- Page 1: Biostatistics for Animal Science
- Page 4 and 5: CABI Publishing is a division of CA
- Page 6 and 7: vi Biostatistics for Animal Science
- Page 8 and 9: viii Biostatistics for Animal Scien
- Page 10 and 11: x Biostatistics for Animal Science
- Page 12 and 13: Preface This book was written to se
- Page 15 and 16: Chapter 1 Presenting and Summarizin
- Page 17 and 18: Brown 5% Simmental 76% Holstein 19%
- Page 19 and 20: Number of calves 18 16 14 12 10 8 6
- Page 21 and 22: Σi y 2 i = 1 2 + 3 2 + 6 2 = 46 Co
- Page 23 and 24: Chapter 1 Presenting and Summarizin
- Page 25 and 26: 1.4.5 Measures of Relative Position
- Page 27: Chapter 1 Presenting and Summarizin
- Page 31 and 32: 2.2.1 Multiplicative Rule Chapter 2
- Page 33 and 34: Chapter 2 Probability 19 event. As
- Page 35 and 36: Chapter 2 Probability 21 P(A ∩ B)
- Page 37 and 38: 2.4 Bayes Theorem First calf Second
- Page 39 and 40: We define: P(A1) = 0.6 is the proba
- Page 41 and 42: Chapter 3 Random Variables and thei
- Page 43 and 44: Chapter 3 Random Variables and thei
- Page 45 and 46: 3.2.3 Binomial Distribution Chapter
- Page 47 and 48: ⎛10⎞ 0 10 0 10 b) P ( y = 0) =
- Page 49 and 50: E(y) = µ = λ and Var(y) = σ 2 =
- Page 51 and 52: Chapter 3 Random Variables and thei
- Page 53 and 54: 2.5% µ−1.96σ µ−σ µ µ+σ F
- Page 55 and 56: Chapter 3 Random Variables and thei
- Page 57 and 58: Chapter 3 Random Variables and thei
- Page 59 and 60: Chapter 3 Random Variables and thei
- Page 61 and 62: e f ( y) = − 1 2 −1 ( y −µ )
- Page 63 and 64: Chapter 3 Random Variables and thei
- Page 65 and 66: The expectation and variance of the
- Page 67 and 68: Chapter 4 Population and Sample A p
- Page 69 and 70: Chapter 4 Population and Sample 55
- Page 71 and 72: 5.2 Maximum Likelihood Estimation C
- Page 73 and 74: Chapter 5 Estimation of Parameters
- Page 75 and 76: By setting both terms to zero the e
- Page 77 and 78: Chapter 5 Estimation of Parameters
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Chapter 6 Hypothesis Testing The fo
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µ 0 y − z ≈ s n Chapter 6 Hypo
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Known values are: y = 4000 kg σ =
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α -zα Figure 6.7 The critical val
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s( y 1− y2 ) = 2 s1 s + n n 1 2 2
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The estimated pooled variance is: s
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Chapter 6 Hypothesis Testing 77 tha
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( y − y2 ) − 0 ( 11. 857 − 21
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Normal Approximation Z 2.0626 One-S
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pˆ − pˆ 1 The estimator has var
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2 χ [ yi E( yi ) ] E( y ) ∑ −
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∑ ∑ y i i p0 = i = 1,..., k n i
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Chapter 6 Hypothesis Testing 89 Exp
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Chapter 6 Hypothesis Testing 91 An
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Decision of a statistical test H 0
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Chapter 6 Hypothesis Testing 95 nor
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Chapter 6 Hypothesis Testing 97 One
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0.45 0.40 0.35 0.30 0.25 0.20 0.15
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SAS output: alpha n mi0 mi1 stdev d
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6.12 Sample Size Chapter 6 Hypothes
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SAS program: DATA a; DO n = 2 TO 10
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Chapter 6 Hypothesis Testing 107 PR
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Chapter 7 Simple Linear Regression
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The measurements of the dependent v
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Chapter 7 Simple Linear Regression
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Chapter 7 Simple Linear Regression
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Chapter 7 Simple Linear Regression
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Chapter 7 Simple Linear Regression
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2 SSRES s = = MSRES = 115. 826 n
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Confidence intervals follow the cla
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spread yi about y A) y y * * * * *
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SS REG ( SSxy ) = SS xx 2 Chapter 7
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E(MSREG) = σ 2 + β1 2 SSxx Chapte
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The likelihood function when H0 is
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2 R = SS SS REG TOT Chapter 7 Simpl
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Chapter 7 Simple Linear Regression
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Chapter 7 Simple Linear Regression
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= (X'X) -1 X'y A maximum likelihood
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Chapter 7 Simple Linear Regression
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DATA a; alpha=0.05; n=6; b=7.52941;
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Chapter 7 Simple Linear Regression
