You have done a pilot experiment testing the effects of two factors on the distance a wooden catapult can flip a miniature bean bag. The two factors are A: block controlling start height (present, not present), and B: fulcrum location (3 positions). The distance of the flip (in inches) for two replicates in the pilot experiment are shown in the table. 1. Eulcrom position 1 Shortest catapult armMedium catapult armLongest catapult arm ulcrom position 3 Block present 29.5, 29.5 Block absent27.5, 28.5 41, 42 35 37 46.5, 47 44.5, 50 Thanks to Laine Close, Richard Pincus, Zack Johnson, Emily Summers, Jimmy Long, and Alexander Moore for providing the data i. Write down the factorial model for this experiment. Define all terms and include all assumptions of the model Fit the model (that is, do the analysis of variance) and plot the residuals against the predicted values, plot the residuals against the block factor (present or absent), and plot the residuals against the fulcrum position. What conclusions do you draw from the esidual plots? Estimate the mean difference between fulcrum position 1 and fulcrum position 3, and give the standard error of this difference. Do this both by hand and using Proc GLM Write a one-sentence description of the result in terms of the length of the catapult arm Estimate the difference between fulcrum position 2 and the mean of positions 1 and 3. This estimates the amount of curvature in the effect of fulcrum position. Give both the estimated contrast and the standard error of the contrast. Do the computations both by hand and using Proc GLM. Is there significant curvature in the effect of fulcrum position? You would like to plan a new experiment to test the same two factors at the same levels as in the pilot study. Suppose that you want to be able to detect a difference of 2 inches when the block is present compared to when the block is not present. Do power calculations to determine how many replicates would be needed. How many replicates would you recommend for the new experiment? ii. iv. v. You have done a pilot experiment testing the effects of two factors on the distance a wooden catapult can flip a miniature bean bag. The two factors are A: block controlling start height (present, not present), and B: fulcrum location (3 positions). The distance of the flip (in inches) for two replicates in the pilot experiment are shown in the table. 1. Eulcrom position 1 Shortest catapult armMedium catapult armLongest catapult arm ulcrom position 3 Block present 29.5, 29.5 Block absent27.5, 28.5 41, 42 35 37 46.5, 47 44.5, 50 Thanks to Laine Close, Richard Pincus, Zack Johnson, Emily Summers, Jimmy Long, and Alexander Moore for providing the data i. Write down the factorial model for this experiment. Define all terms and include all assumptions of the model Fit the model (that is, do the analysis of variance) and plot the residuals against the predicted values, plot the residuals against the block factor (present or absent), and plot the residuals against the fulcrum position. What conclusions do you draw from the esidual plots? Estimate the mean difference between fulcrum position 1 and fulcrum position 3, and give the standard error of this difference. Do this both by hand and using Proc GLM Write a one-sentence description of the result in terms of the length of the catapult arm Estimate the difference between fulcrum position 2 and the mean of positions 1 and 3. This estimates the amount of curvature in the effect of fulcrum position. Give both the estimated contrast and the standard error of the contrast. Do the computations both by hand and using Proc GLM. Is there significant curvature in the effect of fulcrum position? You would like to plan a new experiment to test the same two factors at the same levels as in the pilot study. Suppose that you want to be able to detect a difference of 2 inches when the block is present compared to when the block is not present. Do power calculations to determine how many replicates would be needed. How many replicates would you recommend for the new experiment? ii. iv. v
