437:Hinkelmann, Klaus; 2414:Hinkelmann, Klaus; 1855:Experimental Design 467: 390:experimental design 7951:Reye configuration 7683:Spatial statistics 7563:Medical statistics 7463:First hitting time 7417:Whittle likelihood 7068:Degrees of freedom 7063:Multivariate ANOVA 6996:Heteroscedasticity 6808:Bayesian estimator 6773:Bayesian inference 6622:Kolmogorov–Smirnov 6507:Randomization test 6477:Testing hypotheses 6450:Tolerance interval 6361:Maximum likelihood 6256:Exponential family 6189:Density estimation 6149:Statistical theory 6109:Natural experiment 6055:Scientific control 5972:Survey methodology 5658:Standard deviation 5451:Statistical topics 5043:Statistical design 4884:Spatial statistics 4764:Medical statistics 4664:First hitting time 4618:Whittle likelihood 4269:Degrees of freedom 4264:Multivariate ANOVA 4197:Heteroscedasticity 4009:Bayesian estimator 3974:Bayesian inference 3823:Kolmogorov–Smirnov 3708:Randomization test 3678:Testing hypotheses 3651:Tolerance interval 3562:Maximum likelihood 3457:Exponential family 3390:Density estimation 3350:Statistical theory 3310:Natural experiment 3256:Scientific control 3173:Survey methodology 2859:Standard deviation 2576:Street, Deborah J. 2179:(331): 1095–1108. 1987:10.1111/rssb.12545 1668:Mathematics portal 1590: 1553: 1478: 1441: 1381: 1242: 748: 677: 629: 608: 587: 474:Number of factors 465: 412:Define block sizes 355: 343: 315: 300:experimental units 259: 251: 241:Nuisance variables 168:, administered to 95:experimental units 8046: 8045: 7785: 7784: 7723: 7722: 7719: 7718: 7658:National accounts 7628:Actuarial science 7620:Social statistics 7513: 7512: 7509: 7508: 7505: 7504: 7440:Survival function 7425: 7424: 7287:Granger causality 7128:Contingency table 7103:Survival analysis 7080: 7079: 7076: 7075: 6932:Linear regression 6827: 6826: 6823: 6822: 6798:Credible interval 6767: 6766: 6550: 6549: 6366:Method of moments 6235:Parametric family 6196:Statistical model 6126: 6125: 6122: 6121: 6040:Random assignment 5962:Statistical power 5896: 5895: 5892: 5891: 5741:Contingency table 5711: 5710: 5578:Generalized/power 5459: 5458: 5346:Central composite 5244:Cochran's theorem 5198:Linear regression 5175:Nuisance variable 5088:Random assignment 5065:Experimental unit 4986: 4985: 4924: 4923: 4920: 4919: 4859:National accounts 4829:Actuarial science 4821:Social statistics 4714: 4713: 4710: 4709: 4706: 4705: 4641:Survival function 4626: 4625: 4488:Granger causality 4329:Contingency table 4304:Survival analysis 4281: 4280: 4277: 4276: 4133:Linear regression 4028: 4027: 4024: 4023: 3999:Credible interval 3968: 3967: 3751: 3750: 3567:Method of moments 3436:Parametric family 3397:Statistical model 3327: 3326: 3323: 3322: 3241:Random assignment 3163:Statistical power 3097: 3096: 3093: 3092: 2942:Contingency table 2912: 2911: 2779:Generalized/power 2584:. Oxford U. P. . 2475:978-0-471-55177-5 2462:Kempthorne, Oscar 2452:978-0-471-72756-9 2439:Kempthorne, Oscar 2429:978-0-470-38551-7 2416:Kempthorne, Oscar 2393:Kempthorne, Oscar 2301:978-0-387-98871-9 2258:978-0-521-68357-9 1909:978-0-387-32833-1 1873:978-3-319-64582-7 1600:= average of all 1579: 1551: 1529: 1488:= average of all 1467: 1439: 1417: 1379: 1225: 1132: 1131: 1014: 1013: 891:= 4 * 3 = 12 runs 697: 696: 431:random assignment 79: 78: 71: 8066: 7881:Projective plane 7833:Incidence matrix 7812: 7805: 7798: 7789: 7788: 7773: 7772: 7761: 7760: 7750: 7749: 7735: 7734: 7638:Crime statistics 7532: 7531: 7519: 7518: 7436: 7435: 7402:Fourier analysis 7389:Frequency domain 7369: 7316: 7282:Structural break 7242: 7241: 7191:Cluster analysis 7138:Log-linear model 7111: 7110: 7086: 7085: 7027: 7001:Homoscedasticity 6857: 6856: 6833: 6832: 6752: 6744: 6736: 6735:(Kruskal–Wallis) 6720: 6705: 6660:Cross validation 6645: 6627:Anderson–Darling 6574: 6561: 6560: 6532:Likelihood-ratio 6524:Parametric tests 6502:Permutation test 6485:1- & 2-tails 6376:Minimum distance 6348:Point estimation 6344: 6343: 6295:Optimal decision 6246: 6145: 6144: 6132: 6131: 6114:Quasi-experiment 6064:Adaptive designs 5915: 5914: 5902: 5901: 5779:Rank correlation 5541: 5540: 5532: 5531: 5519: 5518: 5486: 5479: 5472: 5463: 5462: 5439: 5438: 5376:Orthogonal array 5013: 5006: 4999: 4990: 4989: 4974: 4973: 4962: 4961: 4951: 4950: 4936: 4935: 4839:Crime statistics 4733: 4732: 4720: 4719: 4637: 4636: 4603:Fourier analysis 4590:Frequency domain 4570: 4517: 4483:Structural break 4443: 4442: 4392:Cluster analysis 4339:Log-linear model 4312: 4311: 4287: 4286: 4228: 4202:Homoscedasticity 4058: 4057: 4034: 4033: 3953: 3945: 3937: 3936:(Kruskal–Wallis) 3921: 3906: 3861:Cross validation 3846: 3828:Anderson–Darling 3775: 3762: 3761: 3733:Likelihood-ratio 3725:Parametric tests 3703:Permutation test 3686:1- & 2-tails 3577:Minimum distance 3549:Point estimation 3545: 3544: 3496:Optimal decision 3447: 3346: 3345: 3333: 3332: 3315:Quasi-experiment 3265:Adaptive designs 3116: 3115: 3103: 3102: 2980:Rank correlation 2742: 2741: 2733: 2732: 2720: 2719: 2687: 2680: 2673: 2664: 2663: 2659: 2649: 2640:(4): 1569–1581. 2624: 2595: 2567: 2548: 2526: 2514: 2500: 2479: 2456: 2433: 2410: 2388: 2359: 2339: 2328: 2316: 2305: 2283: 2277: 2269: 2267: 2266: 2238: 2196: 2167: 2120: 2119: 2109: 2108: 2098: 2058: 2049: 2048: 2030: 2006: 2000: 1999: 1989: 1980:(5): 1726–1750. 