ANOVA Examples
This Christmas one of the top 10 gift items for college students is a wireless Bluetooth speaker. Three
brands were chosen to see if there is a significant difference in the average price of the various models.
The data below was obtained today from the web.
Bose
149
139
349
209
129
234
399
199
149
1.
2.
3.
4.
5.
6.
7.
Sonos
398
179
399
199
549
349
398
329
180
JBL
129
219
130
130
180
130
230
130
128
Is the data observational or experimental?
Observational
Is the data retrospective or prospective?
Prospective
What is the “experiment”?
Recording speaker prices based on brand.
What is the factor?
Speaker Brand
What are the levels?
Bose, Sonos, JBL
What is the response variable?
Average Price
What type of design should be run? Completely Randomized
8. Test to see if any of the mean prices are different. Alpha = .05
Ho: uB=uS=uJBL Ha: At least 2 means differ F = 7.98 p-value = .0022 < .05 Reject Ho
95% confident at least 2 means are significantly different.
9. How many possible pairs are being compared? 3
10. Which means differ? Sonos costs more
than Bose or JBL.
According to the FTC, Skechers exaggerated claims regarding the
shoes' effectiveness, specifically the ability to tone your body
and lose weight. Reebok shelled out $25 million for falsely
advertising that its shoes guaranteed "a better butt with every step."
The American Council on Exercise randomly assigned 21 physically
active females between the ages of 19 to 24 to walk on treadmills at
3.5 mph wearing the different brands randomly and measured their
maximum voluntary isometric contractions. They controlled the
slant of the treadmills to be at 5%. One of the brands was a generic
running shoe sold at Foot Locker for $60.
11.
Is the data observational or experimental?
Experimental
12.
How many possible pairs are being compared?
6
13.
What is the experiment?
Recording isometric contractions based on shoe brand
14.
What are the factors?
Brand
15.
What are the levels?
Reebok, Skechers, MBT, and Generic
16. What is the control group?
Generic
17. What is the response variable?
Avg. isometric contractions
18. What type of design is this?
Completely Randomized
19. Test the hypothesis to see if any of the means are different based on the brands of shoes worn.
Alpha = .05.
Ho: uR=uS=uMBT =uG Ha: At least 2 means differ F = .143 pvalue = ..9338 > .05 Fail to Reject Ho
95% confident there is no significant difference in the mean
isometric contractions based on brand.
20. Based on the outcomes, do you believe the FTC was
correct in fining the companies?
Yes, they were guilty of false advertising.