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Chapter 2: Multiple Factor Designs and Blocking. Chapter 2: Multiple Factor Designs and Blocking. Objectives. Define blocking effects. Define a randomized complete block design. Generate and analyze a randomized complete block design. Blocking.
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Objectives • Define blocking effects. • Define a randomized complete block design. • Generate and analyze a randomized complete block design.
Blocking • Blocks are groups of experimental units that are formed such that units within blocks are as homogeneous as possible. • Blocking is a statistical technique designed to identify and control variation among groups of experimental units. • Blocking is a restriction on randomization.
Generating a Randomized Complete Block Design • This demonstration illustrates the concepts discussed previously.
The Design P B O B G O P G O P B G B G O P
Is the Blocking Factor Useful? Did the blocking factor help the experiment?
Analysis Concerns: Should the Blocking Factor be Deleted from the Model? ...
Analysis Concerns: Should the Blocking Factor be Deleted from the Model? NEVER!
2.01 Multiple Choice Poll • Which of the following statements is true? • Blocking is a restriction on randomization. • A block effect is not always significant. • A blocking factor should never be removed from a model. • All of the above are true.
2.01 Multiple Choice Poll – Correct Answer • Which of the following statements is true? • Blocking is a restriction on randomization. • A block effect is not always significant. • A blocking factor should never be removed from a model. • All of the above are true.
Analyzing a Randomized Complete Block Design • This demonstration illustrates the concepts discussed previously.
Exercise This exercise reinforces the concepts discussed previously.
2.02 Poll • In the exercise, the blocking factor Mill had an F statistic of 5.0167. Did the blocking factor help this experiment? • Yes • No
2.02 Poll – Correct Answer • In the exercise, the blocking factor Mill had an F statistic of 5.0167. Did the blocking factor help this experiment? • Yes • No
Objectives • Define an incomplete block. • State the requirements for a balanced incomplete block design. • Understand the differences between unbalanced and balanced block designs. • Generate and analyze an incomplete block design.
Properties of a Balanced Incomplete Block Design • Each block has the same number of experimental units. • Each treatment occurs the same number of times in the experiment. • The number of times any two treatments occur together in the same block is the same for all pairs of treatments. • If the design is an incomplete block design (that is, each treatment cannot be applied in each block an equal number of times) and any one of these properties is not met, the design is an unbalanced incomplete block design.
Differences between Balanced and Unbalanced Designs • A balanced design can require too many runs to be practical. • All estimates of treatment means and all comparisons between pairs of treatments have equal precision in a balanced design. • A balanced design is more statistically efficient than an unbalanced design.
Generating and Analyzing an Incomplete Block Design This demonstration illustrates the concepts discussed previously.
Exercise This exercise reinforces the concepts discussed previously.
2.03 Multiple Choice Poll • Which of the following is not a property of the balanced incomplete block design? • Each block contains the same number of experimental units. • Each treatment occurs the same number of times in the experiment. • Each treatment is present in every block. • Each pair of treatments occurs together in the same block the same number of times.
2.03 Multiple Choice Poll – Correct Answer • Which of the following is not a property of the balanced incomplete block design? • Each block contains the same number of experimental units. • Each treatment occurs the same number of times in the experiment. • Each treatment is present in every block. • Each pair of treatments occurs together in the same block the same number of times.
Objectives • Explain the advantages of multiple factor designs. • Define common terms. • Generate and analyze a full factorial design.
Full Factorial • Most experiments involve two or more factors. These factors have two or more levels and can be quantitative or qualitative. • A design is said to be a full factorial design if all possible combinations of factor levels are included in the experiment. • A large number of runs is required for a full factorial design as the number of factors increase. • For example, for a full factorial design with f factors such that factor i has li levels, the number of runs is given by l1*l2*l3…*lf.
Advantages of Factorials • Factorials reveal interactions. • Factorials are more efficient than experiments that use one factor at a time. • Combinations of factor levels provide replication for individual factors, when factors are removed from the design.
2.04 Multiple Choice Poll • How many runs would a full factorial experiment with 4 factors, each at 3 levels, require? • 12 • 64 • 81
2.04 Multiple Choice Poll – Correct Answer • How many runs would a full factorial experiment with 4 factors, each at 3 levels, require? • 12 • 64 • 81
Temperature (categorical) 15, 70, 125 Battery Life Type of Plate Material (categorical) 1, 2, 3 Battery Life Experiment
Generating a Full Factorial Design • This demonstration illustrates the concepts discussed previously.
Exercise This exercise reinforces the concepts discussed previously.
2.05 Quiz • The output from the exercise on fuel use for the aircraft fleet is below. Based on the output, what factors should the company use in future experiments?
2.05 Quiz – Correct Answer • The output from the exercise on fuel use for the aircraft fleet is below. Based on the output, what factors should the company use in future experiments? • WeightandSpeed;the experiment shows that only these two factors are significant so future experiments need only include thesefactors.