1965: 1959: 1956: 1950: 1943: 1937: 1934: 1928: 1925: 1919: 1918: 1917: 1916: 1884: 1878: 1877: 1849: 1836: 1835: 1833: 1832: 1826:www.itl.nist.gov 1818: 1803: 1802: 1800: 1799: 1793:www.itl.nist.gov 1785: 1776: 1775: 1735: 1670: 1665: 1664: 1599: 1597: 1596: 1591: 1589: 1588: 1580: 1572: 1562: 1560: 1559: 1554: 1552: 1544: 1539: 1538: 1530: 1522: 1487: 1485: 1484: 1479: 1477: 1476: 1468: 1460: 1450: 1448: 1447: 1442: 1440: 1432: 1427: 1426: 1418: 1410: 1390: 1388: 1387: 1382: 1380: 1372: 1251: 1249: 1248: 1243: 1241: 1223: 1200: 1199: 1187: 1186: 1168: 1167: 1052: 1051: 898: 897: 757: 755: 754: 749: 686: 684: 683: 678: 638: 636: 635: 630: 617: 615: 614: 609: 596: 594: 593: 588: 468: 464: 116:Ronald A. Fisher 74: 67: 63: 60: 54: 49:this article by 40:inline citations 27: 26: 19: 8074: 8073: 8069: 8068: 8067: 8065: 8064: 8063: 8049: 8048: 8047: 8042: 8021: 7985: 7907: 7842: 7838:Incidence graph 7821: 7816: 7786: 7781: 7744: 7715: 7677: 7614: 7600:quality control 7567: 7549:Clinical trials 7526: 7501: 7485: 7473:Hazard function 7467: 7421: 7383: 7367: 7330: 7326:Breusch–Godfrey 7314: 7291: 7231: 7206:Factor analysis 7152: 7133:Graphical model 7105: 7072: 7039: 7025: 7005: 6959: 6926: 6888: 6851: 6850: 6819: 6763: 6750: 6742: 6734: 6718: 6703: 6682:Rank statistics 6676: 6655:Model selection 6643: 6601:Goodness of fit 6595: 6572: 6546: 6518: 6471: 6416: 6405:Median unbiased 6333: 6244: 6177:Order statistic 6139: 6118: 6085: 6059: 6011: 5966: 5909: 5907:Data collection 5888: 5800: 5755: 5729: 5707: 5667: 5619: 5536:Continuous data 5526: 5513: 5495: 5490: 5460: 5455: 5433: 5415: 5392:Crossover study 5383: 5381:Latin hypercube 5317:Plackett–Burman 5296: 5293: 5292: 5284: 5187: 5179: 5120: 5112: 5029: 5022: 5017: 4987: 4982: 4945: 4916: 4878: 4815: 4801:quality control 4768: 4750:Clinical trials 4727: 4702: 4686: 4674:Hazard function 4668: 4622: 4584: 4568: 4531: 4527:Breusch–Godfrey 4515: 4492: 4432: 4407:Factor analysis 4353: 4334:Graphical model 4306: 4273: 4240: 4226: 4206: 4160: 4127: 4089: 4052: 4051: 4020: 3964: 3951: 3943: 3935: 3919: 3904: 3883:Rank statistics 3877: 3856:Model selection 3844: 3802:Goodness of fit 3796: 3773: 3747: 3719: 3672: 3617: 3606:Median unbiased 3534: 3445: 3378:Order statistic 3340: 3319: 3286: 3260: 3212: 3167: 3110: 3108:Data collection 3089: 3001: 2956: 2930: 2908: 2868: 2820: 2737:Continuous data 2727: 2714: 2696: 2691: 2613:10.2307/2333423 2592: 2564: 2545: 2523: 2497: 2476: 2453: 2430: 2407: 2377:10.2307/2684574 2348: 2325: 2302: 2271: 2270: 2264: 2262: 2259: 2219:10.2307/2984159 2209:. A (General). 2185:10.2307/2284277 2156:10.2307/2681737 2135: 2117: 2113: 2112: 2059: 2052: 2007: 2003: 1966: 1962: 1957: 1953: 1944: 1940: 1935: 1931: 1926: 1922: 1914: 1912: 1910: 1886: 1885: 1881: 1874: 1850: 1839: 1830: 1828: 1820: 1819: 1806: 1797: 1795: 1787: 1786: 1779: 1756:10.2307/2682986 1736: 1729: 1724: 1666: 1659: 1656: 1622: 1620:Generalizations 1610: 1581: 1571: 1570: 1568: 1565: 1564: 1543: 1531: 1521: 1520: 1518: 1515: 1514: 1512: 1498: 1469: 1459: 1458: 1456: 1453: 1452: 1431: 1419: 1409: 1408: 1406: 1403: 1402: 1400: 1371: 1369: 1366: 1365: 1357: 1349: 1338: 1329: 1318: 1303: 1294: 1282: 1271: 1264: 1204: 1195: 1191: 1182: 1178: 1160: 1156: 1154: 1151: 1150: 1144: 1048: 1041: 1034: 1027: 1019: 914: 906: 890: 883: 865: 858: 850: 843: 834: 827: 813: 806: 798: 778: 766: 743: 740: 739: 735: 726: 717: 708: 692: 672: 669: 668: 666: 659: 624: 621: 620: 603: 600: 599: 582: 579: 578: 573: 566: 559: 552: 536: 529: 522: 506: 499: 480:Number of runs 471:Name of design 456: 451: 439: 426: 414: 406: 398: 386: 369: 360: 335: 288: 243: 234:treatment group 154:Male and female 150: 133: 112: 75: 64: 58: 55: 45:Please help to 44: 28: 24: 17: 12: 11: 5: 8072: 8062: 8061: 8044: 8043: 8041: 8040: 8035: 8029: 8027: 8023: 8022: 8020: 8019: 8014: 8012:Beck's theorem 8009: 8004: 7999: 7993: 7991: 7987: 7986: 7984: 7983: 7978: 7973: 7968: 7963: 7958: 7953: 7948: 7943: 7938: 7933: 7928: 7923: 7917: 7915: 7913:Configurations 7909: 7908: 7906: 7905: 7904: 7903: 7895: 7894: 7893: 7885: 7884: 7883: 7878: 7868: 7867: 7866: 7864:Steiner system 7861: 7850: 7848: 7844: 7843: 7841: 7840: 7835: 7829: 7827: 7826:Representation 7823: 7822: 7815: 7814: 7807: 7800: 7792: 7783: 7782: 7780: 7779: 7767: 7755: 7741: 7728: 7725: 7724: 7721: 7720: 7717: 7716: 7714: 7713: 7708: 7703: 7698: 7693: 7687: 7685: 7679: 7678: 7676: 7675: 7670: 7665: 7660: 7655: 7650: 7645: 7640: 7635: 7630: 7624: 7622: 7616: 7615: 7613: 7612: 7607: 7602: 7593: 7588: 7583: 7577: 7575: 7569: 7568: 7566: 7565: 7560: 7555: 7546: 7544:Bioinformatics 7540: 7538: 7528: 7527: 7515: 7514: 7511: 7510: 7507: 7506: 7503: 7502: 7500: 7499: 7493: 7491: 7487: 7486: 7484: 7483: 7477: 7475: 7469: 7468: 7466: 7465: 7460: 7455: 7450: 7444: 7442: 7433: 7427: 7426: 7423: 7422: 7420: 7419: 7414: 7409: 7404: 7399: 7393: 7391: 7385: 7384: 7382: 7381: 7376: 7371: 7363: 7358: 7353: 7352: 7351: 7349:partial (PACF) 7340: 7338: 7332: 7331: 7329: 7328: 7323: 7318: 7310: 7305: 7299: 7297: 7296:Specific tests 7293: 7292: 7290: 7289: 7284: 7279: 7274: 7269: 7264: 7259: 7254: 7248: 7246: 7239: 7233: 7232: 7230: 7229: 7228: 7227: 7226: 7225: 7210: 7209: 7208: 7198: 7196:Classification 7193: 7188: 7183: 7178: 7173: 7168: 7162: 7160: 7154: 7153: 7151: 7150: 7145: 7143:McNemar's test 7140: 7135: 7130: 7125: 7119: 7117: 7107: 7106: 7082: 7081: 7078: 