Four machines are compared to assess the differences in the rate of production of a certain part (Part No. Z-15) (Ostle 1963). The data were collected over 5 days. All four machines were run each day (in random order), thus using a randomized complete block design with “Day” as a blocking factor. The following data are the number of units produced per day.

Machine Day AB C D 1 293 308 323 333 2 298 353 343 363 3 280 323 350 368 4 288 358 365 345 5 260 343 340 330 Machine A is currently in use in a factory, and Machines B, C, and D from three different competitors are being evaluated to replace A. Thus, the management is interested in the following:

1. comparing Machine A with the average production of Machines B, C, and D, 2. comparing B, C, and D Prepare and run a proc glm step necessary and provide complete answers, including hypotheses tested and statistics used, to the following questions (on a separate sheet as before). Use the model shown for the RCBD for analyzing these data.

a. Construct an analysis of variance table and test the hypothesis H0 :

τA = τB = τC = τD. State your conclusion based on the p-value.

b. Use a contrast statement for making comparison 1 by testing H0 :

τA = (τB + τC + τD)/3. What is your conclusion?

c. Use a contrast statement for making comparison 2 by testing HO :

τB = τC = τD. One way to test this hypothesis is to make the comparisons τB − τC and τB + τC − 2τD simultaneously, in a single contrast statement. This results in the computation of a SS with 2 df and an F-test with 2 df for the numerator. Add these tests as lines in an expanded ANOVA table and summarize the results from your analysis.

d. Construct 95% confidence intervals for τB −τC , τB −τD, and τC −τD, using an appropriate statement in the proc glm step. Use the results of parts

(c) and

(d) to make a statement about the new machines being tried out assuming higher production rate is of interest.

e. Include the statement output out=stats p=fitted r=residual;

in proc glm step. Then use proc sgplot and the SAS data set stats to obtain scatter plots of Residuals versus Machine and Residuals versus Fitted. State the purpose for which these plots may be used. Do these plots identify any problems with your model assumptions?

f. Perform Tukey’s test of nonadditivity using a proc glm step and the SAS data set stats created in part (e). What is your conclusion?