This chapter discusses different experimental designs used in business statistics including one-way ANOVA, randomized block design, and two-way factorial designs. It provides examples to demonstrate how to compute and interpret results for each design. Key steps covered include partitioning sums of squares, calculating mean squares, performing F-tests to determine significance of factors, and using multiple comparison techniques for identifying differences between means when factors are significant.
20. One-Way ANOVA: Procedural Summary Rejection Region Critical Value Non rejection Region . H reject , 10 . 3 > 10.18 = F Since o c F
21. Excel Output for the Valve Opening Example Anova: Single Factor SUMMARY Groups Count Sum Average Variance Operator 1 5 31.59 6.318 0.00277 Operator 2 8 50.22 6.2775 0.0110786 Operator 3 7 45.42 6.488571429 0.0101143 Operator 4 4 24.92 6.23 0.0018667 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 0.236580119 3 0.07886004 10.181025 0.00028 3.09839 Within Groups 0.154915714 20 0.007745786 Total 0.391495833 23
30. Freighter Example: Means and Sample Sizes for the Four Operators Operator Sample Size Mean 1 5 6.3180 2 8 6.2775 3 7 6.4886 4 4 6.2300
31. Tukey-Kramer Results for the Four Operators Pair Critical Difference |Actual Differences| 1 and 2 .1405 .0405 1 and 3 .1443 .1706* 1 and 4 .1653 .0880 2 and 3 .1275 .2111* 2 and 4 .1509 .0475 3 and 4 .1545 .2586* *denotes significant at .05
32. Partitioning the Total Sum of Squares in the Randomized Block Design SST (Total Sum of Squares) SSC (Treatment Sum of Squares) SSE (Error Sum of Squares) SSR (Sum of Squares Blocks) SSE’ (Sum of Squares Error)
40. Analysis of Variance for the Tread-Wear Example Source of Variance SS df MS F Treatment 3.484 2 1.742 96.78 Block 1.549 4 0.387 21.50 Error 0.143 8 0.018 Total 5.176 14
48. A 2 3 Factorial Design with Interaction Cell Means C 1 C2 C 3 Row effects R 1 R 2 Column
49. A 2 3 Factorial Design with Some Interaction Cell Means C 1 C 2 C 3 Row effects R 1 R 2 Column
50. A 2 3 Factorial Design with No Interaction Cell Means C 1 C 2 C 3 Row effects R 1 R 2 Column
51. A 2 3 Factorial Design: Data and Measurements for CEO Dividend Example N = 24 n = 4 X=2.7083 1.75 2.75 3.625 Location Where Company Stock is Traded How Stockholders are Informed of Dividends NYSE AMEX OTC Annual/Quarterly Reports 2 1 2 1 2 3 3 2 4 3 4 3 2.5 Presentations to Analysts 2 3 1 2 3 3 2 4 4 4 3 4 2.9167 X j X i X 11 =1.5 X 23 =3.75 X 22 =3.0 X 21 =2.0 X 13 =3.5 X 12 =2.5
52. A 2 3 Factorial Design: Calculations for the CEO Dividend Example (Part 1)
53. A 2 3 Factorial Design: Calculations for the CEO Dividend Example (Part 2)
54. A 2 3 Factorial Design: Calculations for the CEO Dividend Example (Part 3)
55. Analysis of Variance for the CEO Dividend Problem Source of Variance SS df MS F Row 1.0418 1 1.0418 2.42 Column 14.0833 2 7.0417 16.35 * Interaction 0.0833 2 0.0417 0.10 Error 7.7500 18 0.4306 Total 22.9583 23 * Denotes significance at = .01.
56. Excel Output for the CEO Dividend Example (Part 1) Anova: Two-Factor With Replication SUMMARY NYSE ASE OTC Total AQReport Count 4 4 4 12 Sum 6 10 14 30 Average 1.5 2.5 3.5 2.5 Variance 0.3333 0.3333 0.3333 1 Presentation Count 4 4 4 12 Sum 8 12 15 35 Average 2 3 3.75 2.9167 Variance 0.6667 0.6667 0.25 0.9924 Total Count 8 8 8 Sum 14 22 29 Average 1.75 2.75 3.625 Variance 0.5 0.5 0.2679
57. Excel Output for the CEO Dividend Example (Part 2) ANOVA Source of Variation SS df MS F P-value F crit Sample 1.0417 1 1.0417 2.4194 0.1373 4.4139 Columns 14.083 2 7.0417 16.355 9E-05 3.5546 Interaction 0.0833 2 0.0417 0.0968 0.9082 3.5546 Within 7.75 18 0.4306 Total 22.958 23