STA 412 HW 07 (Multiple Comparison) Question: Points: 1 Total 30 30 Bonus Points: Score: 0 0 1. A research group tested the effects of two different herbicides on crop yield. Among 100 acres set aside for the experiment, herbicide 1 was used on a random sample of 30 acres, herbicide 2 was used on a second random sample of 30 acres, no herbicide was used on the remaining 40 acres (i.e. acted as a control). At the end of the growing season, the yields (in bushels per acre) were recorded. The summary statistics are provided below. Treatment Herbicide 1 Herbicide 2 Control Sample size Sample mean Sample variance 30 87.606 35.341 30 88.792 36.316 40 84.095 36.592 ns <- c(30, 30, 40) ybars <- c(87.606, 88.792, 84.095) vars <- c(35.341, 36.316, 36.592) SSW <sum((ns - 1) * vars) df with <- sum(ns - 1) df_with ## [1] 97 MSW SSW/df_with MSW ## [1] 36.14 = 0.05. The goal is to conduct pairwise comparisons while controlling the experiment-wise error rate at a = (a) (15 points) Compute the estimates, standard errors and test statistics for all the pairwise comparisons. Put your numbers into the a table like this. Show how you got these numbers. Contrast Herbicide 1 - Control Estimate SE Test Herbicide 2 _ Control Herbicide 1 - Herbicide 2 (b) (5 points) Obtain the critical value for Bonferroni correction. Identify the contrasts that are significantly different from zero. (c) (5 points) Obtain the critical value for Scheffe's method. Identify the contrasts that are significantly dif- ferent from zero. (d) (5 points) Obtain the critical value for Tukey's method. Identify the contrasts that are significantly different from zero.