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Chapter 8 Correlation 147 of correl
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has a t-distribution with (n - 2) d
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Chapter 8 Correlation 151 under H0:
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Exercises Chapter 8 Correlation 153
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The assumptions of the model are: 1
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where: Chapter 9 Multiple Linear Re
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The residual mean square, which is
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The null and alternative hypotheses
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Chapter 9 Multiple Linear Regressio
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Chapter 9 Multiple Linear Regressio
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yi = the weight of bull i x1i = the
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SAS program: DATA bulls; INPUT weig
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Chapter 9 Multiple Linear Regressio
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9.6.1 Analysis of Residuals Chapter
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y * * 1 * * * * * * * * * 2 * * * 4
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where: Chapter 9 Multiple Linear Re
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SAS program: DATA bull; INPUT weigh
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Chapter 9 Multiple Linear Regressio
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where: SSRES = residual mean square
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Chapter 10 Curvilinear Regression I
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Chapter 10 Curvilinear Regression 1
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The variance estimate is s 2 = 210.
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Chapter 10 Curvilinear Regression 1
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SAS program: DATA a; INPUT age weig
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Chapter 10 Curvilinear Regression 1
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Weight (g) 1000 800 600 400 200 0 0
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Chapter 10 Curvilinear Regression 1
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Chapter 10 Curvilinear Regression 2
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Chapter 10 Curvilinear Regression 2
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Chapter 11 One-way Analysis of Vari
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From the assumptions it follows: Ch
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By defining: SS SS SS TOT TRT RES =
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Chapter 11 One-way Analysis of Vari
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1) Total sum: Σi Σj yij = (270 +
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2 L( µ , σ | y) = The log likelih
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And as shown previously: Thus: 2
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Chapter 11 One-way Analysis of Vari
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The hypotheses can be tested using
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ANOVA table: Chapter 11 One-way Ana
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F 3 = 2890 2 296. 67 = 4. 871 Chapt
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SAS output: Chapter 11 One-way Anal
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Chapter 11 One-way Analysis of Vari
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Chapter 11 One-way Analysis of Vari
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Chapter 11 One-way Analysis of Vari
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Chapter 11 One-way Analysis of Vari
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The effect of sow 1 is: ˆ 1 τ = 0
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Chapter 11 One-way Analysis of Vari
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The log likelihood that is to be ma
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Solution for Random Effects Chapter
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11.3.1.2 Estimating Parameters Chap
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Chapter 11 One-way Analysis of Vari
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The sums of squares needed for test
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The Xr'Xr matrix and its inverse ar
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11.3.2 The Random Effects Model 11.
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Chapter 11 One-way Analysis of Vari
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11.3.2.4 Restricted Maximum Likelih
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Chapter 11 One-way Analysis of Vari
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Chapter 11 One-way Analysis of Vari
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Chapter 12 Concepts of Experimental
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Chapter 12 Concepts of Experimental
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Chapter 12 Concepts of Experimental
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12.5 Required Number of Replication
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SAS output: alfa df1 df2 n power 0.
