Download Statistical Analysis: Peas Variety Trial & Indian Mustard Study and more Exams Experimental Techniques in PDF only on Docsity! 1 1) You wish to compare eight varieties of peas in a field that was determined to have a soil variability index of b=0.6. The last time you conducted a trial in this field you obtained a CV of 16% using a plot size of 12 m2 and four replications in a randomized block design. Determine the size of plot you would you need to have an 80% probability of detecting differences of 30% of the mean, using a significance level of 5%. Assuming that your planter and harvest equipment are designed for a plot that is 2m wide, how long will your plot need to be to attain the optimum plot size? Use the tables at the end of this exam and show your work. 2) A fellow graduate student is planning an experiment. He would like to have a 90% probability of detecting differences that are within 20 units of the mean, using a Type I error rate of 0.05. He is not sure how to determine if his experimental design has the desired level of power. Using the estimate of variance and other parameters that he provides, you calculate a detectable difference of 25 units for his experiment. What advice would you give to him? 3) Five varieties of Indian mustard were compared for glucosinolate content (GLN) in a field study. The trial was conducted as a Randomized Complete Block Design with four blocks. Leaf tissue was sampled from three plants in each plot. Glucosinolate content was measured on each individual plant. The data were analyzed with SAS PROC GLM. Some of the output is shown below. 10 pts 8 pts docsity.com 2 The GLM Procedure Dependent Variable: GLN Source DF Sum of Squares Mean Square Model 19 11949.023 628.896 Error 40 538.773 13.469 Corrected Total 59 12487.796 Source DF Type III SS Mean Square Block 3 1346.003 448.668 Variety 4 10000.396 2500.099 Block*Variety 12 602.624 50.219 a) What value from this output provides an estimate of the variance among plants within each plot? b) Calculate the appropriate F value for testing the null hypothesis that the means of all varieties are equal. Use the F table from the back of this exam to determine whether to accept or reject the null hypothesis, using =0.05. c) Calculate the standard error for a variety mean for this experiment. 4) You have conducted an experiment with seven treatments using a Latin Square Design. a) Complete the ANOVA by filling in the shaded cells below. 8 pts 12 pts 5 pts 8 pts docsity.com 5 6) An experiment has been conducted to evaluate the effect of three methods for pruning blueberries (no pruning, standard method, new method) and two fertilizer levels (low and high) on fruit yield. The experiment includes all possible combinations of these two treatment factors. The graph below shows the results for the experiment (error bars are the standard errors of the means): Effect of Pruning Method and Fertility on Fruit Yield 0 5 10 15 20 25 30 35 None Standard New Pruning Method F ru it Y ie ld LOW HIGH a) Based on the results shown in the graph, do you anticipate that we will be able to interpret the F test from the ANOVA for the main effect of pruning method in this experiment? Explain your answer. b) Assuming that there are only two replications for this experiment, draw a possible layout (randomization) for this experiment in the field. You may use a CRD or an RBD (indicate which design you have chosen.) Include all of the experimental units in your diagram and label the treatments that are assigned to each plot. 8 pts 10 pts docsity.com 6 F Distribution 5% Points Student's t Distribution Denominator Numerator (2-tailed probability) df 1 2 3 4 5 6 7 df 0.4 0.05 0.01 1 161.45 199.5 215.71 224.58 230.16 233.99 236.77 1 1.376 12.706 63.667 2 18.51 19.00 19.16 19.25 19.3 19.33 19.36 2 1.061 4.303 9.925 3 10.13 9.55 9.28 9.12 9.01 8.94 8.89 3 0.978 3.182 5.841 4 7.71 6.94 6.59 6.39 6.26 6.16 6.08 4 0.941 2.776 4.604 5 6.61 5.79 5.41 5.19 5.05 4.95 5.88 5 0.920 2.571 4.032 6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 6 0.906 2.447 3.707 7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 7 0.896 2.365 3.499 8 5.32 4.46 4.07 3.84 3.69 3.58 3.50 8 0.889 2.306 3.355 9 5.12 4.26 3.86 3.63 3.48 3.37 3.29 9 0.883 2.262 3.250 10 4.96 4.10 3.71 3.48 3.32 3.22 3.13 10 0.879 2.228 3.169 11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 11 0.876 2.201 3.106 12 4.75 3.88 3.49 3.26 3.10 3.00 2.91 12 0.873 2.179 3.055 13 4.67 3.80 3.41 3.18 3.02 2.92 2.83 13 0.870 2.160 3.012 14 4.60 3.74 3.34 3.11 2.96 2.85 2.76 14 0.868 2.145 2.977 15 4.54 3.68 3.29 3.06 2.90 2.79 2.71 15 0.866 2.131 2.947 16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 16 0.865 2.120 2.921 17 4.45 3.59 3.20 2.96 2.81 2.70 2.61 17 0.863 2.110 2.898 18 4.41 3.55 3.16 2.93 2.77 2.66 2.58 18 0.862 2.101 2.878 19 4.38 3.52 3.13 2.90 2.74 2.63 2.54 19 0.861 2.093 2.861 20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 20 0.860 2.086 2.845 21 4.32 3.47 3.07 2.84 2.68 2.57 2.49 21 0.859 2.080 2.831 22 4.30 3.44 3.05 2.82 2.66 2.55 2.46 22 0.858 2.074 2.819 23 4.28 3.42 3.03 2.80 2.64 2.53 2.44 23 0.858 2.069 2.807 24 4.26 3.40 3.00 2.78 2.62 2.51 2.42 24 0.857 2.064 2.797 25 4.24 3.38 2.99 2.76 2.60 2.49 2.40 25 0.856 2.060 2.787 26 4.23 3.37 2.98 2.74 2.59 2.47 2.39 26 0.856 2.056 2.779 27 4.21 3.35 2.96 2.73 2.57 2.46 2.37 27 0.855 2.052 2.771 28 4.20 3.34 2.95 2.71 2.56 2.45 2.36 28 0.855 2.048 2.763 29 4.18 3.33 2.93 2.70 2.55 2.43 2.35 29 0.854 2.045 2.756 30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 30 0.854 2.042 2.750 docsity.com
