Two-Factor Experiment and Three or More Factor Experiments
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The document presents an overview of two-factor and multi-factor experiments, including various designs like randomized block design, split-plot design, and strip-plot design. It elaborates on the advantages and disadvantages of factorial experiments and explains the structure of split-split plots and strip-split-plot designs with practical examples. Key references and theoretical underpinnings of these experimental designs are also provided.
Two-Factor Experiment and Three or More Factor Experiments
- 1. Two-Factors Experiment and Three or More Factor Experiments Research Seminar I (RH 630) Dr. Loreto V. Jao Presented by: Mary Anne Portuguez MP-IP-1
- 2. Outline of the report: Two-factors Experiment: Factorial Experiment Two-Factor Experiment in Randomized Block Design Split-Block Design (Strip-Plot) 3 or More Factor Experiments: Split-Split Design Split Strip and Plot Design
- 3. Factor •In analysis of variance, the variable (independent or quasi-independent) that designates the groups being compared (Gravetter & Wallnau, 2012). •A factor is a general type or category of treatments (Easton & McColl, 2004).
- 4. Factorial Experiment •A research study that involves more than one factor (Gravetter & Wallnau, 2012). •One in which all possible combinations of the selected values of each of the independent variables are used (McGuigan, 1990). •An experimental series in which the effects of several experimental variables are assessed (Chaplin, 1986).
- 5. Illustration Consider an experiment that was conducted on learning during hypnosis. These two independent variables are (1) whether the participants are hypnotized and (2) high or low susceptibility to being hypnotized.
- 6. There are four possible combinations of the values of the IV. Each represented in a box.
- 7. Advantages 1. More precision on each factor than with single factor experimentation. 2. Broadening the scope of an experiment. 3. Possible to estimate the interaction effect. 4. Good for exploratory work where we wish to find the most important factor or the optimal level of a factor (or combination of levels of more than one factor).
- 8. Disadvantages: 1. Some people say it’s complex. 2. With a number of factors each at several levels, the experiment can become very large.
- 9. Randomized Block Design (Stratified Random Sampling) •Constructed to reduce the noise or variance in the data. •They require that the researcher divide the sample into relatively homogeneous subgroups or blocks. •Block refers to homogenous experimental unit which is analogous to strata.
- 11. How Blocking Reduces Noise •It reduces variability of the sample •You are ensured that it has stronger treatment effect
- 12. Split-Plot Design •The terminology of Split plots originated from agriculture (Oehlert, 2013). •It is invented by Ronald Fisher, a great statistician and their importance in industrial experimentation has been long recognized. •It is a blocked experiment, where the blocks themselves serve as experimental units. The blocks are refered to as whole plots, while the experimental units within the blocks are called split plots, split units, or subplots.
- 13. Patient 1 Patient 3Patient 2 50 mg 80 mg 100 mg 50 mg 80 mg 100 mg 50 mg 80 mg 100 mg WHOLE PLOTS SPLIT PLOTS
- 14. Why use of Split-plot? •Cost •Efficiency •Validity
- 16. SPLIT-SPLIT PLOTS •An extension of split-plot. •In split-split plot design, there are two restrictions of randomization.
- 17. Patient 1 Patient 3Patient 2 50 mg 80 mg 100 mg 50 mg 80 mg 100 mg 50 mg 80 mg 100 mg 8: 00 A.M. 2: 00 P.M. 8: 00 P.M. 2: 00 A.M. 8: 00 A.M. 2: 00 P.M. 8: 00 P.M. 2: 00 A.M. 8: 00 A.M. 2: 00 P.M. 8: 00 P.M. 2: 00 A.M. WHOLE PLOTS SPLIT PLOTS
- 18. Recap One way to think about split plots is that the units have a structure somewhat like that of nested factorial treatments. In a split plot, the split plots are nested in whole plots; in a split-split plot, the split-split plots are nested in split plots, which are themselves nested in whole plots. In the split-plot design, levels of different factors are assigned to the different kinds of units.
- 19. Strip-Split-Plot Design •It has an extensive application in the agricultural sciences, but it finds occasional use in industrial experimentation. •Factor A is applied to whole plots then factor B is applied to strips (which are just another set of whole plots) which are not important to the original whole plots.
- 20. Sample Problem: From Gary Oehlert “A First Course in Design and Analysis of Experiments (2010)” Machine shop Consider a machine shop that is producing parts cut from metal blanks. The quality of the parts is determined by their strength and fidelity to the desired shape. The shop wishes to determine how brand of cutting tool and sup plier of metal blank affect the quality. An experiment will be performed one week, and then repeated the next week. Four brands of cutting tools will be obtained, and brand of tool will be randomly assigned to four lathes. A different supplier of metal blank will be randomly selected for each of the 5 work days during the week. That way, all brand-supplier combinations are observed.
- 22. Strip Plots are easier to use in this example. The strip plot arises through ease-of-use considerations.It is easier to use one brand of tool on each lathe than it is to change. Simi larly, it is easier to use one supplier all day than to change suppliers during the day. When units are large and treatments difficult to change, but the units and treatments can cross, a strip plot can be the design of choice.
- 23. References: •Chaplin, J.P.(1986). Dictionary of psychology. Bantam Dell: Canada. •Gravetter, F.J. & Wallnau, L.B. (2012). Statistics for behavioral sciences. Philippines: Cengage Learning Asia Pte. Ltd. •McGuigan, F.J. (1990). Experimental psychology (5th ed.). Englewood Cliffs, New Jersey: Prentice Hall. •Montgomery, D.C. (2001). Design and analysis of experiments. (5th ed.). USA: John Wiley & Sons, Inc. •Jones, B. (2009 October). Split-plots: What, why, and how. Journal of Quality Technology. 41 (4). •Oehlert, G.W. (2010). A first course in design and analysis of Experiments. Minitab, Inc. •Oehlert, G.W. Split Plots. Retrieved from http://users.stat.umn.edu/~gary/classes/5303/lectures/SplitPlots.pdf as of July 9, 2014. •Easton, V.J. & McColl, J.H. (2004). Statistics glossary. Retrieved from http://www.stats.gla.ac.uk/steps/glossary/anova.html#treatment as of July 8, 2014. •Factorial experiment. Retrieved from http://www.stat.ncsu.edu/people/nelson/courses/st512/Factorial%20Experiments.pdf as of July 8, 2014. •Randomized block design. Retrieved from http://www.socialresearchmethods.net/kb/expblock.php as of July 8, 2014.