Question

The following data are from a completely randomized design. Treatment 145 145 145 149134 151 140 129 Sample mean Sample variance a. Compute the sum of squares between treatments. 159 310 142 108.8 134 145.2 b. Compute the mean square between treatments. c. Compute the sum of squares due to error d. Compute the mean square due to error (to 1 decimal), e. Set up the ANOVA table for this problem. Round all Sum of Squares to nearest whole numbers. Round all Mean Squares to one decimal place. Round F to two decimal places. Round your p-value to 4 decimal places. Source of Variation Sum of Squares Degrees of Freedom Mean Square p-value Treatments Error Total 1. At the .05 level of significance, test whether the means for the three treatments are equal. Calculate the value of the test statistic (to 2 decimals).

Answer 1

a. Sum of square between treatments = 1956 b. Mean square between treatments = 978 c. Sum of square due to error = 2820 d. Mean square error due to error = 188 e. ANOVA Table: Degrees of freedom Mean square F p-value Source of variation Treatments Error Total Sum of square 1956 2820 4776 5.202 0.0192 978 188 15 17 f. Here level of significance a=0.05, after comparing with p-value which is given in the table we found that p-value is less than significance so we reject the means for three treatments are equal The value of test statistics = 5.20

R Code: A = c(163, 142, 166, 145, 149, 189) B = c(145, 159, 129, 145, 134, 140) C = c(123, 121, 135, 145, 151, 129) data = data.frame(A, B, C) data mydata = stack(data) mydata model=aov(values-ind, mydata) summary(model) Output: > A = c(163, 142, 166, 145, 149, 189) > B = c(145, 159, 129, 145, 134, 140) > C = c(123, 121, 135, 145, 151, 129) > data = data.frame(A, B, C) > data A B C 1 163 145 123 2 142 159 121 3 166 129 135 4 145 145 145 5 149 134 151 6 189 140 129

> mydata = stack(data) > mydata values ind 1 163 A 2 142 A 3 166 A 4 145 A 5 149 A 7 145 B 8 159 B 9 129 B 10 145 B 11 134 B 12 140 B 13 123 C 14 121 C 15 135 C 16 17 145 C 151 C 18 129 C > model=aov(values-ind, mydata) > summary(model) Df Sum Sq Mean Sq F value Pr(>F) ind 2 1956 978 5.202 0.0192 * Residuals 15 2820 188