7077: 7074: 7073: 7071: 7070: 7065: 7060: 7055: 7049: 7047: 7041: 7040: 7038: 7037: 7021: 7015: 7013: 7007: 7006: 7004: 7003: 6998: 6993: 6988: 6983: 6981:Semiparametric 6978: 6973: 6967: 6965: 6961: 6960: 6958: 6957: 6952: 6947: 6942: 6936: 6934: 6928: 6927: 6925: 6924: 6919: 6914: 6909: 6904: 6898: 6896: 6890: 6889: 6887: 6886: 6881: 6876: 6871: 6865: 6863: 6853: 6852: 6849: 6848: 6843: 6837: 6829: 6828: 6825: 6824: 6821: 6820: 6818: 6817: 6816: 6815: 6805: 6800: 6795: 6794: 6793: 6788: 6777: 6775: 6769: 6768: 6765: 6764: 6762: 6761: 6756: 6755: 6754: 6746: 6738: 6722: 6719:(Mann–Whitney) 6714: 6713: 6712: 6699: 6698: 6697: 6686: 6684: 6678: 6677: 6675: 6674: 6673: 6672: 6667: 6662: 6652: 6647: 6644:(Shapiro–Wilk) 6639: 6634: 6629: 6624: 6619: 6611: 6605: 6603: 6597: 6596: 6594: 6593: 6585: 6576: 6564: 6558: 6556:Specific tests 6552: 6551: 6548: 6547: 6545: 6544: 6539: 6534: 6528: 6526: 6520: 6519: 6517: 6516: 6511: 6510: 6509: 6499: 6498: 6497: 6487: 6481: 6479: 6473: 6472: 6470: 6469: 6468: 6467: 6462: 6452: 6447: 6442: 6437: 6432: 6426: 6424: 6418: 6417: 6415: 6414: 6409: 6408: 6407: 6402: 6401: 6400: 6395: 6380: 6379: 6378: 6373: 6368: 6363: 6352: 6350: 6341: 6335: 6334: 6332: 6331: 6326: 6321: 6320: 6319: 6309: 6304: 6303: 6302: 6292: 6291: 6290: 6285: 6280: 6270: 6265: 6260: 6259: 6258: 6253: 6248: 6232: 6231: 6230: 6225: 6220: 6210: 6209: 6208: 6203: 6193: 6192: 6191: 6181: 6180: 6179: 6169: 6164: 6159: 6153: 6151: 6141: 6140: 6128: 6127: 6124: 6123: 6120: 6119: 6117: 6116: 6111: 6106: 6101: 6095: 6093: 6087: 6086: 6084: 6083: 6078: 6073: 6067: 6065: 6061: 6060: 6058: 6057: 6052: 6047: 6042: 6037: 6032: 6027: 6021: 6019: 6013: 6012: 6010: 6009: 6007:Standard error 6004: 5999: 5994: 5993: 5992: 5987: 5976: 5974: 5968: 5967: 5965: 5964: 5959: 5954: 5949: 5944: 5939: 5937:Optimal design 5934: 5929: 5923: 5921: 5911: 5910: 5898: 5897: 5894: 5893: 5890: 5889: 5887: 5886: 5881: 5876: 5871: 5866: 5861: 5856: 5851: 5846: 5841: 5836: 5831: 5826: 5821: 5816: 5810: 5808: 5802: 5801: 5799: 5798: 5793: 5792: 5791: 5786: 5776: 5771: 5765: 5763: 5757: 5756: 5754: 5753: 5748: 5743: 5737: 5735: 5734:Summary tables 5731: 5730: 5728: 5727: 5721: 5719: 5713: 5712: 5709: 5708: 5706: 5705: 5704: 5703: 5698: 5693: 5683: 5677: 5675: 5669: 5668: 5666: 5665: 5660: 5655: 5650: 5645: 5640: 5635: 5629: 5627: 5621: 5620: 5618: 5617: 5612: 5607: 5606: 5605: 5600: 5595: 5590: 5585: 5580: 5575: 5570: 5568:Contraharmonic 5565: 5560: 5549: 5547: 5538: 5528: 5527: 5515: 5514: 5512: 5511: 5506: 5500: 5497: 5496: 5489: 5488: 5481: 5474: 5466: 5457: 5456: 5454: 5453: 5448: 5443: 5431: 5426: 5420: 5417: 5416: 5414: 5413: 5408: 5403: 5395: 5394: 5389: 5378: 5373: 5368: 5363: 5357: 5349: 5348: 5343: 5338: 5333: 5325: 5324: 5319: 5314: 5309: 5301: 5299: 5286: 5285: 5283: 5282: 5277: 5271: 5270: 5258: 5246: 5241: 5233: 5232: 5224: 5219: 5211: 5210: 5205: 5200: 5194: 5192: 5181: 5180: 5178: 5177: 5172: 5167: 5160: 5155: 5150: 5145: 5140: 5135: 5127: 5125: 5114: 5113: 5111: 5110: 5105: 5100: 5095: 5090: 5085: 5078:Optimal design 5073: 5072: 5067: 5062: 5050: 5045: 5040: 5034: 5032: 5024: 5023: 5016: 5015: 5008: 5001: 4993: 4984: 4983: 4981: 4980: 4968: 4956: 4942: 4929: 4926: 4925: 4922: 4921: 4918: 4917: 4915: 4914: 4909: 4904: 4899: 4894: 4888: 4886: 4880: 4879: 4877: 4876: 4871: 4866: 4861: 4856: 4851: 4846: 4841: 4836: 4831: 4825: 4823: 4817: 4816: 4814: 4813: 4808: 4803: 4794: 4789: 4784: 4778: 4776: 4770: 4769: 4767: 4766: 4761: 4756: 4747: 4745:Bioinformatics 4741: 4739: 4729: 4728: 4716: 4715: 4712: 4711: 4708: 4707: 4704: 4703: 4701: 4700: 4694: 4692: 4688: 4687: 4685: 4684: 4678: 4676: 4670: 4669: 4667: 4666: 4661: 4656: 4651: 4645: 4643: 4634: 4628: 4627: 4624: 4623: 4621: 4620: 4615: 4610: 4605: 4600: 4594: 4592: 4586: 4585: 4583: 4582: 4577: 4572: 4564: 4559: 4554: 4553: 4552: 4550:partial (PACF) 4541: 4539: 4533: 4532: 4530: 4529: 4524: 4519: 4511: 4506: 4500: 4498: 4497:Specific tests 4494: 4493: 4491: 4490: 4485: 4480: 4475: 4470: 4465: 4460: 4455: 4449: 4447: 4440: 4434: 4433: 4431: 4430: 4429: 4428: 4427: 4426: 4411: 4410: 4409: 4399: 4397:Classification 4394: 4389: 4384: 4379: 4374: 4369: 4363: 4361: 4355: 4354: 4352: 4351: 4346: 4344:McNemar's test 4341: 4336: 4331: 4326: 4320: 4318: 4308: 4307: 4283: 4282: 4279: 4278: 4275: 4274: 4272: 4271: 4266: 4261: 4256: 4250: 4248: 4242: 4241: 4239: 4238: 4222: 4216: 4214: 4208: 4207: 4205: 4204: 4199: 4194: 4189: 4184: 4182:Semiparametric 4179: 4174: 4168: 4166: 4162: 4161: 4159: 4158: 4153: 4148: 4143: 4137: 4135: 4129: 4128: 4126: 4125: 4120: 4115: 4110: 4105: 4099: 4097: 4091: 4090: 4088: 4087: 4082: 4077: 4072: 4066: 4064: 4054: 4053: 4050: 4049: 4044: 4038: 4030: 4029: 4026: 4025: 4022: 4021: 4019: 4018: 4017: 4016: 4006: 4001: 3996: 3995: 3994: 3989: 3978: 3976: 3970: 3969: 3966: 3965: 3963: 3962: 3957: 3956: 3955: 3947: 3939: 3923: 3920:(Mann–Whitney) 3915: 3914: 3913: 3900: 3899: 3898: 3887: 3885: 3879: 3878: 3876: 3875: 3874: 3873: 3868: 3863: 3853: 3848: 3845:(Shapiro–Wilk) 3840: 3835: 3830: 3825: 3820: 3812: 3806: 3804: 3798: 3797: 3795: 3794: 3786: 3777: 3765: 3759: 3757:Specific tests 3753: 3752: 3749: 3748: 3746: 3745: 3740: 3735: 3729: 3727: 3721: 3720: 3718: 3717: 3712: 3711: 3710: 3700: 3699: 3698: 3688: 3682: 3680: 3674: 3673: 3671: 3670: 3669: 3668: 3663: 3653: 3648: 3643: 3638: 3633: 