Question

Answer the questions and interpret the data.

Colleen is the marketing manager for Virtually Viral, an entertainment company that collects viral videos from around the Internet and aggregates them on their website. Whether it’s videos of cats or unusual marriage proposals, Virtually Viral collects them all. Almost all of Virtually Viral’s revenue comes from clicks on advertisements surrounding the videos. To maximize profits, Colleen tries to match ad content to video content. For example, for the ‘Wacky Weddings’ section of the website, most advertisements link to wedding planners and invitation/paper product suppliers. As part of this effort, Colleen contracted a web design firm to put together a new look for the website, with the goal of improving the amount of time visitors spend on the website. They produced four different versions, each arranging the videos and advertisements differently. Colleen is unsure which of these designs would result in the greatest amount of time spent on the site. To solve this problem, Colleen designs an experiment. She sets up a system to randomly assign visitors to the website to experience one of the four designs, recording the number of seconds that they spend on the site. She wants to compare the groups with each other and see if the different designs result in different lengths of time viewing the website. Whichever results in the longest visits will become the new design for the site in general. She knows from Chapter 7 that she has a research question and that this calls for some type of hypothesis testing. In Chapter 9, she learned that treating groups differently and comparing them means that she has independent data. But the independent-samples t-test only compares two groups with each other and she has four. Should she run multiple independent-samples t-tests? Or is there a better way?

Colleens problem can be solved with an ANOVA and post-hoc test.  

DATA

webdesign	seconds
4	71
4	62
3	86
2	115
2	86
1	55
2	98
3	108
3	66
1	71
2	120
2	115
1	72
4	48
1	62
4	69
4	55
1	67
4	57
2	103
3	37
3	90

Answer 1

ANSWER:

Given that,

The data is independent and wants to compare four groups with each other we have to use ANOVA and post-hoc test.

H₁: At least on pair of population means are different

Calculated F=10.26, P=0.0004 < 0.05 level of significance.

Reject the null hypothesis

We conclude that there is significant difference between the 4 groups.

Post hoc test shows web design 2 significant from other 3 designs.

All other pairs of designs are not significant.

One factor ANOVA
	Mean	n	Std. Dev
	60.3	6	8.76	webdesign4
	77.4	5	27.07	webdesign3
	106.2	6	12.89	webdesign2
	65.4	5	7.02	webdesign1
	77.9	22	23.67	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	7,428.02	3	2,476.008	10.26	.0004
Error	4,342.57	18	241.254
Total	11,770.59	21
Post hoc analysis
p-values for pairwise t-tests
		webdesign4	webdesign1	webdesign3	webdesign2
		60.3	65.4	77.4	106.2
webdesign4	60.3
webdesign1	65.4	.5967
webdesign3	77.4	.0863	.2376
webdesign2	106.2	.0001	.0004	.0068
Tukey simultaneous comparison t-values (d.f. = 18)
		webdesign4	webdesign1	webdesign3	webdesign2
		60.3	65.4	77.4	106.2
web design4	60.3
web design1	65.4	0.54
web design3	77.4	1.81	1.22
web design2	106.2	5.11	4.33	3.06
critical values for experiment wise error rate:
		0.05	2.83
		0.01	3.60