03-09-2011 More 2 Factor ANOVA

03-09-2011 More 2 Factor ANOVA - 3/9/11 Lecture 14: March...

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•3/9/11 •1 Lecture 14: March 9, 2011 • Exam 1 will be returned during discussion this Friday. • Homework 9: one-factor ANOVA – One problem: Number 11.2, page 449 – It is a hypothesis test. It has several parts. – It closes Thursday, March 10 at 9:00 p.m. • This class: – Remaining ANOVA calculations by hand and the hypothesis test – Automation using Minitab – The resulting F-statistic: Is it that horrendous looking? • It resembles other test statistics that we have developed and used. • Readings for March 21: – Multiple Comparisons: pages 450-452 – ANOVA assumptions: 452-455 – Two-Factor ANOVA:pages 456-462 Discussion Session 8: Friday, March 11 First item of business: Returning Exam 1 Second item of business: Go to the “Discussion Data Sets “ menu on my web site. Download the data set titled “Discussion 8 Data, ANOVA Problem 11.1, page 449.” This is an Excel spreadsheet that contains the summary statistics for doing Problem 11.1 You will be doing this problem in Minitab if time permits. Whether or not you have enough time during discussion to do Minitab on this problem, the spreadsheet contains the summary statistics that are needed to do the hypothesis test by hand, which is described in the third item directly below. Third item of business: You will be doing a one-way ANOVA hypothesis test on Problem 11.1 using the steps that we develop in Lecture on March 9. Your TA already has the key summary statistics mentioned above. Fourth item of business: You will convert the Excel spreadsheet to a Minitab spreadsheet. You will use Minitab to confirm the results that you obtained above. Also, your TA will go over the Minitab output. Familiarity with the output (and especially the p-value) is important when answering exam questions. You will be implementing Minitab the same way that you did with Homework No. 9. Our template for setting up an ANOVA • is Table 11.2 on page 444. • Here it is again.
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•3/9/11 •2 Table 11.2 on page 444 of the text • The first row contains the “between treatments” calculations. The second row contains the “within treatments” calculations. Here are calculations we made so far. • We used a simple example and simple numbers. • We did all the “between treatments” calculations. • The concluding calculation was MSA . Calculating MSA (Heads Up! This will become Step (2) in Hypothesis Testing.) We will see this again as Slide No. 20. 222 11 22 33 n (y -y) +n (y -y) +n (y -y) SSA MSA = c-1 3-1 Treatment Sample Sample Means Variances Sizes y =11.0 n =4 y =19.0 n =4 y =6.0 n =4 y=12.0 n=12 “Grand” Given:  2 4(11-12) +4(19-12) +4(6-12) 344 172 3-1 2
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•3/9/11 •3 What’s next? • Have you looked at Homework 9 yet? • In this homework, you have to make insertions into two tables: – Table 1: sample means and sample variances for the different treatments – Table 2: SSA, SSE, MSA, and MSE • What’s the importance of the sample variances?
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This note was uploaded on 10/13/2011 for the course FINOPMGT 250 taught by Professor Kouzehkanani during the Spring '08 term at UMass (Amherst).

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03-09-2011 More 2 Factor ANOVA - 3/9/11 Lecture 14: March...

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