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Preface | |

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Presenting and Summarizing Data | |

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Data and Variables | |

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Graphical Presentation of Qualitative Data | |

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Graphical Presentation of Quantitative Data | |

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Construction of a Histogram | |

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Numerical Methods for Presenting Data | |

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Symbolic Notation | |

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Measures of Central Tendency | |

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Measures of Variability | |

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Measures of the Shape of a Distribution | |

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Measures of Relative Position | |

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Sas Example | |

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Exercises | |

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Probability | |

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Rules About Probabilities of Simple Events | |

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Counting Rules | |

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Multiplicative Rule | |

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Permutations | |

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Combinations | |

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Partition Rule | |

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Tree Diagram | |

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Compound Events | |

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Bayes Theorem | |

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Exercises | |

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Random Variables and Their Distributions | |

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Expectations and Variances of Random Variables | |

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Probability Distributions for Discrete Random Variables | |

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Expectation and Variance of a Discrete Random Variable | |

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Bernoulli Distribution | |

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Binomial Distribution | |

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Hyper-geometric Distribution | |

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Poisson Distribution | |

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Multinomial Distribution | |

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Probability Distributions for Continuous Random Variables | |

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Uniform Distribution | |

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Normal Distribution | |

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Multivariate Normal Distribution | |

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Chi-square Distribution | |

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Student t Distribution | |

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F Distribution | |

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Exercises | |

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Population and Sample | |

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Functions of Random Variables and Sampling Distributions | |

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Central Limit Theorem | |

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Statistics with Distributions Other than Normal | |

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Degrees of Freedom | |

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Estimation of Parameters | |

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Point Estimation | |

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Maximum Likelihood Estimation | |

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Interval Estimation | |

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Estimation of Parameters of a Normal Population | |

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Maximum Likelihood Estimation | |

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Interval Estimation of the Mean | |

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Interval Estimation of the Variance | |

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Exercises | |

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Hypothesis Testing | |

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Hypothesis Test of a Population Mean | |

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P value | |

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A Hypothesis Test Can Be One- or Two-sided | |

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Hypothesis Test of a Population Mean for a Small Sample | |

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Hypothesis Test of the Difference Between Two Population Means | |

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Large Samples | |

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Small Samples and Equal Variances | |

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Small Samples and Unequal Variances | |

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Dependent Samples | |

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Nonparametric Test | |

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SAS Examples for Hypotheses Tests of Two Population Means | |

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Hypothesis Test of a Population Proportion | |

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Hypothesis Test of the Difference Between Proportions from Two Populations | |

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Chi-Square Test of the Difference Between Observed and Expected Frequencies | |

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SAS Example for Testing the Difference between Observed and Expected Frequencies | |

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Hypothesis Test of Differences Among Proportions from Several Populations | |

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SAS Example for Testing Differences among Proportions from Several Populations | |

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Hypothesis Test of Population Variance | |

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Hypothesis Test of the Difference of Two Population Variances | |

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Hypothesis Tests Using Confidence Intervals | |

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Statistical and Practical Significance | |

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Types of Errors in Inferences and Power of Test | |

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SAS Examples for the Power of Test | |

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Sample Size | |

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SAS Examples for Sample Size | |

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Exercises | |

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Simple Linear Regression | |

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The Simple Regression Model | |

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Estimation of the Regression Parameters - Least Squares Estimation | |

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Maximum Likelihood Estimation | |

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Residuals and Their Properties | |

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Expectations and Variances of the Parameter Estimators | |

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Student T Test in Testing Hypotheses About the Parameters | |

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Confidence Intervals of the Parameters | |

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Mean and Prediction Confidence Intervals of the Response Variable | |

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Partitioning Total Variability | |

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Relationships among Sums of Squares | |

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Theoretical Distribution of Sum of Squares | |

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Test of Hypotheses - F Test | |

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Likelihood Ratio Test | |

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Coefficient of Determination | |

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Shortcut Calculation of Sums of Squares and the Coefficient of Determination | |

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Matrix Approach to Simple Linear Regression | |

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The Simple Regression Model | |

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Estimation of Parameters | |

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Maximum Likelihood Estimation | |

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SAS Example for Simple Linear Regression | |

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Power of Tests | |

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SAS Examples for Calculating the Power of Test | |

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Exercises | |

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Correlation | |

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Estimation of the Coefficient of Correlation and Tests of Hypotheses | |

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Numerical Relationship Between the Sample Coefficient of Correlation and the Coefficient of Determination | |

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SAS Example for Correlation | |

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Rank Correlation | |

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SAS Example for Rank Correlation | |

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Exercises | |

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Multiple Linear Regression | |

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Two Independent Variables | |

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Estimation of Parameters | |

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Student t test in Testing Hypotheses | |

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Partitioning Total Variability and Tests of Hypotheses | |

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Partial and Sequential Sums of Squares | |

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Testing Model Fit Using a Likelihood Ratio Test | |

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SAS Example for Multiple Regression | |

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Power of Multiple Regression | |

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SAS Example for Calculating Power | |

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Problems with Regression | |

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Analysis of Residuals | |

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Extreme Observations | |

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Multicollinearity | |

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SAS Example for Detecting Problems with Regression | |

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Choosing the Best Model | |

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SAS Example for Model Selection | |

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Curvilinear Regression | |

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Polynomial Regression | |

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SAS Example for Quadratic Regression | |

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Nonlinear Regression | |

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SAS Example for Nonlinear Regression | |

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Segmented Regression | |

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SAS Examples for Segmented Regression | |

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SAS Example for Segmented Regression with Two Simple Regressions | |