3627: 3625: 3619: 3618: 3616: 3615: 3610: 3609: 3608: 3603: 3602: 3601: 3596: 3581: 3580: 3579: 3574: 3569: 3564: 3553: 3551: 3542: 3536: 3535: 3533: 3532: 3527: 3522: 3521: 3520: 3510: 3505: 3504: 3503: 3493: 3492: 3491: 3486: 3481: 3471: 3466: 3461: 3460: 3459: 3454: 3449: 3433: 3432: 3431: 3426: 3421: 3411: 3410: 3409: 3404: 3394: 3393: 3392: 3382: 3381: 3380: 3370: 3365: 3360: 3354: 3352: 3342: 3341: 3329: 3328: 3325: 3324: 3321: 3320: 3318: 3317: 3312: 3307: 3302: 3296: 3294: 3288: 3287: 3285: 3284: 3279: 3274: 3268: 3266: 3262: 3261: 3259: 3258: 3253: 3248: 3243: 3238: 3233: 3228: 3222: 3220: 3214: 3213: 3211: 3210: 3208:Standard error 3205: 3200: 3195: 3194: 3193: 3188: 3177: 3175: 3169: 3168: 3166: 3165: 3160: 3155: 3150: 3145: 3140: 3138:Optimal design 3135: 3130: 3124: 3122: 3112: 3111: 3099: 3098: 3095: 3094: 3091: 3090: 3088: 3087: 3082: 3077: 3072: 3067: 3062: 3057: 3052: 3047: 3042: 3037: 3032: 3027: 3022: 3017: 3011: 3009: 3003: 3002: 3000: 2999: 2994: 2993: 2992: 2987: 2977: 2972: 2966: 2964: 2958: 2957: 2955: 2954: 2949: 2944: 2938: 2936: 2935:Summary tables 2932: 2931: 2929: 2928: 2922: 2920: 2914: 2913: 2910: 2909: 2907: 2906: 2905: 2904: 2899: 2894: 2884: 2878: 2876: 2870: 2869: 2867: 2866: 2861: 2856: 2851: 2846: 2841: 2836: 2830: 2828: 2822: 2821: 2819: 2818: 2813: 2808: 2807: 2806: 2801: 2796: 2791: 2786: 2781: 2776: 2771: 2769:Contraharmonic 2766: 2761: 2750: 2748: 2739: 2729: 2728: 2716: 2715: 2713: 2712: 2707: 2701: 2698: 2697: 2690: 2689: 2682: 2675: 2667: 2661: 2660: 2625: 2607:(1–2): 70–79. 2596: 2590: 2568: 2562: 2549: 2543: 2527: 2521: 2501: 2495: 2482: 2481: 2480: 2474: 2457: 2451: 2428: 2411: 2405: 2389: 2371:(4): 362–363. 2360: 2346: 2329: 2323: 2306: 2300: 2285: 2257: 2239: 2213:(3): 181–211. 2201:Anscombe, F.J. 2197: 2168: 2134: 2131: 2130: 2129: 2111: 2110: 2050: 2001: 1960: 1951: 1938: 1929: 1920: 1908: 1879: 1872: 1837: 1804: 1777: 1726: 1725: 1723: 1720: 1719: 1718: 1713: 1708: 1703: 1701:Optimal design 1698: 1693: 1688: 1683: 1678: 1672: 1671: 1655: 1652: 1651: 1650: 1645: 1640: 1635: 1629: 1621: 1618: 1617: 1616: 1608: 1587: 1584: 1578: 1575: 1550: 1547: 1542: 1537: 1534: 1528: 1525: 1510: 1504: 1496: 1475: 1472: 1466: 1463: 1438: 1435: 1430: 1425: 1422: 1416: 1413: 1398: 1392: 1378: 1375: 1356: 1353: 1352: 1351: 1347: 1336: 1331: 1327: 1316: 1311: 1305: 1301: 1296: 1292: 1287: 1280: 1269: 1262: 1253: 1252: 1240: 1237: 1234: 1231: 1228: 1222: 1219: 1216: 1213: 1210: 1207: 1203: 1198: 1194: 1190: 1185: 1181: 1177: 1174: 1171: 1166: 1163: 1159: 1143: 1140: 1130: 1129: 1126: 1123: 1120: 1116: 1115: 1112: 1109: 1106: 1102: 1101: 1098: 1095: 1092: 1088: 1087: 1084: 1081: 1078: 1074: 1073: 1068: 1063: 1058: 1046: 1039: 1032: 1025: 1018: 1015: 1012: 1011: 1008: 1004: 1003: 1000: 996: 995: 992: 988: 987: 984: 980: 979: 976: 972: 971: 968: 964: 963: 960: 956: 955: 952: 948: 947: 944: 940: 939: 936: 932: 931: 928: 924: 923: 920: 916: 915: 912: 907: 904: 893: 892: 888: 881: 872: 866: 863: 856: 851: 848: 841: 836: 832: 825: 811: 804: 797: 794: 777: 774: 773: 772: 764: 760: 759: 758: 747: 733: 728: 724: 719: 715: 710: 706: 695: 694: 690: 676: 664: 657: 652: 647: 640: 639: 628: 618: 607: 597: 586: 575: 574: 571: 564: 557: 550: 545: 542: 538: 537: 534: 527: 520: 515: 512: 508: 507: 504: 497: 492: 489: 485: 484: 478: 472: 455: 452: 450: 447: 438: 435: 425: 422: 413: 410: 405: 402: 397: 394: 385: 384:Implementation 382: 377: 376: 368: 365: 359: 356: 334: 331: 294:theory of the 287: 284: 242: 239: 238: 237: 199: 193: 176:patients in a 149: 146: 132: 129: 111: 108: 85:theory of the 77: 76: 31: 29: 22: 15: 9: 6: 4: 3: 2: 8071: 8060: 8057: 8056: 8054: 8039: 8036: 8034: 8031: 8030: 8028: 8024: 8018: 8015: 8013: 8010: 8008: 8005: 8003: 8000: 7998: 7995: 7994: 7992: 7988: 7982: 7979: 7977: 7974: 7972: 7969: 7967: 7964: 7962: 7959: 7957: 7954: 7952: 7949: 7947: 7944: 7942: 7939: 7937: 7934: 7932: 7929: 7927: 7924: 7922: 7919: 7918: 7916: 7914: 7910: 7902: 7899: 7898: 7896: 7892: 7889: 7888: 7887:Graph theory 7886: 7882: 7879: 7877: 7874: 7873: 7872: 7869: 7865: 7862: 7860: 7857: 7856: 7855: 7854:Combinatorics 7852: 7851: 7849: 7845: 7839: 7836: 7834: 7831: 7830: 7828: 7824: 7820: 7813: 7808: 7806: 7801: 7799: 7794: 7793: 7790: 7778: 7777: 7768: 7766: 7765: 7756: 7754: 7753: 7748: 7742: 7740: 7739: 7730: 7729: 7726: 7712: 7709: 7707: 7706:Geostatistics 7704: 7702: 7699: 7697: 7694: 7692: 7689: 7688: 7686: 7684: 7680: 7674: 7673:Psychometrics 7671: 7669: 7666: 7664: 7661: 7659: 7656: 7654: 7651: 7649: 7646: 7644: 7641: 7639: 7636: 7634: 7631: 7629: 7626: 7625: 7623: 7621: 7617: 7611: 7608: 7606: 7603: 7601: 7597: 7594: 7592: 7589: 7587: 7584: 7582: 7579: 7578: 7576: 7574: 7570: 7564: 7561: 7559: 7556: 7554: 7550: 7547: 7545: 7542: 7541: 7539: 7537: 7536:Biostatistics 7533: 7529: 7525: 7520: 7516: 7498: 7497:Log-rank test 7495: 7494: 7492: 7488: 7482: 7479: 7478: 7476: 7474: 7470: 7464: 7461: 7459: 7456: 7454: 7451: 7449: 7446: 7445: 7443: 7441: 7437: 7434: 7432: 7428: 7418: 7415: 7413: 7410: 7408: 7405: 7403: 7400: 7398: 7395: 7394: 7392: 7390: 7386: 7380: 7377: 7375: 7372: 7370: 7368:(Box–Jenkins) 7364: 7362: 7359: 7357: 7354: 7350: 7347: 7346: 7345: 7342: 7341: 7339: 7337: 7333: 7327: 7324: 7322: 7321:Durbin–Watson 7319: 7317: 7311: 7309: 7306: 7304: 7303:Dickey–Fuller 7301: 7300: 7298: 7294: 7288: 7285: 7283: 