lab6 - STAT 350 – Spring 2009 Lab#6 SOLUTION Corrected...

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Unformatted text preview: STAT 350 – Spring 2009 Lab #6 SOLUTION Corrected 2-way ANOVA Unless otherwise indicated, all of the following should be done using SAS. Please put all SAS input (Editor window) and all SAS output (Output window, NOT the Log window) as an appendix. Nothing pasted directly from SAS should be given as an answer to the questions below! The Experiment A wood scientist (yes, there are such people... even right here at Purdue) has come to you for help analyzing an experiment. He had wanted to examine the durability of wood used for decking. Deterioration of wood in use is commonly caused by decay fungi, certain insects (including termites) as well as other organisms, and weathering. He wanted to examine various species of wood and various preservatives. He used 7 species of wood: Maple, Ash, Red Oak, Spruce, Northern White Cedar, Eastern Red Cedar, and Redwood. He used 4 types of preservatives: creosote, pentachlorophenol (PCP), chromated copper arsenate (CCA), and ammoniacal copper arsenate (ACA). He had 20 two-by-four boards of each species: of these 5 were treated with creosote, 5 with PCP, 5 with CCA, and 5 with ACA. The boards were dried and weighed then placed outdoors (all in the same experimental plot) for 10 years. At the end of 10 years, the boards were collected, dried, and re-weighed. For each board, the dry weight-loss (in grams) was recorded. The data are available in the accompanying Excel file. 1. Analyze the data as a 2-way ANOVA, with "preservative" and "species" as the 2 factors. Include the interaction effect. Give sums of squares and mean squares to 2 decimal places, but do not round the F or p-values. a. Present the ANOVA table (with p-values) in a report-quality table. Source Species Preservative S×P Error Total df 6 3 18 112 139 Sum of Squares 13085.49 19.80 68988.65 24542.65 106636.58 Mean Square 2180.91 6.60 3832.70 219.13 F 9.95 0.03 17.49 p-value < 0.0001 0.9929 < 0.0001 b. Was there a significant preservative effect (α = 0.05)? i. Answer either. “Yes, the effect of preservative was significant” or “No, the effect of preservative was not significant”. No, the effect of preservative was not significant ii. Give the value of the appropriate test statistic and its degrees of freedom. The test statistic is 0.03, the degrees of freedom are df1 = 3, df2 = 112 iii. Give the p-value. 0.9929 Lab #6 Page 1 iv. If the effect of preservative is significant, conduct Tukey's multiple comparison procedure on the preservatives and present your results (with the means for each level) using the line method discussed in class (you may draw the lines in by hand). If this effect was not significant, just give a table summarizing the means for each preservative. In either case, give means to 2 decimal places. preservative: mean loss: ACA 101.71 CCA 101.37 Creosote 101.34 PCP 100.67 c. Was there a significant species effect (α = 0.05)? i. Answer either. “Yes, the effect of species was significant” or “No, the effect of species was not significant”. Yes, the effect of species was significant ii. Give the value of the appropriate test statistic and its degrees of freedom. The test statistic is 9.95, the degrees of freedom are df1 = 6, df2 = 112 iii. Give the p-value. < 0.0001 iv. If the effect of preservative is significant, conduct Tukey's multiple comparison procedure on the species and present your results (with the means for each level) using the line method discussed in class (you may draw the lines in by