NAME _______________________

PLS 205 Final [Total Points in Exam = 100]March 12, 2014

Due Date: Tuesday, March 17, by 5:00 pm; 122 Robbins Hall

Include your SAS programs, include only the critical parts of the SAS output, and discuss each result. NO POINTS WILL BE AWARDED TO OUTPUTS WITHOUT A SENTENCE EXPLAINING THE CONCLUSION.

Clarification questions should be directed to Miguel and Dr. Dubcovsky by e-mail only. No consultation with other students is allowed during the exam period (including SAS programming questions). Exams with more than one unlikely identical mistake will receive zeroes, and the incident will be referred to the Office of Student Judicial Affairs.

Problem 1 [25 points]

A grower would like to test if fruit size in blueberry is affected by fungicide application, insecticide application, and insect pollination. The treatments the grower experimented with are:

Fungicide – regular fungicide application or no fungicide applicationInsecticide – regular insecticide application or no insecticide applicationPollination – 25% of the flowers pollinated or 100% of the flowers pollinated

To conduct the experiment the grower picked 4 field sections with 1.8 m wide x 12 m long dimensions. Each field section was divided into two 1.8 m x 6 m subsections and the fungicide treatments were randomly assigned to each subsection. Each subsection was divided into 1.8 m x 3 m sub-sub section and the insecticide treatment was randomly assigned to these sections. Finally the sub-sub sections were divided into sections of 1.8 m x 1.5 m where the pollination treatments were randomly assigned. To apply the 25% pollination treatment, the grower covered the plants with a bee proof net when the flowering for the plants reached 25%. To insure that the flowers were being pollinated the grower installed bumble bee colonies within each cage. When the plants were ready to harvest the grower weighed all of the ripe fruit in bulk from each 1.8 m x 1.5 m section and divided the number by the total number of ripe fruit weighed to get an average fruit weight. While harvesting one of the workers accidentally fell on a box of berries corresponding to the Full fungicide, None insecticide, 25% pollination, in block 2. This data was removed and is indicated by the word MISSING. The data is summarized below:

Block Fungicide Insecticide Pollination Response1 Full None 25 0.6871 Full None 100 0.3611 Full Full 25 0.871 Full Full 100 0.5581 None None 25 0.442

1 None None 100 0.3821 None Full 25 0.391 None Full 100 0.4622 Full None 25 MISSING2 Full None 100 0.4012 Full Full 25 0.5922 Full Full 100 0.5662 None None 25 0.5182 None None 100 0.3812 None Full 25 0.3952 None Full 100 0.6263 Full None 25 0.7133 Full None 100 0.3773 Full Full 25 0.5843 Full Full 100 0.6553 None None 25 0.4423 None None 100 0.3823 None Full 25 0.3943 None Full 100 0.4724 Full None 25 0.7064 Full None 100 0.364 Full Full 25 0.6174 Full Full 100 0.5574 None None 25 0.4474 None None 100 0.3824 None Full 25 0.3934 None Full 100 0.475

1. [5 points] Use the table in the appendix to describe the experimental design.

2. [5 points] Perform the appropriate ANOVA and report the significance of the different treatments and interactions. THERE IS NO NEED TO TEST ASSUMPTION.

3. [5 points] Perform the appropriate tests based on your results for question 2.

4. [5 points] Report the appropriate means for Fungicide and Insecticide at the different levels of pollination.

5. [5 points] Report the recommendations you will give on the application of fungicide and insecticide based on all the previous statistical analyses.

Problem 2 [20 points]

An agronomist wants to test the effect of four treatments (two tillage practices and two cover crop methods) on processing tomato yields and to extend his conclusions to the Central Valley. The two tillage practices include Standard tillage (ST) vs. Conservation tillage (CT) and the two cover crop treatments include No Cover crop (NO) vs. Cover crop (CC). The researcher also wants to test if there are significant interactions between the cover crop and tillage.