7280: 7278: 7277:Cointegration 7275: 7273: 7270: 7268: 7265: 7263: 7260: 7258: 7255: 7253: 7252:Decomposition 7250: 7249: 7247: 7243: 7240: 7238: 7234: 7224: 7221: 7220: 7219: 7216: 7215: 7214: 7211: 7207: 7204: 7203: 7202: 7199: 7197: 7194: 7192: 7189: 7187: 7184: 7182: 7179: 7177: 7174: 7172: 7169: 7167: 7164: 7163: 7161: 7159: 7155: 7149: 7146: 7144: 7141: 7139: 7136: 7134: 7131: 7129: 7126: 7124: 7123:Cohen's kappa 7121: 7120: 7118: 7116: 7112: 7108: 7104: 7100: 7096: 7092: 7087: 7083: 7069: 7066: 7064: 7061: 7059: 7056: 7054: 7051: 7050: 7048: 7046: 7042: 7036: 7032: 7028: 7022: 7020: 7017: 7016: 7014: 7012: 7008: 7002: 6999: 6997: 6994: 6992: 6989: 6987: 6984: 6982: 6979: 6977: 6976:Nonparametric 6974: 6972: 6969: 6968: 6966: 6962: 6956: 6953: 6951: 6948: 6946: 6943: 6941: 6938: 6937: 6935: 6933: 6929: 6923: 6920: 6918: 6915: 6913: 6910: 6908: 6905: 6903: 6900: 6899: 6897: 6895: 6891: 6885: 6882: 6880: 6877: 6875: 6872: 6870: 6867: 6866: 6864: 6862: 6858: 6854: 6847: 6844: 6842: 6839: 6838: 6834: 6830: 6814: 6811: 6810: 6809: 6806: 6804: 6801: 6799: 6796: 6792: 6789: 6787: 6784: 6783: 6782: 6779: 6778: 6776: 6774: 6770: 6760: 6757: 6753: 6747: 6745: 6739: 6737: 6731: 6730: 6729: 6726: 6725:Nonparametric 6723: 6721: 6715: 6711: 6708: 6707: 6706: 6700: 6696: 6695:Sample median 6693: 6692: 6691: 6688: 6687: 6685: 6683: 6679: 6671: 6668: 6666: 6663: 6661: 6658: 6657: 6656: 6653: 6651: 6648: 6646: 6640: 6638: 6635: 6633: 6630: 6628: 6625: 6623: 6620: 6618: 6616: 6612: 6610: 6607: 6606: 6604: 6602: 6598: 6592: 6590: 6586: 6584: 6582: 6577: 6575: 6570: 6566: 6565: 6562: 6559: 6557: 6553: 6543: 6540: 6538: 6535: 6533: 6530: 6529: 6527: 6525: 6521: 6515: 6512: 6508: 6505: 6504: 6503: 6500: 6496: 6493: 6492: 6491: 6488: 6486: 6483: 6482: 6480: 6478: 6474: 6466: 6463: 6461: 6458: 6457: 6456: 6453: 6451: 6448: 6446: 6443: 6441: 6438: 6436: 6433: 6431: 6428: 6427: 6425: 6423: 6419: 6413: 6410: 6406: 6403: 6399: 6396: 6394: 6391: 6390: 6389: 6386: 6385: 6384: 6381: 6377: 6374: 6372: 6369: 6367: 6364: 6362: 6359: 6358: 6357: 6354: 6353: 6351: 6349: 6345: 6342: 6340: 6336: 6330: 6327: 6325: 6322: 6318: 6315: 6314: 6313: 6310: 6308: 6305: 6301: 6300:loss function 6298: 6297: 6296: 6293: 6289: 6286: 6284: 6281: 6279: 6276: 6275: 6274: 6271: 6269: 6266: 6264: 6261: 6257: 6254: 6252: 6249: 6247: 6241: 6238: 6237: 6236: 6233: 6229: 6226: 6224: 6221: 6219: 6216: 6215: 6214: 6211: 6207: 6204: 6202: 6199: 6198: 6197: 6194: 6190: 6187: 6186: 6185: 6182: 6178: 6175: 6174: 6173: 6170: 6168: 6165: 6163: 6160: 6158: 6155: 6154: 6152: 6150: 6146: 6142: 6138: 6133: 6129: 6115: 6112: 6110: 6107: 6105: 6102: 6100: 6097: 6096: 6094: 6092: 6088: 6082: 6079: 6077: 6074: 6072: 6069: 6068: 6066: 6062: 6056: 6053: 6051: 6048: 6046: 6043: 6041: 6038: 6036: 6033: 6031: 6028: 6026: 6023: 6022: 6020: 6018: 6014: 6008: 6005: 6003: 6002:Questionnaire 6000: 5998: 5995: 5991: 5988: 5986: 5983: 5982: 5981: 5978: 5977: 5975: 5973: 5969: 5963: 5960: 5958: 5955: 5953: 5950: 5948: 5945: 5943: 5940: 5938: 5935: 5933: 5930: 5928: 5925: 5924: 5922: 5920: 5916: 5912: 5908: 5903: 5899: 5885: 5882: 5880: 5877: 5875: 5872: 5870: 5867: 5865: 5862: 5860: 5857: 5855: 5852: 5850: 5847: 5845: 5842: 5840: 5837: 5835: 5832: 5830: 5829:Control chart 5827: 5825: 5822: 5820: 5817: 5815: 5812: 5811: 5809: 5807: 5803: 5797: 5794: 5790: 5787: 5785: 5782: 5781: 5780: 5777: 5775: 5772: 5770: 5767: 5766: 5764: 5762: 5758: 5752: 5749: 5747: 5744: 5742: 5739: 5738: 5736: 5732: 5726: 5723: 5722: 5720: 5718: 5714: 5702: 5699: 5697: 5694: 5692: 5689: 5688: 5687: 5684: 5682: 5679: 5678: 5676: 5674: 5670: 5664: 5661: 5659: 5656: 5654: 5651: 5649: 5646: 5644: 5641: 5639: 5636: 5634: 5631: 5630: 5628: 5626: 5622: 5616: 5613: 5611: 5608: 5604: 5601: 5599: 5596: 5594: 5591: 5589: 5586: 5584: 5581: 5579: 5576: 5574: 5571: 5569: 5566: 5564: 5561: 5559: 5556: 5555: 5554: 5551: 5550: 5548: 5546: 5542: 5539: 5537: 5533: 5529: 5525: 5520: 5516: 5510: 5507: 5505: 5502: 5501: 5498: 5494: 5487: 5482: 5480: 5475: 5473: 5468: 5467: 5464: 5452: 5449: 5447: 5444: 5442: 5437: 5432: 5430: 5427: 5425: 5422: 5421: 5418: 5412: 5409: 5407: 5404: 5402: 5401: 5397: 5396: 5393: 5390: 5388: 5387: 5382: 5379: 5377: 5374: 5372: 5369: 5367: 5364: 5361: 5358: 5356: 5355: 5351: 5350: 5347: 5344: 5342: 5339: 5337: 5334: 5332: 5331: 5327: 5326: 5323: 5320: 5318: 5315: 5313: 5310: 5308: 5307: 5303: 5302: 5300: 5298: 5291: 5287: 5281: 5278: 5276: 5275:Compare means 5273: 5272: 5269: 5267: 5263: 5259: 5257: 5255: 5251: 5247: 5245: 5242: 5240: 5239: 5235: 5234: 5231: 5228: 5225: 5223: 5220: 5218: 5217: 5216:Random effect 5213: 5212: 5209: 5206: 5204: 5201: 5199: 5196: 5195: 5193: 5191: 5186: 5182: 5176: 5173: 5171: 5168: 5166: 5165: 5161: 5159: 5158:Orthogonality 5156: 5154: 5151: 5149: 5146: 5144: 5141: 5139: 5136: 5134: 5133: 5129: 5128: 5126: 5124: 5119: 5115: 5109: 5106: 5104: 5101: 5099: 5096: 5094: 5093:Randomization 5091: 5089: 5086: 5084: 5080: 5079: 5075: 5074: 5071: 5068: 5066: 5063: 5061: 5058: 5054: 5051: 5049: 5046: 5044: 5041: 5039: 5036: 5035: 5033: 5031: 5025: 5021: 5014: 5009: 5007: 5002: 5000: 4995: 4994: 4991: 4979: 4978: 4969: 4967: 4966: 4957: 4955: 4954: 4949: 4943: 4941: 4940: 4931: 4930: 4927: 4913: 4910: 4908: 4907:Geostatistics 4905: 4903: 4900: 4898: 4895: 4893: 4890: 4889: 4887: 4885: 4881: 4875: 4874:Psychometrics 