Course Overview
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Course Synopsis
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The course STA-643 is planned for those interested in the design, conduct, and analysis of experiments in the physical, chemical, biological, medical, social, psychological, economic, engineering, or industrial sciences. The course will examine how to design experiments, carry them out, and analyze the data they yield. Various designs are discussed and their respective differences, advantages, and disadvantages are noted. In particular, factorial and fractional factorial designs are discussed in greater detail. These are designs in which two or more factors are varied simultaneously; the experimenter wishes to study not only the effect of each factor, but also how the effect of one factor changes as the levels of other factors change.
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Course Learning Outcomes
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At the end of the course, you should be able to understand:
- Encounter the principles of randomization, replication and stratification, and understand how they apply to practical examples.
- List the different types of formal experimental designs (e.g. completely randomized, randomized block, repeated measures, Latin square and factorial experimental designs)
- Explore the general theory of factorial and block designs and understand this theory sufficiently to find appropriate designs for specific applications
- Evaluate designs using common optimality criteria and used them to critically compare competing designs
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Course Calendar
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Week 01
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2
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Design of Experiment (DOE)
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3
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Objectives of an experiment
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4
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Application of Experimental Design in engineering design
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6
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Application of Experimental Design in agriculture
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7
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Examples of Experimental Design in agriculture
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8
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Application of Experimental Design in life sciences
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9
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Examples of Experimental Design in life sciences
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10
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Application of Experimental Design in environmental sciences
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11
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Examples of Experimental Design in enviromental sciences
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12
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Application of Experimental Design in physical sciences
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13
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Examples of Experimental Design in physical sciences
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14
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Application of Experimental Design in management sciences
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15
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Examples of Experimental Design in management sciences
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16
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Application of Experimental Design in social sciences
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17
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Examples of Experimental Design in social sciences
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18
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Historical Perspective
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19
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Definition of Basic Terms
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20
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Basic Principles of DOE: Randomization
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21
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Examples of Randomization
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22
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Basic Principles of DOE: Replication
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23
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Examples of Replication
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24
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Basic Principles of DOE: Local Control/Blocking
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25
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Example of local control/Blocking
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26
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Steps involved in designing of an experiment
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27
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Some practical advises for experimentation
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Week 02
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29
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Testing mean of population
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31
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Testing equality of two population means
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32
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Testing equality of two population means-independent samples when population variances are equal
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33
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Example of testing equality of two population means-independent samples when population variances are equal
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34
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Testing equality of two population means-independent samples when population variances are unequal
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35
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Examples of testing equality of two population means-independent samples when population variances are unequal
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36
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Testing equality of two population means-paired samples
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37
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Example of testing equality of two population means-paired samples
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38
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Analysis of variance (ANOVA)
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41
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Definition of a model and Types of model
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43
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Examples of fixed effect Models
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45
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Examples of random effect model
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46
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Analysis of fixed effects models
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Week 03
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48
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Decomposition of total sum of squares
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49
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Expected values of mean squares of error
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50
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Expected values of mean squares of treatment
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51
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Model adequacy checking tools
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52
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Coefficient of determination and model
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53
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The Normality Assumption: Histogram of residuals
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54
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The Normality Assumption: Normal probability plot
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55
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The Normality Assumption: Plot of residuals in time series
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56
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The Normality Assumption: Plot of residuals vs fitted values
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Week 04
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57
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Test the equality of variances- The Bartlett's test
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58
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Other plots based on residuals
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59
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Violation of the assumptions and transformations
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60
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Nonparametric methods in ANOVA
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61
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The Kruskal-Wallis test
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64
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Inference for Contrasts
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66
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Post-hoc tests in ANOVA
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68
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Examples of Scheffe's test
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Week 05
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72
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Examples of Tukey's test
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73
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Duncan's Multiple Range (DMR) test
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74
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Examples of Duncan's Multiple Range (DMR) test
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76
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Example of Dunnet's test
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Week 06
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78
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Examples of The Neuman-Keuls test
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79
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Which post-hoc test should we use
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80
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Basic experimental designs/One-factor-at-a-time designs
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81
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Completely randomized design (CRD)- Layout and ANOVA
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82
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Completely randomized design (CRD)- Advantages and disadvantages
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85
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Repeated measures design
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86
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Model and layout of repeated measures design