hand). If this effect was not significant, just give a table summarizing the means for each species. In either case, give means to 2 decimal places. Species: Mean: Maple 119.53 Red Oak 103.79 Redwood 103.54 Spruce 102.91 White Cedar 97.34 Ash 97.08 Red Cedar 84.73 d. Was the effect of the interaction between species and preservative significant (α = 0.05)? i. Answer either. “Yes, there was a significant interaction effect” or “No, there was not a significant interaction effect”. Yes, there was a significant interaction effect. ii. Give the value of the appropriate test statistic and its degrees of freedom. The test statistic is 17.49, the degrees of freedom are df1 = 18, df2 = 112 iii. Give the p-value. < 0.0001 Lab #6 Page 2 e. Give interaction plots (I recommend making these in Excel). Make 2 separate plots. The first should have the species levels on the x-axis and a separate series for each preservative. The second should have the preservative levels on the x-axis and a separate series for each species. Be sure that the x-axis and series are unambiguously labeled. If you print in black-and-white, make sure the different series are distinguishable after printing! 180 160 140 120 Creosote 100 PCP 80 CCA 60 ACA 40 20 0 Maple Ash Spruce Red Oak White Cedar Redwood Red Cedar 180 160 140 Maple 120 Ash Spruce 100 Red Oak 80 White Cedar 60 Redwood 40 Red Cedar 20 0 Creosote PCP CCA ACA 2. Now assume that instead of testing these preservatives on several different species of wood, the wood scientist had only used boards made of Red Cedar. Using only the data collected with Red Cedar boards, analyze the data as a 1-way ANOVA with preservative as the only factor. a. Present the ANOVA table (with p-values) in a report-quality table. Give sums of squares and mean squares to 2 decimal places, but do not round the F or p-values. Source Preservative Error Total Lab #6 df 3 16 19 Sum of Squares 33830.22 3038.40 36868.62 Mean Square 11276.74 189.90 F 59.38 p-value < 0.0001 Page 3 b. Was there a significant preservative effect (α = 0.05)? i. Answer either. “Yes, the effect of preservative was significant” or “No, the effect of preservative was not significant”. Yes, the effect of preservative was significant. ii. Give the value of the appropriate test statistic and its degrees of freedom. The test statistic is 59.38, the degrees of freedom are df1 = 3, df2 = 16 iii. Give the p-value. < 0.0001 iv. If the effect of preservative is significant, conduct Tukey's multiple comparison procedure on the preservatives and present your results (with the means for each level) using the line method discussed in class (you may draw the lines in by hand). If this effect was not significant, just give a table summarizing the means for each preservative. In either case, give means to 2 decimal places. preservative: mean loss: ACA 144.98 CCA 100.14 PCP 51.16 Creosote 42.64 3. Were the conclusions you obtained regarding the preservatives the same for both analyses? Explain why or why not. No, the conclusions regarding the preservatives were not the same in both analyses. In the first analysis, it appeared that the four preservatives were equally effective. In the second analysis, there was a clear difference in effectiveness among these preservatives. The reason for the apparent inconsistency was the strong and significant interaction effect. Looking at the interaction plots, you can see (for example) that Creosote was the most effective preservative when used with Red Cedar and the least effective when used with Maple. ACA, on the other hand, was most effective when used on Maple, and least effective when used on Red Cedar. These differences between species are canceled out when the effectiveness of a preservative is averaged across species. 