4872: 4870: 4867: 4865: 4862: 4860: 4857: 4855: 4852: 4850: 4847: 4845: 4842: 4840: 4837: 4835: 4832: 4830: 4827: 4826: 4824: 4822: 4818: 4812: 4809: 4807: 4804: 4802: 4798: 4795: 4793: 4790: 4788: 4785: 4783: 4780: 4779: 4777: 4775: 4771: 4765: 4762: 4760: 4757: 4755: 4751: 4748: 4746: 4743: 4742: 4740: 4738: 4737:Biostatistics 4734: 4730: 4726: 4721: 4717: 4699: 4698:Log-rank test 4696: 4695: 4693: 4689: 4683: 4680: 4679: 4677: 4675: 4671: 4665: 4662: 4660: 4657: 4655: 4652: 4650: 4647: 4646: 4644: 4642: 4638: 4635: 4633: 4629: 4619: 4616: 4614: 4611: 4609: 4606: 4604: 4601: 4599: 4596: 4595: 4593: 4591: 4587: 4581: 4578: 4576: 4573: 4571: 4569:(Box–Jenkins) 4565: 4563: 4560: 4558: 4555: 4551: 4548: 4547: 4546: 4543: 4542: 4540: 4538: 4534: 4528: 4525: 4523: 4522:Durbin–Watson 4520: 4518: 4512: 4510: 4507: 4505: 4504:Dickey–Fuller 4502: 4501: 4499: 4495: 4489: 4486: 4484: 4481: 4479: 4478:Cointegration 4476: 4474: 4471: 4469: 4466: 4464: 4461: 4459: 4456: 4454: 4453:Decomposition 4451: 4450: 4448: 4444: 4441: 4439: 4435: 4425: 4422: 4421: 4420: 4417: 4416: 4415: 4412: 4408: 4405: 4404: 4403: 4400: 4398: 4395: 4393: 4390: 4388: 4385: 4383: 4380: 4378: 4375: 4373: 4370: 4368: 4365: 4364: 4362: 4360: 4356: 4350: 4347: 4345: 4342: 4340: 4337: 4335: 4332: 4330: 4327: 4325: 4324:Cohen's kappa 4322: 4321: 4319: 4317: 4313: 4309: 4305: 4301: 4297: 4293: 4288: 4284: 4270: 4267: 4265: 4262: 4260: 4257: 4255: 4252: 4251: 4249: 4247: 4243: 4237: 4233: 4229: 4223: 4221: 4218: 4217: 4215: 4213: 4209: 4203: 4200: 4198: 4195: 4193: 4190: 4188: 4185: 4183: 4180: 4178: 4177:Nonparametric 4175: 4173: 4170: 4169: 4167: 4163: 4157: 4154: 4152: 4149: 4147: 4144: 4142: 4139: 4138: 4136: 4134: 4130: 4124: 4121: 4119: 4116: 4114: 4111: 4109: 4106: 4104: 4101: 4100: 4098: 4096: 4092: 4086: 4083: 4081: 4078: 4076: 4073: 4071: 4068: 4067: 4065: 4063: 4059: 4055: 4048: 4045: 4043: 4040: 4039: 4035: 4031: 4015: 4012: 4011: 4010: 4007: 4005: 4002: 4000: 3997: 3993: 3990: 3988: 3985: 3984: 3983: 3980: 3979: 3977: 3975: 3971: 3961: 3958: 3954: 3948: 3946: 3940: 3938: 3932: 3931: 3930: 3927: 3926:Nonparametric 3924: 3922: 3916: 3912: 3909: 3908: 3907: 3901: 3897: 3896:Sample median 3894: 3893: 3892: 3889: 3888: 3886: 3884: 3880: 3872: 3869: 3867: 3864: 3862: 3859: 3858: 3857: 3854: 3852: 3849: 3847: 3841: 3839: 3836: 3834: 3831: 3829: 3826: 3824: 3821: 3819: 3817: 3813: 3811: 3808: 3807: 3805: 3803: 3799: 3793: 3791: 3787: 3785: 3783: 3778: 3776: 3771: 3767: 3766: 3763: 3760: 3758: 3754: 3744: 3741: 3739: 3736: 3734: 3731: 3730: 3728: 3726: 3722: 3716: 3713: 3709: 3706: 3705: 3704: 3701: 3697: 3694: 3693: 3692: 3689: 3687: 3684: 3683: 3681: 3679: 3675: 3667: 3664: 3662: 3659: 3658: 3657: 3654: 3652: 3649: 3647: 3644: 3642: 3639: 3637: 3634: 3632: 3629: 3628: 3626: 3624: 3620: 3614: 3611: 3607: 3604: 3600: 3597: 3595: 3592: 3591: 3590: 3587: 3586: 3585: 3582: 3578: 3575: 3573: 3570: 3568: 3565: 3563: 3560: 3559: 3558: 3555: 3554: 3552: 3550: 3546: 3543: 3541: 3537: 3531: 3528: 3526: 3523: 3519: 3516: 3515: 3514: 3511: 3509: 3506: 3502: 3501:loss function 3499: 3498: 3497: 3494: 3490: 3487: 3485: 3482: 3480: 3477: 3476: 3475: 3472: 3470: 3467: 3465: 3462: 3458: 3455: 3453: 3450: 3448: 3442: 3439: 3438: 3437: 3434: 3430: 3427: 3425: 3422: 3420: 3417: 3416: 3415: 3412: 3408: 3405: 3403: 3400: 3399: 3398: 3395: 3391: 3388: 3387: 3386: 3383: 3379: 3376: 3375: 3374: 3371: 3369: 3366: 3364: 3361: 3359: 3356: 3355: 3353: 3351: 3347: 3343: 3339: 3334: 3330: 3316: 3313: 3311: 3308: 3306: 3303: 3301: 3298: 3297: 3295: 3293: 3289: 3283: 3280: 3278: 3275: 3273: 3270: 3269: 3267: 3263: 3257: 3254: 3252: 3249: 3247: 3244: 3242: 3239: 3237: 3234: 3232: 3229: 3227: 3224: 3223: 3221: 3219: 3215: 3209: 3206: 3204: 3203:Questionnaire 3201: 3199: 3196: 3192: 3189: 3187: 3184: 3183: 3182: 3179: 3178: 3176: 3174: 3170: 3164: 3161: 3159: 3156: 3154: 3151: 3149: 3146: 3144: 3141: 3139: 3136: 3134: 3131: 3129: 3126: 3125: 3123: 3121: 3117: 3113: 3109: 3104: 3100: 3086: 3083: 3081: 3078: 3076: 3073: 3071: 3068: 3066: 3063: 3061: 3058: 3056: 3053: 3051: 3048: 3046: 3043: 3041: 3038: 3036: 3033: 3031: 3030:Control chart 3028: 3026: 3023: 3021: 3018: 3016: 3013: 3012: 3010: 3008: 3004: 2998: 2995: 2991: 2988: 2986: 2983: 2982: 2981: 2978: 2976: 2973: 2971: 2968: 2967: 2965: 2963: 2959: 2953: 2950: 2948: 2945: 2943: 2940: 2939: 2937: 2933: 2927: 2924: 2923: 2921: 2919: 2915: 2903: 2900: 2898: 2895: 2893: 2890: 2889: 2888: 2885: 2883: 2880: 2879: 2877: 2875: 2871: 2865: 2862: 2860: 2857: 2855: 2852: 2850: 2847: 2845: 2842: 2840: 2837: 2835: 2832: 2831: 2829: 2827: 2823: 2817: 2814: 2812: 2809: 2805: 2802: 2800: 2797: 2795: 2792: 2790: 2787: 2785: 2782: 2780: 2777: 2775: 2772: 2770: 2767: 2765: 2762: 2760: 2757: 2756: 2755: 2752: 2751: 2749: 2747: 2743: 2740: 2738: 2734: 2730: 2726: 2721: 2717: 2711: 2708: 2706: 2703: 2702: 2699: 2695: 2688: 2683: 2681: 2676: 2674: 2669: 2668: 2665: 2657: 2653: 2648: 2643: 2639: 2635: 2631: 2626: 2622: 2618: 2614: 2610: 2606: 2602: 2597: 2593: 2591:0-19-853256-3 2587: 2583: 2582: 2577: 2573: 2569: 2565: 2563:0-387-96991-8 2559: 2555: 2550: 2546: 2544:981-256-360-1 2540: 2536: 2532: 2528: 2524: 2522:0-486-65685-3 2518: 2513: 2512: 2506: 2502: 2498: 2496:0-9616255-2-X 2492: 2488: 2483: 2477: 2471: 2467: 2463: 2458: 2454: 2448: 2444: 2440: 2435: 2434: 2431: 2425: 2421: 2417: 2412: 2408: 2406:0-88275-105-0 2402: 2398: 2394: 2390: 2386: 2382: 2378: 2374: 2370: 2366: 2361: 2357: 2353: 2349: 2347:0-387-95470-8 2343: 2338: 2337: 2330: 2326: 2324:0-387-98578-6 2320: 2315: 2314: 2307: 2303: 2297: 2293: 2292: 2286: 2281: 2275: 2260: 2254: 2250: 2249: 2244: 2240: 2236: 2232: 2228: 2224: 2220: 2216: 2212: 2208: 2207: 2202: 2198: 2194: 2190: 2186: 2182: 2178: 2174: 2169: 2165: 2161: 2157: 2153: 2149: 2145: 2141: 2137: 2136: 2128: 2125:from the 2124: 2115: 2114: 2106: 2102: 2097: 2092: 2088: 2084: 2080: 2076: 2072: 2068: 2064: 2057: 2055: 2046: 2042: 2038: 2034: 2029: 2024: 2021:(1): 69–100. 