Question

A researcher is studying groups of freshman, sophomore, and junior students and finds a significant ANOVA with regards to the number of trips to the library each quarter. His data is summarized below. (Each group had 10 subjects; use α = .01)

_F= 4             _S= 10                       _J[s1]= 13                       MS_error (within) = 5

Assuming a significant F ratio (one way-between subjects ANOVA), do a Fisher’s Post-Hoc test with this information. Set α = .01.                                                                              

a)  What is the critical value for the above test?                                (1 point)

Q16: Critical value in proper format

b)  Compute all the pairwise comparisons!!! Show your work!!

                                                                                                                        (2 points)

Q17: Standard Error

Q18: All three (3) t-obtained values

c)  Interpret your findings/results.                                                      (1 point)

Q19: Conclude in words

[s1]Craig, I couldn’t figure out how to make the bar above the X’s

Answer 1

Each group has 10 subjects therefore for total number of observation n=3*10=30. Total df=30-1=29

The group df=3-1=2, hence the error df=29-2=27.

a)  What is the critical value for the above test?                                (1 point)

Q16: Critical value in proper format

Therefore the critical value of the above test is

It is given that . The standard error for the difference is

  

  

The critical difference CD=Critical value*SE

The critical difference CD=2.7564*1=2.7564

Q17: Standard Error=1

Q18: All three (3) t-obtained values

Group	Mean	Comparison	Abs(Difference)	Critical difference	Significant?
Freshmen	4	Freshman Vs. Sophomore	6	2.7564	Yes
Sophomore	10	Freshman Vs. Junior	9	2.7564	Yes
Junior	13	Sophomore Vs. Junior	3	2.7564	Yes

We can see from the table above that all the three comparisons are significant.

Q19. We can see from the table table above that all the three pairwise comparisons are statistically significant. Hence, there is no bar over X's.