Question

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

1. Verify the required conditions of AOV.
2. Assuming that the conditions are satisfied, use SPSS to see whether there is any significant difference among the contributions from the four universities.A
3. i.    Determine the significantly different pairs using

1. Fisher’s LSD.
2. the SNK procedure.
3. 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.

4. Transform the variables using logarithmic transformation.
5. Apply the AOV F test to the transformed variables.
6. 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?

Answer 1

a) Before we can conduct a one-way ANOVA, we must first check to make sure that three assumptions are met.

1. Normality – Each sample is drawn from a normally distributed population.

2. Equal Variances – The variances of the populations that the samples come from are equal.

3. Independence – The observations in each group are independent of each other and the observations within groups were obtained by a random sample.

Since all these assumptions are met, then the results of our one-way ANOVA is unreliable.

SUMMARY OF DATA is given below

The f-ratio value is 1.68822. The p-value is .179938.

Tukey's HSD (alpha=0.05):
No significant difference between any two groups.

c(i)(A)