Question

A random sample of students was studied. Whether the student chose to sit in the front, middle, or back row in a college class was recorded, along with the person’s GPA. The results of an ANOVA gave F=7.47 and p=.003.

Would it make sense to do a post-hoc procedure in this case?

Assuming it does, the Tukey tests give the following results

Treatments pair	Tukey HSD Q statistic	Tukey HSD p-value	Tukey HSD inferfence
Front vs Middle	4.2624	0.0148325	* p<0.05
Front vs Back	5.0778	0.0035778	** p<0.01
Middle vs Back	0.8154	0.8210868	insignificant

If the mean GPA for those sitting in the front was 3.44, the mean GPA for those sitting in the middle was 2.91, and the mean GPA for those sitting in the back was 2.81; what is the conclusion?

Answer 1

Because p-value of the ANOVA is 0.003, which is well below 0.05, this means that there is a significant difference between the mean GPA of the student sitting in Frongt, Middle and Back row. i.e not all the mean GPA across different seating are same. So, we may wish to investigate how they differ. So, post-hoc procedure completely makes sense here.

Now, in terms of mean GPA, from higher to low, the order is following

Front(3.44) > Middle(2.91) > Back(2.81)

The test of difference between mean GPA of Front and Middle appears significant(p-value < 0.05). Which means mean GPA for Front is significantly higher than that for Middle.

The test of difference between mean GPA of Middle and Back appears insignificant. Which means mean GPA for Middle does not differ with that for Back.

Which means in term of GPA, seating in Front differs from all other seating preference, which the other two are same.