A large laboratory has four types of devices used to determine the pH of soil samples. The laboratory wants to determine whether there are differences in the average readings given by these devices. The lab uses 24 soil samples having known pH in the study and randomly assigns six of the samples to each device. The soil samples are tested and the response recorded for teach sample is the difference between the pH reading of the device and the known pH of the soil. The data is appended to this document.

a. Conduct an Analysis of Variance to test whether there is any difference among the mean differences in pH readings for the four devices.

i. Create the ANOVA table by hand (feel free to use a program to add up values, but don't automate the process)

ii. Calculate the test statistic (again, by hand)

iii. Report the conclusion.

iv. Use SAS to verify your values; append your code to the end of your homework.

b. What conditions must be satisfied for your analysis from part a to be valid?

c. Check the conditions for this ANOVA, and comment on the validity of your conclusion from part a.iii. Use SAS to answer this question, and append the code.

d. Suppose the soil samples have widely different pH values. What problems may occur by simply randomly assigning the soil samples to different devices?

Device Response

A -0.307

A -0.294

A 0.079

A 0.019

A -0.136

A -0.324

B -0.176

B 0.125

B -0.013

B 0.082

B 0.091

B 0.459

C 0.137

C -0.063

C 0.24

C -0.05

C 0.318

C 0.154

D -0.042

D 0.69

D 0.201

D 0.166

D 0.219

D 0.407