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Chapter 13 Blocking 273 environment
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1) Total sum: Σi Σj yij 2) Correc
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Chapter 13 Blocking 277 Example: Th
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13.1.3 SAS Example for Block Design
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Animal No. (Treatment) Blocks I II
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Mean square for treatments: Mean sq
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= s y − y MS ij . i' j' . RES ⎛
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1347. 90 F = = 7. 67 175. 83 F test
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Dependent Variable: d_gain i/j 1 2
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Chapter 13 Blocking 291 the adjuste
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Exercises Chapter 13 Blocking 293 1
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µ = the overall mean τi = the fix
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BLOCK II The hypotheses are: Chapte
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The results are shown in the ANOVA
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Chapter 14 Change-over Designs 301
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3) Total (corrected) sum of squares
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3) Total (corrected) sum of squares
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Least Squares Means Adjustment for
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Chapter 14 Change-over Designs 309
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Chapter 14 Change-over Designs 311
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Chapter 15 Factorial Experiments A
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1) Total sum: Σi Σj Σk yijk 2) C
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Chapter 15 Factorial Experiments 31
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5) Sum of squares for vitamin II: (
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Chapter 15 Factorial Experiments 32
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Chapter 16 Hierarchical or Nested D
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6) Sum of squares within factor B (
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3) Total sum of squares: Chapter 16
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SAS output of the NESTED procedure:
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Chapter 17 More about Blocking If t
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Chapter 17 More about Blocking 333
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SAS program: DATA steer; INPUT pen
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SAS output of the GLM procedure: De
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Chapter 17 More about Blocking 339
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The ANOVA table is: Source Degrees
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The model for this design is: where
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Chapter 18 Split-plot Design 345 su
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Least Squares Means Chapter 18 Spli
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Source Degrees of freedom Factor A
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Effects Means Estimators Standard e
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Chapter 18 Split-plot Design 353 Ex
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Chapter 19 Analysis of Covariance A
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DATA gain; INPUT treatment $ initia
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Chapter 19 Analysis of Covariance 3
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For males (M) the model is: E(yi) =
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Chapter 19 Analysis of Covariance 3
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Chapter 20 Repeated Measures Experi
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Chapter 20 Repeated Measures 367 Ex
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8 9 1 1.3 8 10 1 1.3 8 11 1 1.3 8 1
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SAS output: Covariance Parameter Es
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where: Chapter 20 Repeated Measures
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Chapter 20 Repeated Measures 375 Ex
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σ ⎡ σ b σ ⎡ ⎤ 0 b0b1 [ 1 t
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⎡1 ⎢ ⎢ 1 R ˆ = ⎢1 ⎢ ⎣1
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⎡1 ⎢ ˆR ⎢ 1 = ⎢1 ⎢ ⎣1
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Chapter 20 Repeated Measures 383
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Chapter 21 Analysis of Numerical Tr
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Chapter 21 Analysis of Numerical Tr
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Chapter 21 Analysis of Numerical Tr
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21.2.1 SAS Example for Polynomial C
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Chapter 21 Analysis of Numerical Tr
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Chapter 22 Discrete Dependent Varia
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Chapter 22 Discrete Dependent Varia
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where: pi = the proportion with mas
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Chapter 22 Discrete Dependent Varia
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Analysis Of Parameter Estimates Cha
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SAS program: DATA a; INPUT n y farm
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Chapter 22 Discrete Dependent Varia
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Farm The model is: where: Total no.
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LR Statistics For Type 1 Analysis C
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Chapter 22 Discrete Dependent Varia
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Chapter 22 Discrete Dependent Varia
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Chapter 22 Discrete Dependent Varia
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Solutions of Exercises 1.1. Mean =
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Appendix A: Vectors and Matrices A
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⎡a A + B = ⎢ ⎢ a ⎢⎣ a A +
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a = (X'X) -1 X'y Appendix A: Vector
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Critical Values of Student t Distri
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Critical Values of Chi-square Distr
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Critical Values of F Distributions,
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Critical Value of F Distributions,
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Critical Values of the Studentized
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References 437 Gianola, D. and Hamm
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Subject Index accuracy, 266 Akaike
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y hypothesis testing, 56 by paramet
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hypothesis test, 186 t test, 186 ra
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of regression estimators, 119, 159