4. Write a brief paragraph explaining your findings. Be sure to address your conclusions regarding the species and preservatives (e.g., which would you recommend?) Overall we found a significant difference in the durability among the 7 species tested. Red Cedar, Ash, and White Cedar were the most durable species (these had the least loss of mass) while Maple was clearly the least durable species. Results among the preservatives were less conclusive. There was a highly significant interaction effect between species and preservative, indicating that which preservative is most effectives depends on the species of wood being used. With Red Cedar, Creosote and PCP proved to be the most effective preservatives, while ACA was clearly the least effective. Separate analyses should be done for each of the other 6 species of wood to determine if there is a significant difference in the effectiveness of the 4 preservatives for each species. Lab #6 Page 4 Appendix Do not forget to include your SAS code (contents of the Editor window) and all SAS output (contents of the Output window, NOT the Log window) as an appendix. data wood; input species $ preserv $ loss; cards; Maple Creosote 161.3 Maple Creosote 148.9 Maple Creosote 173.8 Maple Creosote 134.1 Maple Creosote 154.1 Ash Creosote 127.8 Ash Creosote 110 Ash Creosote 119.8 Ash Creosote 109.2 Ash Creosote 117 Spruce Creosote 112.3 Spruce Creosote 104.7 Spruce Creosote 118.5 Spruce Creosote 89.8 Spruce Creosote 129.6 RedOak Creosote 91.1 RedOak Creosote 79.3 RedOak Creosote 93.4 RedOak Creosote 127.9 RedOak Creosote 99 WhiteCedar Creosote 118.3 WhiteCedar Creosote 78 WhiteCedar Creosote 87.2 WhiteCedar Creosote 95.6 WhiteCedar Creosote 87.2 Redwood Creosote 103.6 Redwood Creosote 84.8 Redwood Creosote 84.8 Redwood Creosote 95.3 Redwood Creosote 97.4 RedCedar Creosote 54.6 RedCedar Creosote 22.9 RedCedar Creosote 59.9 RedCedar Creosote 36 RedCedar Creosote 39.8 Maple PCP 138.4 Maple PCP 111.2 Maple PCP 142.7 Maple PCP 142 Maple PCP 115.7 Ash PCP 100.2 Ash PCP 106 Ash PCP 107.6 Ash PCP 100.2 Ash PCP 98.7 Spruce PCP 84 Spruce PCP 125 Spruce PCP 137 Spruce PCP 102.9 Spruce PCP 118.7 RedOak PCP 92.5 RedOak PCP 95 RedOak PCP 127.4 RedOak PCP 89.9 RedOak PCP 99.6 WhiteCedar PCP 87.8 WhiteCedar PCP 119.1 WhiteCedar PCP 83.5 WhiteCedar PCP 105.6 WhiteCedar PCP 104.2 Redwood PCP 106.3 Redwood PCP 111.3 Redwood PCP 116.2 Redwood PCP 104.2 Redwood PCP 94.8 Lab #6 RedCedar RedCedar RedCedar RedCedar RedCedar Maple CCA Maple CCA Maple CCA Maple CCA Maple CCA Ash CCA Ash CCA Ash CCA Ash CCA Ash CCA Spruce CCA Spruce CCA Spruce CCA Spruce CCA Spruce CCA RedOak CCA RedOak CCA RedOak CCA RedOak CCA RedOak CCA WhiteCedar WhiteCedar WhiteCedar WhiteCedar WhiteCedar Redwood CCA Redwood CCA Redwood CCA Redwood CCA Redwood CCA RedCedar RedCedar RedCedar RedCedar RedCedar Maple ACA Maple ACA Maple ACA Maple ACA Maple ACA Ash ACA Ash ACA Ash ACA Ash ACA Ash ACA Spruce ACA Spruce ACA Spruce ACA Spruce ACA Spruce ACA RedOak ACA RedOak ACA RedOak ACA RedOak ACA RedOak ACA WhiteCedar WhiteCedar WhiteCedar WhiteCedar WhiteCedar Redwood ACA Redwood ACA Redwood ACA PCP PCP PCP PCP PCP 115.4 130.4 115.4 144.5 107 88.5 106.7 121.9 86.4 105.9 107.8 83.4 101.3 111.9 107.3 116.5 112.9 90.1 112.5 117.4 CCA CCA CCA CCA CCA 43.9 88.1 105.2 105.5 76.1 CCA CCA CCA CCA CCA 55.9 85.1 68.6 76 70.1 53.7 45.4 77.1 75.9 83.5 73.2 68.8 90.3 94.2 97.5 131.2 87.2 121.7 123.1 68.1 ACA ACA