Chapter15_STAT1100.ppt", filename="Chapter15_STAT1100.ppt", filename="Chapter15_

Chapter15_STAT1100.ppt", filename="Chapter15_STAT1100.ppt", filename="Chapter15_

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Analysis of Variance (ANOVA) Statistics for Management and Economics Chapter 15
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Objectives One-Way Analysis of Variance Analysis of Variance Experimental Designs Randomized Blocks (Two-Way) Analysis of Variance Two-Factor Analysis of Variance Multiple Comparisons
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Analysis of Variance… Analysis of variance is a technique that allows us to compare two or more populations of interval data. Analysis of variance is: an extremely powerful and widely used procedure. a procedure which determines whether differences exist between population means . a procedure which works by analyzing sample variance .
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One-Way Analysis of Variance Independent samples are drawn from k populations These populations are referred to as treatments . It is not a requirement that n 1 = n 2 = … = n k
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One Way Analysis of Variance New Terminology: x is the response variable , and its values are responses . x ij refers to the i th observation in the j th sample. e.g., x 35 is the third observation of the fifth sample. The grand mean , , is the mean of all the observations, i.e.: n = n 1 + n 2 + … + n k
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One Way Analysis of Variance New Terminology (cont.): The unit that we measure is the experimental unit . Population classification criterion is called a factor . Each population is a factor level .
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Example In the economics department of a large university, many students change their major the first year. A detailed study of 256 economics majors was undertaken to help understand this phenomenon. Students were classified on the basis of their status at the beginning of their second year as: economics, mathematics, or other major. Several variables, including SAT mathematics score, were obtained.
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Example n s Economics 103 619 86 Math 31 629 67 Other 122 575 83 x ONE NOMINAL OR ORDINAL (CATEGORICAL) VARIABLE WITH >2 CATEGORIES INTERVAL DATA MEASURED WITHIN EACH CATEGORY THIS IS NOT A 3x3 CONTINGENCY TABLE – NOTICE THE COLUMNS REPRESENT SUMMARY STATISTICS!
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Example x is the response variable , and its values are responses . SAT score is the response variable; the actual SAT math score  are the responses in this example. x ij refers to the i th observation in the j th sample. e.g., x 4,2 is the fourth SAT score for math and other science majors: 670 Terminology comma added for clarity
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The unit that we measure is the experimental unit . SAT math scores for students with three different majors Population classification criterion is called a factor . The major is the factor we’re interested in. This is the only factor under consideration (hence the term “one way” analysis of variance). Each population is a
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Chapter15_STAT1100.ppt", filename="Chapter15_STAT1100.ppt", filename="Chapter15_

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