To conduct the experiment the researcher randomly picks six random locations in the Central Valley in California. In each location he selects one field, divides it in four homogeneous sections with 4 large plots in each section. In each location he randomly assigns each of the four possible cover by tillage treatment combinations to one of the 4 large plots available within each section. The researcher measures tomato yield in each plot and records the yield in tons per acre. The data is reported below:

Location Block Tillage Crop Yieldloc1 1 ST NO 54loc2 1 ST NO 65loc3 1 ST NO 42loc4 1 ST NO 49loc5 1 ST NO 55loc6 1 ST NO 33loc1 1 ST CC 58loc2 1 ST CC 68loc3 1 ST CC 54loc4 1 ST CC 47loc5 1 ST CC 48loc6 1 ST CC 46loc1 1 CT NO 52loc2 1 CT NO 62loc3 1 CT NO 51loc4 1 CT NO 51loc5 1 CT NO 59loc6 1 CT NO 34loc1 1 CT CC 69loc2 1 CT CC 64loc3 1 CT CC 55loc4 1 CT CC 61loc5 1 CT CC 52loc6 1 CT CC 59loc1 2 ST NO 54loc2 2 ST NO 59loc3 2 ST NO 41

loc4 2 ST NO 48loc5 2 ST NO 50loc6 2 ST NO 32loc1 2 ST CC 53loc2 2 ST CC 71loc3 2 ST CC 64loc4 2 ST CC 47loc5 2 ST CC 56loc6 2 ST CC 41loc1 2 CT NO 50loc2 2 CT NO 55loc3 2 CT NO 52loc4 2 CT NO 63loc5 2 CT NO 57loc6 2 CT NO 42loc1 2 CT CC 58loc2 2 CT CC 69loc3 2 CT CC 66loc4 2 CT CC 55loc5 2 CT CC 60loc6 2 CT CC 48loc1 3 ST NO 55loc2 3 ST NO 54loc3 3 ST NO 36loc4 3 ST NO 52loc5 3 ST NO 51loc6 3 ST NO 38loc1 3 ST CC 52loc2 3 ST CC 70loc3 3 ST CC 51loc4 3 ST CC 51loc5 3 ST CC 58loc6 3 ST CC 40loc1 3 CT NO 63loc2 3 CT NO 55loc3 3 CT NO 51loc4 3 CT NO 53loc5 3 CT NO 62loc6 3 CT NO 35loc1 3 CT CC 56loc2 3 CT CC 73loc3 3 CT CC 59loc4 3 CT CC 58

loc5 3 CT CC 63loc6 3 CT CC 58loc1 4 ST NO 51loc2 4 ST NO 50loc3 4 ST NO 51loc4 4 ST NO 49loc5 4 ST NO 57loc6 4 ST NO 28loc1 4 ST CC 52loc2 4 ST CC 61loc3 4 ST CC 56loc4 4 ST CC 47loc5 4 ST CC 48loc6 4 ST CC 41loc1 4 CT NO 52loc2 4 CT NO 58loc3 4 CT NO 46loc4 4 CT NO 53loc5 4 CT NO 53loc6 4 CT NO 41loc1 4 CT CC 59loc2 4 CT CC 65loc3 4 CT CC 57loc4 4 CT CC 56loc5 4 CT CC 52loc6 4 CT CC 57

[Don’t worry about testing the assumptions]

1. [5 points] Perform appropriate analysis of variance on the data. Report the results of the analysis and answer the following questions:

a) Are there significant differences in yield between tillage methods or cover crop methods?b) Is the interaction between tillage and cover crop significant?c) Are the effects of tillage, cover crop, and their interaction consistent across locations? If yes, show an interaction plot for the significant interaction.

2. [5 points] Create two plots using SAS, R, or Excel where the first plot shows the main effects of tillage and the second plot shows the main effects of the crop treatments. Based on this result and the previous ANOVA provide your conclusion and recommendations for the complete Central Valley.

3. [5 points] Please report the means of the main effects of tillage and cover crop. Is the difference between standard tillage and conventional tillage larger than the difference between no cover crop and cover crop? Does the largest difference correspond to the most significant result? If not

explain why.

4. [5 points] Using the same model as in question 1, estimate the variance components for all of the random effects in your model. Which of these random effects had the largest variance?

Problem 3 [25 points]

A table grape breeder has developed two potential varieties and would like to release the variety that produces the largest berries upon application of gibberellic acid (GA), as well as confirm that these two new varieties are better than the traditional variety Thompson Seedless. The breeder selects three homogeneous sections in a vineyard and plants 18 10-plant plots in each section. Within each section he randomly assigns two plots to one of the 9 combinations of the three varieties and three GA treatments (0 ppm, 10 ppm, and 20 ppm). At harvest, he randomly picks 50 berries per plant per plot and weighs them in bulk. The average individual berry weights (g) calculated for each plot are reported below:

GA application rate (ppm)Section Variety 0 10 20

1

TS4.15 4.90 5.454.19 4.81 5.17

Var14.84 5.28 6.394.77 5.37 6.10

Var24.92 5.64 5.664.58 5.29 6.01

2 TS4.27 4.83 5.904.83 4.95 5.76

Var15.21 6.02 6.065.24 5.50 6.56

Var25.34 5.79 5.955.11 5.29 6.29

3

TS5.01 5.25 5.674.80 5.35 5.87

Var15.61 6.20 6.785.06 6.13 6.70

Var25.58 5.57 6.335.44 5.91 6.24

1. [3 points] Describe the experimental design in detail using the table in the appendix.