2020: 2016: 2012: 2005: 1997: 1993: 1988: 1983: 1979: 1975: 1971: 1964: 1955: 1948: 1942: 1933: 1924: 1911: 1905: 1901: 1897: 1893: 1889: 1883: 1875: 1869: 1865: 1861: 1857: 1856: 1848: 1846: 1844: 1842: 1827: 1823: 1817: 1815: 1813: 1811: 1809: 1794: 1790: 1784: 1782: 1773: 1769: 1765: 1761: 1757: 1753: 1749: 1745: 1741: 1734: 1732: 1727: 1717: 1716:Blockmodeling 1714: 1712: 1709: 1707: 1704: 1702: 1699: 1697: 1694: 1692: 1689: 1687: 1684: 1682: 1679: 1677: 1674: 1673: 1669: 1663: 1658: 1649: 1646: 1644: 1641: 1639: 1636: 1633: 1632:Latin squares 1630: 1627: 1624: 1623: 1614: 1607: 1603: 1585: 1582: 1573: 1545: 1540: 1535: 1532: 1523: 1509: 1506:Estimate for 1505: 1502: 1495: 1491: 1473: 1470: 1461: 1433: 1428: 1423: 1420: 1411: 1397: 1394:Estimate for 1393: 1373: 1363: 1360:Estimate for 1359: 1358: 1346: 1342: 1335: 1332: 1326: 1322: 1315: 1312: 1309: 1306: 1300: 1297: 1291: 1288: 1286: 1279: 1275: 1268: 1261: 1258: 1257: 1256: 1201: 1196: 1192: 1188: 1183: 1179: 1175: 1172: 1169: 1164: 1161: 1157: 1149: 1148: 1147: 1139: 1137: 1127: 1124: 1121: 1118: 1117: 1113: 1110: 1107: 1104: 1103: 1099: 1096: 1093: 1090: 1089: 1085: 1082: 1079: 1076: 1075: 1072: 1069: 1067: 1064: 1062: 1059: 1057: 1054: 1053: 1050: 1045: 1038: 1031: 1024: 1009: 1006: 1005: 1001: 998: 997: 993: 990: 989: 985: 982: 981: 977: 974: 973: 969: 966: 965: 961: 958: 957: 953: 950: 949: 945: 942: 941: 937: 934: 933: 929: 926: 925: 921: 918: 917: 911: 908: 903: 900: 899: 896: 887: 880: 876: 873: 870: 867: 862: 855: 852: 847: 840: 837: 831: 824: 820: 817: 816: 815: 810: 803: 793: 789: 785: 782: 771: 767: 761: 745: 738: 737: 732: 729: 723: 720: 714: 711: 705: 702: 701: 700: 693: 674: 663: 656: 653: 651: 648: 645: 642: 641: 626: 619: 605: 598: 584: 577: 576: 570: 563: 556: 549: 546: 543: 541:4-factor RBD 540: 539: 533: 526: 519: 516: 513: 511:3-factor RBD 510: 509: 503: 496: 493: 490: 488:2-factor RBD 487: 486: 483: 479: 477: 473: 470: 469: 463: 461: 446: 444: 434: 432: 421: 419: 409: 401: 393: 391: 381: 380:randomizing. 374: 373: 372: 364: 351: 347: 339: 330: 328: 324: 319: 311: 307: 305: 301: 297: 293: 283: 279: 275: 273: 272:Randomization 267: 265: 255: 247: 235: 231: 230:control group 227: 223: 219: 215: 211: 207: 203: 200: 197: 194: 191: 187: 183: 179: 175: 171: 167: 166: 161: 160: 155: 152: 151: 145: 144:interaction. 142: 138: 128: 125: 121: 117: 107: 105: 101: 100:Ronald Fisher 96: 92: 88: 84: 73: 70: 62: 52: 48: 42: 41: 35: 30: 21: 20: 8026:Applications 7900: 7859:Block design 7774: 7762: 7743: 7736: 7648:Econometrics 7598: / 7581:Chemometrics 7558:Epidemiology 7551: / 7524:Applications 7366:ARIMA model 7313:Q-statistic 7262:Stationarity 7158:Multivariate 7101: / 7097: / 7095:Multivariate 7093: / 7033: / 7029: / 6803:Bayes factor 6702:Signed rank 6614: 6588: 6580: 6568: 6263:Completeness 6099:Cohort study 6024: 5997:Opinion poll 5932:Missing data 5919:Study design 5874:Scatter plot 5796:Scatter plot 5789:Spearman's ρ 5751:Grouped data 5398: 5384: 5366:Latin square 5352: 5328: 5304: 5265: 5261: 5254:multivariate 5253: 5249: 5236: 5214: 5163: 5162: 5130: 5122: 5076: 4975: 4963: 4944: 4937: 4849:Econometrics 4799: / 4782:Chemometrics 4759:Epidemiology 4752: / 4725:Applications 4567:ARIMA model 4514:Q-statistic 4463:Stationarity 4359:Multivariate 4302: / 4298: / 4296:Multivariate 4294: / 4234: / 4230: / 4004:Bayes factor 3903:Signed rank 3815: 3789: 3781: 3769: 3464:Completeness 3300:Cohort study 3225: 3198:Opinion poll 3133:Missing data 3120:Study design 3075:Scatter plot 2997:Scatter plot 2990:Spearman's ρ 2952:Grouped data 2637: 2633: 2604: 2600: 2580: 2553: 2534: 2510: 2486: 2465: 2442: 2419: 2396: 2368: 2364: 2335: 2312: 2290: 2263:. Retrieved 2247: 2243:Bailey, R. A 2210: 2204: 2176: 2172: 2150:(4): 35–36. 2147: 2143: 2140:Addelman, S. 2133:Bibliography 2070: 2066: 2018: 2014: 2004: 1977: 1973: 1963: 1954: 1941: 1932: 1923: 1913:, retrieved 1891: 1882: 1854: 1829:. Retrieved 1825: 1796:. Retrieved 1792: 1747: 1743: 1681:Block design 1612: 1605: 1601: 1507: 1500: 1493: 1489: 1395: 1361: 1344: 1340: 1333: 1324: 1320: 1313: 1307: 1298: 1289: 1284: 1277: 1273: 1266: 1259: 1254: 1145: 1135: 1133: 1070: 1065: 1060: 1055: 1043: 1036: 1029: 1022: 1020: 909: 901: 894: 885: 878: 874: 868: 860: 853: 845: 838: 829: 822: 818: 808: 801: 799: 790: 786: 783: 779: 769: 762: 730: 721: 712: 703: 698: 688: 661: 654: 649: 646:-factor RBD 643: 568: 561: 554: 547: 531: 524: 517: 501: 494: 481: 475: 457: 440: 427: 415: 407: 399: 387: 378: 370: 361: 344: 323:S. Bernstein 320: 316: 289: 280: 276: 268: 260: 236:block design 226:block design 213: 209: 205: 202:Intervention 201: 195: 189: 185: 181: 178:double blind 173: 169: 163: 157: 153: 141:interactions 134: 