Question

A study measuring the fatigue of air traffic controllers resulted in proposals for modficiation and redesign of the controllers' workstation. After consideration of several designs for the workstation, three specific alternatives are selected as having the best potential for reducing controller stress. The key question is: To what extent do the three alternatives differ in terms of their effect on controller stress? A randomized block design is used to test the hypothesis of no difference in stress levels for the three workstation alternatives. The data for the experiment is located in the Microsoft Excel Online file below. Use ? = 0.01 to test for any significant differences.

Set up the ANOVA table for this problem. Show the entries to 2 decimals, if necessary.

	System A	System B	System C
Controller 1	15	16	19
Controller 2	15	15	15
Controller 3	11	12	15
Controller 4	13	13	18
Controller 5	16	14	17
Controller 6	14	14	13

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F
Treatments
Blocks
Error
Total

Calculate the value of the test statistic (to 2 decimals).

Answer 1

using excel>data analysis>two way ANOVA

we have

Anova: Two-Factor Without Replication
SUMMARY	Count	Sum	Average	Variance
Controller 1	3	50	16.66667	4.333333
Controller 2	3	45	15	0
Controller 3	3	38	12.66667	4.333333
Controller 4	3	44	14.66667	8.333333
Controller 5	3	47	15.66667	2.333333
Controller 6	3	41	13.66667	0.333333
system A	6	84	14	3.2
system B	6	84	14	2
system C	6	97	16.16667	4.966667
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
treatments	30.27778	5	6.055556	2.95	0.068658	3.325835
Blocks	18.77778	2	9.388889	4.57	0.03898	4.102821
Error	20.55556	10	2.055556
Total	69.61111	17

since p value of treatments and blocks is greater than 0.01

we conclude that there no difference in stress levels for the three workstation alternatives