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SAS Example for Segmented Regression with Plateau | |

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One-Way Analysis of Variance | |

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The Fixed Effects One-Way Model | |

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Partitioning Total Variability | |

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Hypothesis Test - F Test | |

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Estimation of Group Means | |

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Maximum Likelihood Estimation | |

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Likelihood Ratio Test | |

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Multiple Comparisons among Group Means | |

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Least Significance Difference (LSD) | |

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Tukey Test | |

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Contrasts | |

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Orthogonal contrasts | |

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Scheffe Test | |

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Test of Homogeneity of Variance | |

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SAS Example for the Fixed Effects One-way Model | |

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Power of the Fixed Effects One-way Model | |

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SAS Example for Calculating Power | |

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The Random Effects One-Way Model | |

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Hypothesis Test | |

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Prediction of Group Means | |

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Variance Component Estimation | |

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Intraclass Correlation | |

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Maximum Likelihood Estimation | |

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Restricted Maximum Likelihood Estimation | |

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SAS Example for the Random Effects One-way Model | |

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Matrix Approach to the One-Way Analysis of Variance Model | |

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The Fixed Effects Model | |

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Linear Model | |

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Estimating Parameters | |

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Maximum Likelihood Estimation | |

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Regression Model for the One-way Analysis of Variance | |

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The Random Effects Model | |

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Linear Model | |

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Prediction of Random Effects | |

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Maximum Likelihood Estimation | |

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Restricted Maximum Likelihood Estimation | |

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Mixed Models | |

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Prediction of Random Effects | |

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Maximum Likelihood Estimation | |

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Restricted Maximum Likelihood Estimation | |

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Exercises | |

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Concepts of Experimental Design | |

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Experimental Units and Replications | |

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Experimental Error | |

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Precision of Experimental Design | |

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Controlling Experimental Error | |

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Required Number of Replications | |

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SAS Example for the Number of Replications | |

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Blocking | |

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Randomized Complete Block Design | |

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Partitioning Total Variability | |

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Hypotheses Test - F test | |

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SAS Example for Block Design | |

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Randomized Block Design - Two or More Units Per Treatment and Block | |

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Partitioning Total Variability and Test of Hypotheses | |

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SAS Example for Two or More Experimental Unit per Block x Treatment | |

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Power of Test | |

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SAS Example for Calculating Power | |

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Exercises | |

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Change-over Designs | |

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Simple Change-Over Design | |

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Change-Over Designs with the Effects of Periods | |

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SAS Example for Change-over Designs with the Effects of Periods | |

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Latin Square | |

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SAS Example for Latin Square | |

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Change-over Design Set as Several Latin Squares | |

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SAS Example for Several Latin Squares | |

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Exercises | |

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Factorial Experiments | |

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The Two Factor Factorial Experiment | |

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SAS Example for Factorial Experiment | |

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Exercise | |

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Hierarchical or Nested Design | |

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Hierarchical Design with Two Factors | |

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SAS Example for Hierarchical Design | |

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More About Blocking | |

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Blocking with Pens, Corrals and Paddocks | |

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SAS Example for Designs with Pens and Paddocks | |

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Double Blocking | |

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Split-Plot Design | |

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Split-Plot Design - Main Plots in Randomized Blocks | |

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SAS Example: Main Plots in Randomized Blocks | |

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Split-Plot Design - Main Plots in a Completely Randomized Design | |

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SAS Example: Main Plots in a Completely Randomized Design | |

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Exercise | |

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Analysis of Covariance | |

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Completely Randomized Design with a Covariate | |

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SAS Example for a Completely Randomized Design with a Covariate | |

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Testing the Difference Between Regression Slopes | |

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SAS Example for Testing the Difference between Regression Slopes | |

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Repeated Measures | |

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Homogeneous Variances and Covariances Among Repeated Measures | |

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SAS Example for Homogeneous Variances and Covariances | |

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Heterogeneous Variances and Covariances Among Repeated Measures | |

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SAS Examples for Heterogeneous Variances and Covariances | |

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Random Coefficient Regression | |

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SAS Examples for Random Coefficient Regression | |

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Homogeneous Variance-Covariance Parameters across Treatments | |

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Heterogeneous Variance-Covariance Parameters across Treatments | |

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Analysis of Numerical Treatment Levels | |

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Lack of Fit | |

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SAS Example for Lack of Fit | |

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Polynomial Orthogonal Contrasts | |

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SAS Example for Polynomial Contrasts | |

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Discrete Dependent Variables | |

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Logit Models, Logistic Regression | |

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Testing Hypotheses | |

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SAS Examples for Logistic Models | |

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Probit Model | |

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SAS Example for a Probit model | |

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Log-Linear Models | |

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SAS Example for a Log-Linear Model | |

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Solutions of Exercises | |

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Vectors and Matrices | |

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Types and Properties of Matrices | |

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Matrix and Vector Operations | |

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Statistical Tables | |

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Area Under the Standard Normal Curve, Z [greater than sign] Z[subscript alpha] | |

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Critical Values of Student T Distributions, T [greater than sign] T[subscript alpha] | |

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Critical Values of Chi-Square Distributions, x[superscript 2] [greater than sign] x[superscript 2 subscript alpha] | |

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Critical Values of F Distributions, F [greater than sign] F[subscript alpha], [alpha] = 0.05 | |

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Critical Value of F Distributions, F [greater than sign] F[subscript alpha], [alpha] = 0.01 | |

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Critical Values of the Studentized Range, Q(A,V) | |

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References | |

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Subject Index | |