Analysis of Variance Example

A manager wishes to determine whether the mean times required to complete a certain task differ for the three levels of employee training. He randomly selected 10 employees with each of the three levels of training (Beginner, Intermediate and Advanced). Do the data provide sufficient evidence to indicate that the mean times required to complete a certain task differ for at least two of the three levels of training? The data is summarized in the table.
 
 
Level of Training n   s2
Advanced 10 24.2 21.54
Intermediate 10 27.1 18.64
Beginner 10 30.2 17.76
Ha: The mean times required to complete a certain task differ for at least two of the three levels of training. 

Ho: The mean times required to complete a certain task do not differ the three levels of training. ( µB = µI = µA)

Assumptions:   The samples were drawn independently and randomly from the three populations. The time required to complete the task is normally distributed for each of the three levels of training. The populations have equal variances.

Test Statistic: 

RR: or 

Calculations:  =  10(24.2 - 27.16...)2 + 10(27.1 - 27.16...)2 + 10(30.2 - 27.16...)2 = 180.066....

 

 = 9(21.54) + 9(18.64) + 9(17.76) = 521.46
 


 
Source df SS MS F
Treatments 2 180.067 90.033 4.662
Error 27 521.46 19.313
Total 29 702.527
 

Decision: Reject Ho.

Conclusion:     There is sufficient evidence to indicate that the mean times required to complete a certain task differ for at least two of the three levels of training.
 

Which pairs of means differ?

The Bonferroni Test is done for all possible pairs of means.

Decision rule:     Reject Ho, if the interval  does not contain 0.

 c = # of pairs c = p(p-1)/2 = 3(2)/2 = 3

 t.0083 = 2.554
(This value is not in the t table; it was obtained from     a computer program.)
 
Since t.010 < t.0083 < t.0050 (2.473 < t.0083 < 2.771), use t.005 when using a table. If you reject the null hypothesis when t = 2.771; you will also reject it for t.0083.
 


 

There is sufficient evidence to indicate that the mean response time for the advanced level of training is less than the mean response time for the beginning level. There is not sufficient evidence to indicate that the mean response time for the intermediate level differs from the mean response time of either of the other two levels.