Index
- a
- Akaike criterion 405, 447
- alternative hypothesis 39, 62, 76, 376, 384, 477
- analysis of covariance (ANCOVA) 339, 366
- analysis of variance (ANOVA) 105, 108, 115, 135
- approximate confidence interval 93
- approximately normally distributed 324
- approximate test 60, 68
- areal data analysis 432
- ASN 60, 326, 487
- asymptotic
- b
- balanced 106, 115, 122, 359, 376, 398, 465
- Bertalanffy function 306, 320
- Bessel function 439
- best linear unbiased estimator (BLUE) 112, 131, 145, 264, 351, 487
- best linear unbiased prediction (BLUP) 441, 487
- best population 371
- best quadratic unbiased estimator (BQUE) 161, 487
- bias 283, 333, 359
- BIC 447
- binomial distribution 18, 78, 100, 395, 418, 489
- block design 115, 358
- Bonferroni inequality 379, 380, 385
- Box–Cox transformation 434
- c
- canonical form 394, 400, 489
- censored sample 20, 22, 460
- central
- chi‐squared (χ2) distribution 54, 92, 139, 169, 372
- class see subclass number
- classification
- closed sequential test 60
- cluster sampling 5, 9
- comparison 367, 375
- comparison‐wise, risk 376
- complete
- composite hypothesis 39
- concrete design 318
- concrete sample 4
- confidence band see confidence belt
- confidence belt 274
- confidence coefficient 284, 294, 296, 383
- confidence estimation 148, 294, 298, 334
- confidence interval 169, 274
- confidence level 83
- confidence region 316
- connected cross‐classification 126
- contingency table 29
- contrast
- correlation coefficient 322–323
- partial 333
- covariance
- covariance matrix 273
- estimated 272
- critical function 49
- cross‐classification 223
- d
- degrees of freedom 4, 47, 88, 106, 416, 485
- design
- disconnected cross‐classification 119
- distribution 11–12, 41, 67, 367
- asymptotic 283
- binomial 18, 50, 78, 100, 395
- continuous 51, 70, 74, 80, 223
- conditional 334
- discrete 49, 395
- empirical 16, 73
- exponential families of 394, 453
- finite 23
- of Fleishman system 73
- gamma 395, 418, 423
- lognormal 17
- multinomial 395, 426
- normal 22, 41, 47, 54, 84, 91, 333, 370, 375, 431
- Poisson 19, 51, 395, 411
- truncated 20
- uniform 489
- Dunnett method 387
- e
- easting 432
- effect
- error 123
- estimable function 109, 117
- estimated asymptotic covariance matrix 284
- estimate 11, 18, 26, 42, 74, 99, 113, 161
- estimation 11, 17, 83, 117, 160, 166, 263, 333, 441
- estimator
- exact
- expected
- experiment 106, 112
- experimental design 105, 315, 334
- experimental unit 339
- exponential family 393–394, 396, 453
- exponential regression 290, 320
glmpackage 397
- i
- incomplete, cross‐classification 115, 118, 182
- indifference zone 368, 372
- inferior factor see nested factor
- inflection point 299, 306, 312
- information 1, 366, 398, 416
- interaction 105, 119, 126, 131, 136, 220, 224, 226, 340, 360
- interval estimation 43
- intra‐class correlation coefficient (ICC) 160, 172, 174
- intrinsically non‐linear regression 226, 283, 315, 322, 332
- invariant 166
- copula 453
- iteration 21, 91, 223
‐optimal - m
- main effect 106, 110, 116, 129, 136, 144, 147, 159, 224–226, 466
- Mann–Whitney test 67, 73
- mathematical model 39, 105
- maximum‐likelihood (ML)
- maximum minimal size see maximum size
- maximum size 107, 148, 222, 223
- mean 1, 3, 6, 21
- mean square error (MSE) 23, 348, 364
- median 14, 16, 51, 52, 57, 70, 76
- minimal
- minimum
- minimum norm quadratic unbiased estimator (MINQUE) 167
- mixed classification 135, 148–151, 154–155, 195–198, 223, 239–255
- mixed model 105, 166, 168, 172, 182, 184, 201–256
- ML‐estimate 18, 165, 167–169, 171–172, 179–180, 393, 412, 459, 467
- model
- model I
- model II
- model III 223, 224, 226, 227, 230
- model IV 231, 239, 241, 242, 247
- model V 243–245
- model VI 245, 253, 254
- model VII 254, 255
- model VIII 255, 256
- m‐point design 316, 318, 320
- multiple
- multivariate
- n
- natural parameter 78, 394, 396
- negative binomial distribution 418
- nested classification 116, 131, 134, 144, 183, 192, 201, 214, 230
- nested factor 131, 147, 148, 201, 214
- Neyman–Pearson lemma 49
- non‐centrality parameter 3, 42, 48, 457
- non‐centrally
- non‐linear regression 262, 282, 317
- non‐linearity parameter 282, 290, 299, 312
- non‐parametric test 52
- normal
- o
- one‐parametric exponential family 394
- one sample 11, 57
- one‐sided
- open sequential test 60
- optimal
