Question

Short Answer 1

Fred, a researcher at Podunk University, conducts an experiment on the effects of traffic noise level (low, moderate, high) on the ability to concentrate on a complex cognitive task. Participants in a simulated office setting are exposed to one of the three traffic noise levels and are then asked to complete a difficult word puzzle. Fred measures the number of times each participant breaks their attention by looking away from the puzzle. Ginger, a researcher at Cowpie College, decides to conduct the same experiment, using the same methods as Fred does.

Fred and Ginger obtain the following results:

Fred’s Study:                                                    Ginger’s Study:

n = 10 participants per group                             n = 10 participants per group

M Low Noise = 5                                               M Low Noise = 5

M Moderate Noise = 10                                     M Moderate Noise = 10

M High Noise = 15                                             M High Noise = 15

s for each group = 3                                          s for each group = 8

a. Based on the data presented above, which researcher is more likely to obtain a significant ANOVA F-value: Fred, Ginger, or are they both equally likely? (List one option.)  (5 pts.)

b. Explain your choice.  (10 pts.)

Answer 1

a.

F-value = MS Between / MS Error

Since all mean values are same in each group and the standard deviation (s) for each group in Fred’s Study is lower, the SS Error and MS Error term will be lower.

Thus, F-value in Fred’s Study is larger and will be more significant.

b.

Fred’s Study :

Grand mean, = (5 + 10 + 15)/10

SS Between = = 10 * (5 - 10)^2 + 10 * (10 - 10)^2 + 10 * (15 - 10)^2 = 500

SS Error = = (10 - 1) * 3^2 + (10 - 1) * 3^2 + (10 - 1) * 3^2 = 243

df Between = Number of groups - 1 = 3-1 = 2

df Error = Number of observations - Number of groups = (10 * 3) - 3 = 27

MS Between = SS Between / df Between = 500 / 2 = 250

MS Error = SS Error / df Error = 243 / 27 = 9

F value = MS Between / MS Error = 250 / 9 =  27.78

Ginger’s Study:

MS Between = 250 (Since all mean values are same)

SS Error = = (10 - 1) * 8^2 + (10 - 1) * 8^2 + (10 - 1) * 8^2 = 1728

MS Error = SS Error / df Error = 1728 / 27 = 64

F value = MS Between / MS Error = 250 / 64 =  3.91

Thus, F-value in Fred’s Study is larger and will be more significant.