2. [2 points] Test all three required ANOVA assumptions for this design.

3. [4 points] Perform ANOVA with the correct model and discuss the results.

4. [3 points] Present an interaction plot of GA concentration by variety on the effect of berry weight. Comment on the interaction plot in light of the ANOVA results.

5. [5 points] Are any of the components of the GA*Variety interaction significant?

6. [6 points] Based on your answer to question 5, answer the following questions based on the appropriate analyses:

a. Was there a significant difference in berry weight between Thompson Seedless and the two new varieties?b. Was there a significant difference in berry weight between the two new varieties? c. How would you describe the response of berry weight to GA concentration?

7. [2 points] What recommendations would you make to the breeder if the difference in cost between the 10 and 20 ppm GA applications is small?

Problem 4 [5 points]

Two levels of Nitrogen (N0 and N1) and two levels of Potassium (K0 and K1) are tested in a 2 x 2 factorial organized in a RCBD with three blocks. A third factor, Varieties (A, B, and C) is added as a split plot of the Nitrogen Potassium combinations. Show an actual field layout of how you would design this experiment.

Problem 5 [25 points]

Black point is a common disease of wheat in the Sacramento region. The incidence of the disease is estimated as the % of grains with a black discoloration at the end of the grain. A researcher wants to test the differences in resistance among four specific varieties (designated 1 to 4) and three fungicides (designated 1-3). He selects three homogeneous blocks of land and divides each in 4 large plots, and randomizes the four varieties separately in each block. He plants the field in a North-South direction, changing variety in each plot. By head emergence he cut two aisles in a West-East direction dividing each block in three horizontal sections. He then drives his tractor in a West-East zigzag applying only one fungicide in each pass through the block. The order in which the three fungicides will be applied is randomized independently in each of the blocks. A design of the field is included below. Since Black point is affected by lodging (the falling spikes are more likely to show the disease), the researcher records the lodging of each of the 12 plots in each block after the fungicide was applied and before harvesting. The data for the percentage of grains with black point and the % lodging in each plot is included in the Table below the graph of the field.

1. [5 points] Are there significant differences among varieties and among fungicides in the percentage of black point, once the values were adjusted for lodging?

2. [5 points] Are the differences the same if the values are not adjusted for lodging? If different provide a potential explanation of the source of the discrepancies.

3. [3 points] Were the responses to fungicides different at the different varieties when the values were corrected for lodging?

4. [5 points] Based on the previous answer (and using the adjusted values) use the most sensitive fixed range mean comparison test controlling the experiment wise error rate to compare all four varieties and all three fungicides separately. What would be your recommendation?

5. [4 points] Test all the required assumptions required to perform the test on the adjusted values (no need to show Tukey 1-df test for multiplicative effects)

6. [3 points] Was the test with the adjusted values more efficient than the test with the unadjusted values? Quantify the difference.

Var.1 Var.2 Var.3 Var.4Block Fung Y X Y X Y X Y X1 1 39.6 14 55.2 15 38.9 15 38.6 152 1 52.5 17 55.2 16 58.3 16 46.3 163 1 47.1 15 61.5 16 45.5 16 51.3 161 2 54.5 16 76.7 16 73.4 16 56.4 152 2 63.5 17 60.6 15 53.3 15 63.2 163 2 63.0 16 68.0 16 67.2 16 59.6 151 3 60.4 17 78.5 16 63.7 15 65.3 162 3 68.6 19 62.7 14 66.2 17 50.2 133 3 67.4 18 80.6 18 73.1 17 70.4 18

Appendix

When you are asked to "describe in detail the design of this experiment," please do so by completing the following template:

Design:Response Variable:Experimental Unit:

ClassVariable

Block orTreatment

Number ofLevels

Fixed orRandom Description

12↓n

Subsamples? YES / NOCovariable? YES / NO