ACA ACA ACA 135.7 126.2 129.4 44.5 28.7 59.6 53.7 69.3 64.5 98.9 80 90.6 111.2 85.5 115.4 86.5 114.7 98.6 113.2 104 104.4 101 112.4 Page 5 Redwood ACA Redwood ACA RedCedar RedCedar 119.1 142.9 ACA ACA RedCedar RedCedar RedCedar ; 159.3 140 ACA ACA ACA 149.5 136.3 139.8 title 'All species 2-way ANOVA'; proc anova data=wood; class species preserv; model loss = species preserv species*preserv; means species/tukey; means preserv; run; title 'Redwood only 1-way ANOVA'; data redcedarwood; set wood; if species = 'RedCedar'; run; *proc print data=redcedarwood; *run; proc anova data=redcedarwood; class preserv; model loss=preserv; means preserv/tukey; run; All species 2-way ANOVA 1 The ANOVA Procedure Class Level Information Class Levels Values species 7 Ash Maple RedCedar RedOak Redwood Spruce WhiteCed preserv 4 ACA CCA Creosote PCP Number of Observations Read Number of Observations Used 140 140 All species 2-way ANOVA 2 The ANOVA Procedure Dependent Variable: loss Source DF Sum of Squares Mean Square F Value Pr > F Model 27 82093.9289 3040.5159 13.88 <.0001 Error 112 24542.6480 219.1308 Corrected Total 139 106636.5769 R-Square Coeff Var Root MSE loss Mean 0.769848 14.61701 14.80307 101.2729 Source Anova SS Mean Square F Value Pr > F species preserv species*preserv Lab #6 DF 6 3 18 13085.48586 19.79686 68988.64614 2180.91431 6.59895 3832.70256 9.95 0.03 17.49 <.0001 0.9929 <.0001 Page 6 All species 2-way ANOVA 3 The ANOVA Procedure Tukey's Studentized Range (HSD) Test for loss NOTE: This test controls the Type I experimentwise error rate, but it generally has a higher Type II error rate than REGWQ. Alpha 0.05 Error Degrees of Freedom 112 Error Mean Square 219.1308 Critical Value of Studentized Range 4.24635 Minimum Significant Difference 14.056 Means with the same letter are not significantly different. Tukey Grouping Mean N A 119.530 20 Maple B B B B B B B B B 103.790 20 RedOak 103.540 20 Redwood 102.910 20 Spruce 97.335 20 WhiteCed 97.075 20 Ash 84.730 20 RedCedar C C C C C species All species 2-way ANOVA 4 The ANOVA Procedure Level of preserv ACA CCA Creosote PCP Lab #6 N 35 35 35 35 -------------loss-----------Mean Std Dev 101.708571 101.368571 101.342857 100.671429 30.6168578 19.1031684 33.9074457 26.1486089 Page 7 Redwood only 1-way ANOVA 5 The ANOVA Procedure Class Level Information Class Levels preserv 4 Values ACA CCA Creosote PCP Number of Observations Read Number of Observations Used 20 20 Redwood only 1-way ANOVA 6 The ANOVA Procedure Dependent Variable: loss DF Sum of Squares Mean Square F Value Pr > F Model 3 33830.21800 11276.73933 59.38 <.0001 Error 16 3038.40400 189.90025 Corrected Total 19 36868.62200 Source R-Square Coeff Var Root MSE loss Mean 0.917588 16.26393 13.78043 84.73000 Source DF Anova SS Mean Square F Value Pr > F preserv 3 33830.21800 11276.73933 59.38 <.0001 Redwood only 1-way ANOVA 7 The ANOVA Procedure Tukey's Studentized Range (HSD) Test for loss NOTE: This test controls the Type I experimentwise error rate, but it generally has a higher Type II error rate than REGWQ. Alpha 0.05 Error Degrees of Freedom 16 Error Mean Square 189.9002 Critical Value of Studentized Range 4.04609 Minimum Significant Difference 24.935 Means with the same letter are not significantly different. Tukey Grouping N preserv A 144.980 5 ACA B 100.140 5 CCA C C C Lab #6 Mean 51.160 5 PCP 42.640 5 Creosote Page 8 ...
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This note was uploaded on 02/16/2010 for the course STAT 350 taught by Professor Staff during the Spring '08 term at Purdue.

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