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87
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ANOVA of repeated measures design
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88
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Example of repeated measures design
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89
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Randomized complete block dsign (RCBD)- Basics of blocking
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90
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Randomized complete block design- Precautions
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91
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RCBD- Model, assumptions
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97
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Partitioning Total Sum of Squares (TSS) into component parts in an RCBD
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98
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Expected values of mean squares of treatment of RCBD
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99
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Expected values of mean squares of error of RCBD
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100
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Expected values of mean squares of blocks
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Week 07
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102
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Estimation of one missing observation in RCBD
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103
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Emissing stimation of more than one observation in RCBD
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104
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Relative efficiency of RCBD comaped to CRD
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105
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RCBD- Practical example
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106
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Latin squares design (LS design)/Double grouping design- Definition and model
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107
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Layout of 3*3 and 4*4 LS design, properties
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109
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Replication of Latin Squares
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110
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ANOVA of replicated LS design case-I
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111
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ANOVA of replicated LS design case-II
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112
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ANOVA of replicated LS design case-III
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113
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Estimation of missing observation in LS design
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114
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Relative efficiency of LS design
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115
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Practical example of LS design
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Week 08
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117
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Graeco-Latin squares design (GLS design)- Definition and Layout
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118
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Statistical model for G LS design
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120
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Advantages of GLS design
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121
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Disadvantages and limitations of GLS design
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122
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Practical example of GLS design
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123
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Incomplete Block Design (IBD), different types of IBD
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124
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Balanced Incomplete Block Design (BIBD)
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125
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Layout and notations of BIBD
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127
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Real Life Examples of BIBD
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126
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Model and ANOVA of a BIBD
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128
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Estimation of treatment effects of a BIBD
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129
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Intra block analysis of BIBD
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130
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Partially balanced incomplete block design (PBIBD)
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133
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Association scheme of PBIBD
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135
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Model and assumptions of PBIBD
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Week 09
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138
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Youden squares design
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139
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Construction of a Youden squares design
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140
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The design rules for a Youden squares design
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141
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Analysis of a Youden squares design
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142
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Factorial Experiments
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143
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Advantages of factorial experiments over one-factor-at-a-time experiments
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144
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Factor effects- main and interaction effect of 2^2 design
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145
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Layout of 2^2 factorial experiment
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146
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Statistical analysis of 2^2 factorial experiment- model and assumptions
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147
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Statistical analysis of 2^2 factorial experiment- model estimates
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148
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Statistical analysis of factorial experiment- ANOVA of a 2^2 factorial experiment
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149
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2-level factorial experiments assumptions
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150
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Notations, coding of 2-level factorial design
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151
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Sign table of 2^2 factorial
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152
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Geometrical view of 2-level factorial design
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153
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Estimation of effects of a 2^2 factorial experiment
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154
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sums of squares of a 2^2 experiment
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155
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Use of contrasts in the analysis of 2^2 factorial experiment
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Week 10
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156
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2^3 factorial experiment-sign table
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157
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Layout of 2^3 factorial experiment
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158
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Factor effects of 2^3 factorial experiment
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159
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Geometrical view of 2^3 factorial design
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160
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Yate's algorithm for computing sums of squares in 2-level factorial experiment
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161
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Blocking and Confounding in factorial experiments
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162
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Methods of confounding: geometrical concept
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163
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Methods of confounding: Sign table method
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164
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Methods of confounding: Defining contrast method
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165
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2^k factorial experiment in 4 blocks-sign table method
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166
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2^k factorial experiment in 4 blocks-contrast method
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167
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2^k design in 2^p blocks of 2^k-p runs
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168
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Complete and partial confounding in 2-level experiment
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169
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Analysis in case of Complete and partial confounding
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170
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2^4 factorial experiment in 4 blocks
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171
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2^4 factorial experiment in 8 blocks
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172
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Two level factorial experiment in more than 8 blocks
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Week 11
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173
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Fractional factorial design (FFD)
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174
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Motivation of using a fractional factorial design
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176
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One-half fraction of 2-level fractional factorial design
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177
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One-quarter fraction of 2-level fractional factorial design
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178
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Aliasing in fractional factorial experiment