124:Latin square 113: 90: 80: 65: 59:January 2018 56: 37: 7897:Statistics 7776:WikiProject 7691:Cartography 7653:Jurimetrics 7605:Reliability 7336:Time domain 7315:(Ljung–Box) 7237:Time-series 7115:Categorical 7099:Time-series 7091:Categorical 7026:(Bernoulli) 6861:Correlation 6841:Correlation 6637:Jarque–Bera 6609:Chi-squared 6371:M-estimator 6324:Asymptotics 6268:Sufficiency 6035:Interaction 5947:Replication 5927:Effect size 5884:Violin plot 5864:Radar chart 5844:Forest plot 5834:Correlogram 5784:Kendall's τ 5341:Box–Behnken 5222:Mixed model 5153:Confounding 5148:Interaction 5138:Effect size 5108:Sample size 4977:WikiProject 4892:Cartography 4854:Jurimetrics 4806:Reliability 4537:Time domain 4516:(Ljung–Box) 4438:Time-series 4316:Categorical 4300:Time-series 4292:Categorical 4227:(Bernoulli) 4062:Correlation 4042:Correlation 3838:Jarque–Bera 3810:Chi-squared 3572:M-estimator 3525:Asymptotics 3469:Sufficiency 3236:Interaction 3148:Replication 3128:Effect size 3085:Violin plot 3065:Radar chart 3045:Forest plot 3035:Correlogram 2985:Kendall's τ 1343:(of factor 1323:(of factor 437:Replication 304:variability 292:statistical 218:randomizing 83:statistical 51:introducing 7926:Fano plane 7891:Hypergraph 7643:Demography 7361:ARMA model 7166:Regression 6743:(Friedman) 6704:(Wilcoxon) 6642:Normality 6632:Lilliefors 6579:Student's 6455:Resampling 6329:Robustness 6317:divergence 6307:Efficiency 6245:(monotone) 6240:Likelihood 6157:Population 5990:Stratified 5942:Population 5761:Dependence 5717:Count data 5648:Percentile 5625:Dispersion 5558:Arithmetic 5493:Statistics 5297:randomized 5295:Completely 5266:covariance 5028:Scientific 4844:Demography 4562:ARMA model 4367:Regression 3944:(Friedman) 3905:(Wilcoxon) 3843:Normality 3833:Lilliefors 3780:Student's 3656:Resampling 3530:Robustness 3518:divergence 3508:Efficiency 3446:(monotone) 3441:Likelihood 3358:Population 3191:Stratified 3143:Population 2962:Dependence 2918:Count data 2849:Percentile 2826:Dispersion 2759:Arithmetic 2694:Statistics 2601:Biometrika 2265:2010-02-22 2028:2010.14078 1947:RootzĂ©n H. 1915:2023-12-11 1831:2023-12-11 1798:2023-12-11 1750:(1): 1–7. 1722:References 1604:for which 1492:for which 418:confounded 137:confounded 34:references 7876:Incidence 7024:Logistic 6791:posterior 6717:Rank sum 6465:Jackknife 6460:Bootstrap 6278:Bootstrap 6213:Parameter 6162:Statistic 5957:Statistic 5869:Run chart 5854:Pie chart 5849:Histogram 5839:Fan chart 5814:Bar chart 5696:L-moments 5583:Geometric 5306:Factorial 5190:inference 5170:Covariate 5132:Treatment 5118:Treatment 4225:Logistic 3992:posterior 3918:Rank sum 3666:Jackknife 3661:Bootstrap 3479:Bootstrap 3414:Parameter 3363:Statistic 3158:Statistic 3070:Run chart 3055:Pie chart 3050:Histogram 3040:Fan chart 3015:Bar chart 2897:L-moments 2784:Geometric 2274:cite book 2087:0146-0404 2073:(8): 11. 2045:1076-9986 1764:0003-1305 1583:⋅ 1577:¯ 1549:¯ 1541:− 1533:⋅ 1527:¯ 1474:⋅ 1465:¯ 1437:¯ 1429:− 1424:⋅ 1415:¯ 1377:¯ 1355:Estimates 1173:μ 1056:Treatment 746:⋮ 675:⋯ 627:⋮ 606:⋮ 585:⋮ 443:replicate 420:effects. 196:Elevation 8053:Category 7990:Theorems 7901:Blocking 7871:Geometry 7738:Category 7431:Survival 7308:Johansen 7031:Binomial 6986:Isotonic 6573:(normal) 6218:location 6025:Blocking 5980:Sampling 5859:Q–Q plot 5824:Box plot 5806:Graphics 5701:Skewness 5691:Kurtosis 5663:Variance 5593:Heronian 5588:Harmonic 5429:Category 5424:Glossary 5230:Bayesian 5208:Bayesian 5164:Blocking 5143:Contrast 5123:blocking 5083:Bayesian 5070:Blinding 5060:validity 5057:external 5053:Internal 4939:Category 4632:Survival 4509:Johansen 4232:Binomial 4187:Isotonic 3774:(normal) 3419:location 3226:Blocking 3181:Sampling 3060:Q–Q plot 3025:Box plot 3007:Graphics 2902:Skewness 2892:Kurtosis 2864:Variance 2794:Heronian 2789:Harmonic 2578:(1987). 2507:(1988). 2464:(2005). 2441:(2008). 2418:(2008). 2395:(1979). 2245:(2008). 2105:32645134 1654:See also 1513: : 1401: : 1364: : 182:blocking 148:Examples 91:blocking 81:In the 7764:Commons 7711:Kriging 7596:Process 7553:studies 7412:Wavelet 7245:General 6412:Plug-in 6206:L space 5985:Cluster 5686:Moments 5504:Outline 5322:Taguchi 5290:Designs 5048:Control 4965:Commons 4912:Kriging 4797:Process 4754:studies 4613:Wavelet 4446:General 3613:Plug-in 3407:L space 3186:Cluster 2887:Moments 2705:Outline 2656:2238364 2621:2333423 2385:2684574 2356:1994124 2235:0030181 2227:2984159 2193:2284277 2164:2681737 2096:7425741 1996:4515556 1772:2682986 1071:Block 3 1066:Block 2 1061:Block 1 776:Example 449:Example 333:Example 290:In the 190:females 165:placebo 110:History 47:improve 7847:Fields 7633:Census 7223:Normal 7171:Manova 6991:Robust 6741:2-way 6733:1-way 6571:-test 6242:  5819:Biplot 5610:Median 5603:Lehmer 5545:Center 5362:(GRBD) 5262:Ancova 5250:Manova 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Index

references
inline citations
improve
introducing
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statistical
design of experiments
experimental units
Ronald Fisher
ANOVA
Ronald A. Fisher
analysis of variance
Latin square
confounded
interactions
drug
placebo
double blind
randomizing
completely randomized design
block design
control group
treatment group


independent and dependent variables
Randomization
statistical
design of experiments
experimental units

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