Statistics Quiz 11
The following data was collected by a team of engineers studying the effect of two manufacturing techniques on the thickness of composite skin for military aircraft. They separated the skin samples into three Blocks within which all samples were similar on their roving material, resin, and curing temperature. Then they randomly assigned materials from each block to one of two conditions, Experimental process and Control process, and measured their thickness following manufacture. The data is listed below. Using an appropriate analysis, explain if the new Experimental manufacturing process created thinner skin on average, than the old, Control process. What is the value of SSerror to the nearest whole number? Block Experimental Control 1 243.27 253.00 1 252.31 258.23 1 245.23 253.05 1 236.30 259.27 1 228.46 263.17 1 231.28 265.32 1 230.61 269.80 1 239.38 276.62 1 231.19 273.16 1 241.01 270.87 2 239.63 266.53 2 240.68 265.02 2 237.93 273.12 2 244.29 283.25 2 246.64 288.04 2 244.49 292.25 2 236.15 285.86 2 226.75 289.06 2 227.30 296.80 2 219.33 309.38 3 215.02 320.17 3 221.24 315.32 3 223.87 316.37 3 227.10 335.51 3 227.83 347.34 3 234.61 366.97 3 233.25 380.34 3 228.85 391.11 3 229.20 397.48 3 223.35 413.72
2.6 0 5 0 10 0 7.6 0 8.4 0 169.33 0 213.5 0 252 0 233 0 200 0 18 0 55 0 65627.225?
How many blocks were used in the experiment represented in the following ANOVA table? Source SS DF MS F p Treatment 1010.56 2 505.28 92.54 <.05 Block 323.83 [BLK] 107.94 19.77 <.05 Error 169.33 31 5.46 Total 1503.72 36
4
Given the table below depicting the results of an experiment, if X2 is the block, what proportion of the error variation did it remove compared to a one-way ANOVA? Express your answer as a whole number percent instead of a fraction or decimal.
99
When should blocking be performed? A. When you have a nuisance variable that might impact the variation in the dependent variable B. In the Sampling phase of the experiment C. In the Testing phase of the experiment D. In the Analysis phase of the experiment
A, B
Why is the Randomized Block design important for statistical hypothesis testing?2 A. It makes the regression equation more precise (increases R^2) B. It increases the power of the analysis C. It reduces the overall variation in the independent variable. D. It provides a second predictor that can interact with the independent variable E. It reduces the residual error
A, B, E
The following file presents the results of an experiment where paper airplanes were tested to see if the addition of winglets made them more aerodynamically efficient. Two samples of airplanes were made: 1 with winglets and 1 without winglets. The researcher decided to block on the manufacturers: Mechanical Engineers versus Aerospace Engineers. Did the addition of the winglets impact the distance the airplanes flew from a given height with a constant initial velocity (alpha = 0.01)? A. Yes because MSbetween groups divided by MSresidual is less than the critical value of F B. Yes because MSbetween groups divided by MSresidual is greater than the critical value of F C. Yes, because F(1,105) = 17.51, p = .0001 D. No, because F(1,105) = 17.51, p = .0001 E. Yes, because F(1,105) = 8.3, p = .0048
B, E
This is a variable that the researcher isn't interested in studying the effect of, but that might impact the expression of the dependent variable. A. Factor B. Covariate C. Between Groups Factor D. Within Groups Factor E. Blocking Variable
B, E
The following data was collected by a team of engineers studying the effect of two manufacturing techniques on the thickness of composite skin for military aircraft. They separated the skin samples into three Blocks within which all samples were similar on their roving material, resin, and curing temperature. Then they randomly assigned materials from each block to one of two conditions, Experimental process and Control process, and measured their thickness following manufacture. The data is listed below. Using an appropriate analysis, explain if the new Experimental manufacturing process created thinner skin on average, than the old, Control process. What is the result of the omnibus test? Block Experimental Control 1 243.27 253.00 1 252.31 258.23 1 245.23 253.05 1 236.30 259.27 1 228.46 263.17 1 231.28 265.32 1 230.61 269.80 1 239.38 276.62 1 231.19 273.16 1 241.01 270.87 2 239.63 266.53 2 240.68 265.02 2 237.93 273.12 2 244.29 283.25 2 246.64 288.04 2 244.49 292.25 2 236.15 285.86 2 226.75 289.06 2 227.30 296.80 2 219.33 309.38 3 215.02 320.17 3 221.24 315.32 3 223.87 316.37 3 227.10 335.51 3 227.83 347.34 3 234.61 366.97 3 233.25 380.34 3 228.85 391.11 3 229.20 397.48 3 223.35 413.72 A. The experimental process created thinner skin on average because F is less than Fcritical B. The experimental process created thinner skin on average because p is greater than alpha C. The experimental process created thinner skin on average because p is less than alpha D. The experimental process created thinner skin on average because F is greater than Fcritical
C, D
A Two-way ANOVA table from a Randomized Block design experiment returned the following output. Fill in the blanks (good to the hundredths place for everything but df). Source SS df MS F p Treatment 1010.56 4 ____ ____ Block ___ ___ 64.765 ____ Error 169.33 20 Total 1503.72
Treatment MS 252.64 Treatment F 29.84 Block SS 323.83 Block df 5 Block F 7.65