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179
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Confounding in fractional replications
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181
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Resolution III designs
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182
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Resolution IV designs
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184
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Design resolution and minimum aberration
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185
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Fold-over design (Mirror image fold-over design)
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186
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Example of a Fold-over design
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188
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Layout of a split plot design
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189
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Model of a split plot design
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190
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Sums of squares of a split plot design
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191
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ANOVA of split plot experiment
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192
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Advantages of split plot design
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193
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Disadvantages of split plot design
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194
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points to be noted about a split plot design
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195
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Difference between split plot experiment and factorial experiment
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Week 12
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196
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3-level factorial design
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197
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Design matrix of 3-level factorial experiment
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198
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Geometry of 3^2 factorial design
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199
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Effects and their components in 3-level factorial experiment
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200
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Geometry of 3^3 factorial design
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201
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Analysis of 3^k factorial experiment
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202
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Yate's algorithm for computing sums of squares in 3-level factorial experiment
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203
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Blocking in 3-level factorial experiment
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204
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3-level factorial design in 3 blocks
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205
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3-level factorial design in 9 blocks
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206
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3-level factorial design in 3^p blocks
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207
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3-level fractional factorial experiment
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208
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The one-third fraction of the 3^k design
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209
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Other 3^k-p fractional factorial designs
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210
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Mixed level factorial designs
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211
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Factorials with factors at two and three levels
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212
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Factorials with factors at two and four levels
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213
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Response surface methodology (RSM)
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214
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Sequential nature of RSM
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215
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First order RS model and its matrix structure
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Week 13
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216
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First order response surface (RS) designs
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217
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First order orthogonal RS designs
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218
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Variance-optimal first order designs
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219
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Variance-optimal first order designs-situation-I
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220
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Variance-optimal first order designs-situation-II
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221
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Variance-optimal first order designs-comparison of two situations
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223
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Scaled prediction variance
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224
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Example of Scaled prediction variance
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225
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Second order RS model
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226
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Models and least squares
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227
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Simple regression in matrix notations
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228
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Quadratic regression in matrix notattions
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229
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Second order RS designs
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230
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Screening stage of RSM
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231
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Different screening stratigies
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232
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Some screening designs
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233
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Selection of best screening design
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234
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Region of experimentation, region of interest, operability region
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Week 14
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239
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Properties of a good RS design
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241
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3-D response surface plot
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242
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Central Composite Design (CCD)
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243
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Geometrical structure of a CCD
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246
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Design moments of a CCD
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249
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Choosing number of center runs in CCD
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250
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Box-Behnken design (BBD)
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251
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Geometrical structure of a BBD
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254
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Comparison of CCD and BBD
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255
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Comparison of 3^3 factorial design and a face-centered CCD
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256
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Small Composite Design (SCD)
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257
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Use of Plackett-Burman design in SCD
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258
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Application of a SCDs
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259
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Alphabetic design optimalities
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260
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D-optimality and D-efficiency
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Week 15
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261
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A-optimality and A-efficiency
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262
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E-optimality and E-efficiency
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263
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G-optimality and G-efficiency
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264
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Variance dispersion graphs
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265
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Tradeoff between different optimality criteria
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266
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Orthogonal blocking in second order designs
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267
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Conditions for Orthogonal blocking in second order designs
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268
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Orthogonal blocking in two blocks of CCD
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269
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General comments on blocking of CCD
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271
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Analysis of a second-order blocked experiment under blocked CCD
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272
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Use of statistical software in DOE
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273
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Use of statistical software in DOE 1
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274
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Use of statistical software in DOE 2
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275
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Use of statistical software in DOE 3
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