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9.68 The next table gives data for a 2 × 2 factorial experiment with two observations per factor-level combination. L09068 Factor B Level 1 2 29.6, 35.2 12.9, 17.6 47.3, 42.1 28.4, 22.7 Factor A 1 2 a. Identify the treatments for this experiment. Calculate and plot the treatment means, using the response vari- able as the y-axis and the levels of factor B as the x-axis. Use the levels of factor A as plotting symbols. Do the treatment means appear to differ? Do the factors ap- pear to interact? b. Use the computational formulas in Appendix C to cre- ate an ANOVA table for this experiment. c. Test to determine whether the treatment means differ at the a = .05 level of significance. Does the test sup- port your visual interpretation from part a? d. Does the result of the test in part b warrant a test for interaction between the two factors? If so, perform it using e. Do the results of the previous tests warrant tests of the two factor main effects? If so, perform them using .05. Yes. .05. a = f. Interpret the results of the tests. Do they support your visual interpretation from part a? g. Given the results of your tests, which pairs of means, if any, should be compared?

9.68 The next table gives data for a 2 × 2 factorial experiment with two observations per factor-level combination. L09068 Factor B Level 1 2 29.6, 35.2 12.9, 17.6 47.3, 42.1 28.4, 22.7 Factor A 1 2 a. Identify the treatments for this experiment. Calculate and plot the treatment means, using the response vari- able as the y-axis and the levels of factor B as the x-axis. Use the levels of factor A as plotting symbols. Do the treatment means appear to differ? Do the factors ap- pear to interact? b. Use the computational formulas in Appendix C to cre- ate an ANOVA table for this experiment. c. Test to determine whether the treatment means differ at the a = .05 level of significance. Does the test sup- port your visual interpretation from part a? d. Does the result of the test in part b warrant a test for interaction between the two factors? If so, perform it using e. Do the results of the previous tests warrant tests of the two factor main effects? If so, perform them using .05. Yes. .05. a = f. Interpret the results of the tests. Do they support your visual interpretation from part a? g. Given the results of your tests, which pairs of means, if any, should be compared?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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a, b, and c

**Title: 2 x 2 Factorial Experiment Analysis** The table below provides data from a 2 x 2 factorial experiment, which includes two observations per factor-level combination. | | **Factor B** | | |--------------|--------------|-----------| | | **Level 1** | **Level 2** | | **Factor A** | | | | **1** | 29.6, 35.2 | 47.3, 42.1 | | **2** | 12.9, 17.6 | 28.4, 22.7 | --- **Analytical Questions:** **a. Treatment Identification and Plotting:** - Identify the treatments for this experiment. - Calculate the treatment means, using the response variable as the y-axis and the levels of Factor B as the x-axis. - Use the levels of Factor A as plotting symbols. - Analyze whether the treatment means differ and if factors appear to interact. **b. ANOVA Table Creation:** - Use the computational formulas in Appendix C to create an ANOVA table for this experiment. **c. Treatment Mean Differentiation:** - Test if the treatment means differ at the α = 0.05 level of significance. - Verify if the test supports your visual interpretation from part (a). **d. Factor Interaction Test:** - Assess whether the result of the test in part (b) necessitates a test for interaction between the two factors at α = 0.05. **e. Main Effects Tests:** - Evaluate if results from previous tests warrant tests of the two factor main effects at α = 0.05. **f. Test Result Interpretation:** - Interpret whether the test results support your visual interpretation from part (a). **g. Mean Comparison:** - Based on test results, determine which pairs of means, if any, should be compared. Ensure to follow statistical protocols for analysis, including ANOVA procedures for factorial designs, to accurately interpret and conclude the effects and interactions between factors.
Transcribed Image Text:**Title: 2 x 2 Factorial Experiment Analysis** The table below provides data from a 2 x 2 factorial experiment, which includes two observations per factor-level combination. | | **Factor B** | | |--------------|--------------|-----------| | | **Level 1** | **Level 2** | | **Factor A** | | | | **1** | 29.6, 35.2 | 47.3, 42.1 | | **2** | 12.9, 17.6 | 28.4, 22.7 | --- **Analytical Questions:** **a. Treatment Identification and Plotting:** - Identify the treatments for this experiment. - Calculate the treatment means, using the response variable as the y-axis and the levels of Factor B as the x-axis. - Use the levels of Factor A as plotting symbols. - Analyze whether the treatment means differ and if factors appear to interact. **b. ANOVA Table Creation:** - Use the computational formulas in Appendix C to create an ANOVA table for this experiment. **c. Treatment Mean Differentiation:** - Test if the treatment means differ at the α = 0.05 level of significance. - Verify if the test supports your visual interpretation from part (a). **d. Factor Interaction Test:** - Assess whether the result of the test in part (b) necessitates a test for interaction between the two factors at α = 0.05. **e. Main Effects Tests:** - Evaluate if results from previous tests warrant tests of the two factor main effects at α = 0.05. **f. Test Result Interpretation:** - Interpret whether the test results support your visual interpretation from part (a). **g. Mean Comparison:** - Based on test results, determine which pairs of means, if any, should be compared. Ensure to follow statistical protocols for analysis, including ANOVA procedures for factorial designs, to accurately interpret and conclude the effects and interactions between factors.
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