1. Winter Injury in American chestnut James Sharpe Rebecca Stern April 20, 2015 Stat 231 James Sharpe Rebecca Stern April 20, 2015 Stat 231

2. Main Objective  Examine winter injury in American chestnut trees to see if small and large chestnut trees at two different levels of canopy openness are affected differentially by winter injury.  Main goal is to contribute information about restoration of American chestnuts in Northern Forests.  Examine winter injury in American chestnut trees to see if small and large chestnut trees at two different levels of canopy openness are affected differentially by winter injury.  Main goal is to contribute information about restoration of American chestnuts in Northern Forests.

3. Sources of Variation  Experimental Units: Individual trees.  Observational Units: Individual trees.  Experimental Units: Individual trees.  Observational Units: Individual trees. Factor/ Type of Effect LevelsCode Size of tree Fixed Small: 25.0 cm or less1 Medium: 25.1 cm - 85.0 cm2 Large: 85.1 cm or larger3 Light Treatment Fixed Partially open canopy1 Fully open canopy2

4. Measurements  Percent injury will be measured for each tree. This is amount of dieback a tree experiences after winter.  This will be assessed via visual examination of trees; after leaf-out, any visible dieback will be considered winter injury.  Percent injury will be measured for each tree. This is amount of dieback a tree experiences after winter.  This will be assessed via visual examination of trees; after leaf-out, any visible dieback will be considered winter injury. Notice the dead leaves that occurred due to winter injury. Normally, the leaves would be robust and green. Poor sapling.

5. Experimental Procedure  A planting of American chestnut trees was established in the Green Mountain National Forest in 2009 in two different treatments: open canopy and partially open canopy. Open canopy treatmentPartially open canopy treatment

6. Anticipated Difficulties  Tree death  Voles and other animals eating tree roots  Measurement error, such as inaccuracies due to subjectivity of measuring percentage of dieback.  Differences in collecting the data: differences in person measuring, specific day and weather conditions.  Natural variability of planting sites: for example, one site may be naturally more wet than another, which could affect ability of tree to recover from winter injury.  Tree death  Voles and other animals eating tree roots  Measurement error, such as inaccuracies due to subjectivity of measuring percentage of dieback.  Differences in collecting the data: differences in person measuring, specific day and weather conditions.  Natural variability of planting sites: for example, one site may be naturally more wet than another, which could affect ability of tree to recover from winter injury. A vole. Deadly for American chestnut.

7. Statistical Model i=1,2,3 j=1,2 K=1,2,…,r iid

8. Analyses  We would perform an ANOVA.  To check assumptions, we would construct a QQ-Plot to make sure the residuals are normally distributed. If the residuals are not normally distributed, then an appropriate transformation would be made.  HOV test and spread-location plot to make sure variances are equal. Since this is a CRD, the assumption of independence is met.  We would perform an ANOVA.  To check assumptions, we would construct a QQ-Plot to make sure the residuals are normally distributed. If the residuals are not normally distributed, then an appropriate transformation would be made.  HOV test and spread-location plot to make sure variances are equal. Since this is a CRD, the assumption of independence is met.

9. Analyses - Continued ContrastSmallMediumLargeTreatment C1a 01Partial C1b 01Open C2a 10Partial C2b 10Open C3a 10Partial C3b 10Open To perform multiple comparisons we would use the Tukey Procedure since we are making all pairwise comparisons with respect to tree size.

10. Power Analysis  Using the effect size method, we found that 8 observations per group were needed to attain 90% power to detect a two standard deviation change. From previous literature, we guesstimated that two standard deviations corresponds to 15.2% change.  We used PROC POWER in SAS to get a range of replications needed for 90% power to detect previously stated changes in variance components. The minimum standard error used was 0.05 and the maximum standard error estimate used was 0.30. This yielded r=3 to r=53.  For this study, we will go with 8 obs. per group, since this was within the range given by SAS.  Using the effect size method, we found that 8 observations per group were needed to attain 90% power to detect a two standard deviation change. From previous literature, we guesstimated that two standard deviations corresponds to 15.2% change.  We used PROC POWER in SAS to get a range of replications needed for 90% power to detect previously stated changes in variance components. The minimum standard error used was 0.05 and the maximum standard error estimate used was 0.30. This yielded r=3 to r=53.  For this study, we will go with 8 obs. per group, since this was within the range given by SAS. Reference: Saielli, T.M., Schaberg, P.G., Hawley, G.J., Halman, J.M., & Gurney, K.M. (2014). Genetics and silvicultural treatments influence the growth and shoot winter injury of American chestnut in Vermont. Forest Science, 60, 1-9