The yields of wheat (in bushels per acre) were compared for five different varieties, A, B, C, D, and E, at six different locations. Each variety was randomly assigned to a plot at each location. The results of the experiment are shown in the accompanying table, along with a MINITAB printout of the analysis of variance. Analyze the experiment using the appropriate method. Identify the treatments or factors of interest to the researcher and investigate any effects that exist. Use the diagnostic plots to comment on the validity of the analysis of variance assumptions. What are the practical implications of this experiment? Write a paragraph explaining the results of your analysis.

MINITAB output for Exercise 11.68
Two-way ANOVA: Yield versus Varieties, Location

MINITAB diagnostic plots for Exercise 11.68

Transcribed Image Text:

Location Variety 35.3 31.0 32.7 30.7 32.2 31.4 38.2 33.4 33.6 34.9 36.1 35.2 32.4 28.9 29.2 36.8 31.7 37.1 38.3 30.7 37.2 33.1 35.0 32.7 37.3 38.2 40.2 36.0 33.9 32.1 2 DE 4 Sourcee Varieties Locations Error Total sS 142.670 68.142 38.303 249.142 MS 35.6675 13.6283 1.9165 18.61 7.11 0.000 0.001 20 29 S 1.384 R-Sq 84.62% R-Sq (adj ) =77.69% = = Individual 95% CIs For Mean Based on Pooled StDev Varieties Mean +----+--+---- 34.3500 32.2833 36.3000 36.7833 31.2000 (-_-*-_-) 30.0 32.0 34.0 36.0 Normal Probability Plot of the Residuals (res ponse is Yield) 95 80 70 60 50 3 40 30 20 10 -3 Residual Residuals versus the Fitted Values (response is Yield 30 34 Fitted Value 32 36 38 40