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Factorial Designs

Factorial Designs. Week 9 Lecture 2. Agenda. Basic factorial design concepts Main and interaction effect Factorial design in computer system performance analysis. What are factorial designs. Two or more independent variables are manipulated in a single experiment

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Factorial Designs

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  1. Factorial Designs Week 9 Lecture 2 ISYS3015 Analytical Methods for IS Professionals School of IT, The University of Sydney

  2. Agenda • Basic factorial design concepts • Main and interaction effect • Factorial design in computer system performance analysis ISYS3015 Analytical Methods for IS Professionals School of IT, The University of Sydney

  3. What are factorial designs • Two or more independent variables are manipulated in a single experiment • They are referred to as factors • The major purpose of the research is to explore their effects jointly • Factorial design produce efficient experiments, each observation supplies information about all of the factors ISYS3015 Analytical Methods for IS Professionals School of IT, The University of Sydney

  4. A simple example • Investigate an education program with a variety of variations to find out the best combination • Amount of time receiving instruction • 1 hour per week vs. 4 hour per week • Settings • In-class vs. pull out • 2 X 2 factorial design • Number of numbers tells how many factors • Number values tell how many levels • The result of multiplying tells how many treatment groups that we have in a factorial design ISYS3015 Analytical Methods for IS Professionals School of IT, The University of Sydney

  5. Null outcome • None of the treatment has any effect • Main effect • is an outcome that is a consistent difference between levels of a factor. • Interaction effect • An interaction effect exists when differences on one factor depend on the level you are on another factor. ISYS3015 Analytical Methods for IS Professionals School of IT, The University of Sydney

  6. Main effects • Main effect of time • Main effect of setting • Main effects on both ISYS3015 Analytical Methods for IS Professionals School of IT, The University of Sydney

  7. Interaction effect • An interaction effect exists when differences on one factor depend on the level of another factor • How do we know if there is an interaction in a factorial design? • Statistical analysis will report all main effects and interactions. • If you can not talk about effect on one factor without mentioning the other factor • Spot an interaction in the graphs – whenever there are lines that are not parallel there is an interaction present! ISYS3015 Analytical Methods for IS Professionals School of IT, The University of Sydney

  8. Interaction effect • Interaction as a difference in magnitude of response • Interaction as a difference in direction of response ISYS3015 Analytical Methods for IS Professionals School of IT, The University of Sydney

  9. Factorial design variations • A 2 X 3 example • study the effect of different treatment combinations for cocaine abuse. • Factor 1: treatment • psychotherapy • behavior modification • Factor 2: • inpatient • day treatment • outpatient • Dependent variable • severity of illness rating ISYS3015 Analytical Methods for IS Professionals School of IT, The University of Sydney

  10. Factorial designs in computer system performance analysis • Personal workstation design • Processor: 68000, Z80, 8086 • Memory size: 512K 2M or 8M bytes • Number of disks: one, two or three • Workload: Secretarial, managerial or scientific • User education: high school, college, post-graduate level • Dependent variable • Throughput, response time ISYS3015 Analytical Methods for IS Professionals School of IT, The University of Sydney

  11. 22 factorial design • Two factors, each at two levels • Example: workstation design • Factor 1: memory size • Factor 2: cache size • DV: performance in MIPS ISYS3015 Analytical Methods for IS Professionals School of IT, The University of Sydney

  12. Quantify effects • We want to learn which factor contribute more to the performance. • Define two variable • The regression model ISYS3015 Analytical Methods for IS Professionals School of IT, The University of Sydney

  13. Quantifying results (cont) • Resolving those coefficients • We get • How do you read this? ISYS3015 Analytical Methods for IS Professionals School of IT, The University of Sydney

  14. Quantify effects by sign table • Sign table method ISYS3015 Analytical Methods for IS Professionals School of IT, The University of Sydney

  15. 2K factorial design • K factors, each at two level • 2K experiments • 23 design example • In designing a personal workstation, the three factors needed to be studied are: cache size, memory size and number of processors ISYS3015 Analytical Methods for IS Professionals School of IT, The University of Sydney

  16. 2k factorial design with replication • r replications of 2k experiments • 2Kr observations • Allows estimation of experimental errors • 223 design example • The memory-cache experiments were repeated three times each. The result is shown below ISYS3015 Analytical Methods for IS Professionals School of IT, The University of Sydney

  17. Full and fractional factorial design • Full factorial design • Study all combinations • Can find effect of all factors • May try 2K factorial design first • Fractional (incomplete) factorial design • Leave some treatment groups empty • Less information • May not get all interactions • No problem if interaction is negligible ISYS3015 Analytical Methods for IS Professionals School of IT, The University of Sydney

  18. 2k-pFractional factorial design • Large number of factors • Large number of experiments • Full factorial design too expensive • Use a fractional factorial design • 2k-p design allows analyzing k factors with only 2k-pexperiments. • 2k-1design requires only half as many experiments • 2k-2design requires only one quarter of the experiments ISYS3015 Analytical Methods for IS Professionals School of IT, The University of Sydney

  19. Example: 27-4Design • Study 7 factors with only 8 experiments • When quantify the effects, just calculate the main effects • Will be able to eliminate some factors in further study. ISYS3015 Analytical Methods for IS Professionals School of IT, The University of Sydney

  20. Quantify model ISYS3015 Analytical Methods for IS Professionals School of IT, The University of Sydney

  21. Preparing the sign table • Choose k - p factors and prepare a complete sign table for a full factorial design with k-p factors • Of the 2k-p –k +p -1 column on the right, choose p columns and mark them with the p factors that were not chosen in step 1. ISYS3015 Analytical Methods for IS Professionals School of IT, The University of Sydney

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