- optimal design of experiments (OPDOE) 1, 49, 62, 74, 93, 99, 106, 112, 153, 213, 385
- optimality criterion (condition) 83, 315, 318, 442
- order statistic 13, 24, 382
- orthogonal (linear) contrast 270, 377
- outlier 13, 52, 397, 409
- overdispersion 396, 409, 418
- p
- parameter
- parametrisation see reparametrisation
- partial
- permutation 367
- point estimation 11
- Poisson distribution 1, 51, 395, 411, 414, 418, 427, 486
- polynomial regression 318
- population 4, 23, 62, 367
- statistical 5
- power 41, 74, 111, 386
- p‐point design 319
- precision requirement 44, 59, 90, 106, 315, 334, 368
- prediction
- probability 56, 93
- program package
R1 - projection orthogonal see orthogonal
- q
- quadratic
- quantile 274
- quasilinear
- r
- random
- random sampling (procedure), stratified 9
- random sampling
- randomisation 339
- randomised
- range 13, 24, 25, 382, 446
- rank 52, 57, 70
- realisation 5, 6, 11, 13, 18, 22–24, 39, 44, 55
- region 83
- regressand 260–262, 321, 322, 330, 393, 396
- regression
- analysis 257, 261, 270, 304, 308, 310, 321–322, 335
- coefficient 40, 263–265, 269, 271–275, 282, 339, 341, 342, 416, 445
- exponential 290, 298, 320
- intrinsically non‐linear 260, 282–284, 315, 317, 322, 334
- line 265–267, 274–276, 280, 339–341, 344, 347, 353, 357, 358, 360
- logistic 298–300, 302, 320, 321, 393, 397, 399–400
- model 261, 262, 274, 280, 282, 290, 316, 317, 321, 322, 330, 340, 358, 396, 400, 437, 439, 452
- multiple linear 267, 322, 339
- quasilinear see quasilinear, regression
- simple linear 264–265, 271, 274, 279, 316
- regression function 261, 263, 268–271, 273, 276, 280, 282, 284, 299, 300, 302, 306, 307, 309, 312, 315, 317–319, 334, 400, 445
- regressor 260–262, 265, 267, 270, 275, 278, 282, 315, 317, 321–323, 325, 393, 396–400, 411, 412, 418, 426, 427
- reparametrisation 108–111, 299
- replication 130, 413
- residual variance 271, 273, 286
- restricted maximum likelihood (REML) 166–169, 172, 176, 179–181, 183–185, 187, 193, 195, 197, 204–205, 208, 217, 221
- risk
- robust 41, 52, 73, 83
- robustness 72, 73, 79
- s
- sample
- sample size 5, 9, 11–12, 40, 43–45, 47, 56, 57, 60, 66, 68, 70, 74, 87–88, 94, 97–100, 222, 227, 315, 370–371, 373, 376, 384–385, 387–388
- sampling
- sampling procedure 1, 4–5, 8
- SAS 27–28, 106, 323, 411, 431
- scale parameter 12, 24, 26, 411, 426
- scatter plot 257, 260, 266, 270, 275, 357
- Scheffé method 379
- secondary unit 5, 9
- second order interaction 136–137, 139
- selection
- sequential likelihood ratio test (SLRT) 60
- sequential path 324
- sequential test 40, 59–61, 74
- sequential triangular test 61, 74, 324, 326, 328
- side condition 108–109, 112, 116–117, 126, 131–132, 137, 145, 148, 154, 169, 176, 186, 201, 214, 341–342, 350, 358–359, 432
- simple linear regression 264–265, 271, 274, 277, 279, 316
- simulation experiment 67, 73, 79, 298, 305, 312, 315, 325, 372–374
- size
- skewness 12, 27, 53, 73, 298
- small sample 5
- SS see sum of squares
- statistic
- statistical
- strata 24
- stratum 4, 23
- studentised range 382–383
- student distribution 385, 387 see also t‐distribution
- student's t‐test 67 see also t‐test
- subclass number 118–119, 121, 134, 135, 141, 144, 147–148, 377
- sufficient statistic 166
- sum of squares 109, 132–133, 137, 176, 182, 225, 265, 399
- systematic sampling 8, 23
- t
- t‐distribution 52, 87, 274, 373, 380
- test
- three‐point design 320
- three‐way analysis of variance
- three‐way classification 223
- total mean 105, 108, 110, 119, 131, 144
- t‐procedure, multiple 376, 384–386
- treatment 110–111, 116, 142, 339–343, 350–351, 356, 358–359, 365–366, 372, 376, 382, 384–386, 433
- triangular test, sequential 61, 74, 324, 326, 328
- trimmed mean 14–15
- truncation 20–22
- t‐test 63, 66–68, 70, 73–74, 275, 344, 353, 361, 376
- multiple 384
- Tukey method 383
- two‐dimensional normal distribution 333, 394
- two‐sample
- two‐sided alternative 41–42, 46–49, 52, 55, 66, 73, 85, 275, 278, 280
- two‐way
- u
- unbiased
- α‐test 105
- estimator 4, 11, 18, 23, 25–26, 54, 63, 92, 96, 100, 112, 161, 167, 264, 323, 332, 351
- with minimal variance 112
- prediction 441
- unequal subclass number see subclass number, unequal
- uniform distribution 489
- uniformly distributed 9, 24, 49, 50, 453
- uniformly most powerful unbiased (UMPU)
- universe 4–6, 23–24, 57, 108, 159
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