Use SPSS to answer the questions below. Interpret the output: running the test alone will not give you full credit.  Keep in mind the requirements spelled out at the beginning of this assignment as well for all hypothesis testing questions.

A study has been carried out to compare the United Way contributions made by university professors from four universities. A sample of 15 professors from each university is selected. The dollar amounts of their contributions are shown below. 

University 1 University 2 University 3 University 4

200                 119                 179                 115

257                 136                 409             238

194                 278                 536                 159

296                 356                 105                 118

278                 135                 321                 149

342                 237                 357                 175

212                 496                 519                 207

396                 238                188                 312

403                 512                 524                 319

254                 367             419                 248

178                 94                 238                 287

195                 165             497                 279

139                 411             256                 326

438                 281             325                 371

326                 431             158                 295

a. Verify the required conditions of AOV.

b. Assuming that the conditions are satisfied, use SPSS to see whether there is any significant difference among the contributions from the four universities.

c. i. Determine the significantly different pairs using

A. Fisher’s LSD.

B. the SNK procedure.

C. Tukey’s HSD procedure.

ii. Are there any differences in the three tests?

iii. Consider a contrast {-1, -1, 3, -1}. What hypothesis is this contrast testing? Use SPSS to perform this test. 

d. Transform the variables using logarithmic transformation.

e. Apply the AOV F test to the transformed variables.

f. Did transforming the data alter the conclusion that you arrived at in part (b), above?  And why do researchers sometimes transform their data via use of logarithms and similar mathematical operations?