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6166 UNIT 3 Section 2 Answers

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We continue using SAS to answer this question. We will perform the analysis on the square root transformed diameters. The SAS program which performs these calculations can be found here. You can run the program to get the output. Here we will only show part of the output. Note, you can attempt to compute these by hand and compare your results with the results below. Note also that the analysis is performed on the squareroot transformed values, not the original values. We always perform the multiple comparison procedures on the values on which the original analysis of variance was performed.
The SAS program to do the full analysis is given here.
proc glm data=shield; class machine; model sdia = machine /solution; means machine / hovtest=bartlett; means machine / hovtest=bf ; /*Perform multiple comparison tests*/ means machine / LSD SNK Tukey duncan waller ; /* Test requested contrast */ contrast "l1" machine .5 .5 1 ; /* Output residuals and predicted values */ output out=outdia r=rdia p=pdia; title1 'Problem 8.30,page 424 Ott and Longnecker'; title2 'Square Root transformed response'; footnote ''; run;
Printout from SAS GLM Problem 8.30,page 424 Ott and Longnecker Square Root transformed response The GLM Procedure WallerDuncan Kratio t Test for sdia NOTE: This test minimizes the Bayes risk under additive loss and other assumptions. Kratio 100 Error Degrees of Freedom 17 Error Mean Square 4.627549 < From AOV F Value 4.48 < From AOV Critical Value of t 2.18066 < From Waller Table Minimum Significant Difference 2.7083 < From equation Harmonic Mean of Cell Sizes 6 < since sample sizes are unequal use this for n. NOTE: Cell sizes are not equal. Means with the same letter are not significantly different. Waller Grouping Mean N machine A 5.949 10 c B A 3.575 5 b B 2.700 5 a t Tests (LSD) for sdia NOTE: This test controls the Type I comparisonwise error rate, experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 17 Error Mean Square 4.627549 Critical Value of t 2.10982 < From Table 2 Least Significant Difference 2.6204 < From Equation Harmonic Mean of Cell Sizes 6 < since sample sizes are unequal use this for n. NOTE: Cell sizes are not equal. Means with the same letter are not significantly different. t Grouping Mean N machine A 5.949 10 c B A 3.575 5 b B 2.700 5 a Duncan's Multiple Range Test for sdia NOTE: This test controls the Type I comparisonwise error rate, experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 17 Error Mean Square 4.627549 Harmonic Mean of Cell Sizes 6 NOTE: Cell sizes are not equal. Number of Means 2 3 Critical Range 2.620 2.749 < From equation use q = 2.98, 3.13 of Duncan Table Means with the same letter are not significantly different. Duncan Grouping Mean N machine A 5.949 10 c B A 3.575 5 b B 2.700 5 a StudentNewmanKeuls Test for sdia NOTE: This test controls the Type I experimentwise error rate complete null hypothesis but not under partial null hypotheses Alpha 0.05 Error Degrees of Freedom 17 Error Mean Square 4.627549 Harmonic Mean of Cell Sizes 6 NOTE: Cell sizes are not equal. Number of Means 2 3 Critical Range 2.6203508 3.1861245 < From equation use q = 2.98, 3.63 of Table 10 Means with the same letter are not significantly different. SNK Grouping Mean N machine A 5.949 10 c B A 3.575 5 b B 2.700 5 a Tukey's Studentized Range (HSD) Test for sdia NOTE: This test controls the Type I experimentwise error rate, generally has a higher Type II error rate than REGWQ. Alpha 0.05 Error Degrees of Freedom 17 Error Mean Square 4.627549 Critical Value of Studentized Range 3.62796 < From Table 10 Minimum Significant Difference 3.1861 Harmonic Mean of Cell Sizes 6 NOTE: Cell sizes are not equal. Means with the same letter are not significantly different. Tukey Grouping Mean N machine A 5.949 10 c B A 3.575 5 b B 2.700 5 a We can summarize the results as follows: Level of sdia diameter machine N Mean Std Dev LSD TUKEY SNK DUNCAN WALLER Mean Std Dev a 5 2.70040161 1.14446010 B B B B B 8.3400000 6.521732 b 5 3.57461248 2.24224933 AB AB AB AB AB 16.8000000 22.431116 c 10 5.94879442 2.43398279 A A A A A 40.7200000 34.519939
Note that to say that the square root transformed means are statistically different is the same as saying that the untransformed means are different. Hence the results of the multiple range test holds for the untransformed means as well.
To test the contrast in SAS we use a contrast statement. The only difficult thing is to make sure we get the correct contrast coefficients into the correct positions in the statement.
Dependent Variable: sdia Contrast DF Contrast SS Mean Square F Value Pr > F l1 1 39.51668344 39.51668344 8.54 0.0095