Statistics and Advertising

In Week 4, you explored ttests, which allowed you to compare a sample to a population or compare twogroups to one another. You analyzed a study about how visualization techniquesimpact how long it takes people with insomnia to fall asleep. But what if youwant to compare the effectiveness of more than two types of insomniatreatments? Analysis of variance, or ANOVA, allows you to do just that-comparemultiple groups (called levels) based on an independent variable (called afactor). So in a study about insomnia treatments, you might compare a groupthat receives muscle relaxation training to a second group that receivesvisualization training and, finally, to a third group that receives deepbreathing training. An ANOVA will allow you to compare all of the levels atonce to see if, in general, the type of treatment influences how long it takesto fall sleep. Post hoc analyses can provide even more information byidentifying which specific groups differ from one another, showing you whichspecific treatments are more effective than others.

In this Discussion youwill use your knowledge of one-way ANOVAs to evaluate a research study scenarioand make suggestions about what could be done to gain even better information.

Scenario:

The Alpha Shoe Company'sadvertising department wants to publish an ad about a new basketball shoe itclaims will enable athletes to jump higher. Alpha attributes this increase inlift to a new sole design, core, and tread.

An independent testinginstitute conducted a study on the shoe, called the "Pluto," to determine if itreally does result in higher jumping heights, in comparison to four othershoes. Five groups of four professional basketball players tested the shoes.The mean jumping height for each shoe was reported as follows:

1. Pluto: 29.3 inches

2. Omega II: 29.0 inches

3. Beta Super: 28.7 inches

4. Delta: 28.4 inches

5. Gamma: 28.0 inches

Alpha did not report any inferentialstatistics in their ad, but it stated, "As you can clearly see, our Pluto shoesoffer an obvious vertical lift advantage in comparison to other leading brands.Even a fraction of an inch can make all the difference in a big game!" Beingthe good consumer of research that you now are, what questions would you haveafter reading Alpha Shoe Company's ad?

Post by Day 3 your answers to thefollowing questions:
What questions about the statistics do you have after reading the ad?
What was done correctly with regards to how the researchers analyzed the data?
What criticisms do you have of the company's statistical approach?
How would you use ANOVA to follow up on the research institute's preliminaryresults presented here?

Be sure to support each of your answerswith evidence and citations from the Learning Resources.

Readings

Heiman, G. (2015). Behavioralsciences STAT 2 (2nd ed). Stamford, CT: Cengage.

• Chapter 11, "Hypothesis Testing Using theOne-Way Analysis of Variance" (pp.184-199)
• Chapter 11 Review Card p. (11.4)

Media

LaureateEducation (Producer). (2013a). ComputingANOVAs and post hoc testing [Video file]. Retrieved from LaureateMyMedia player. (PSYC 3002/PUBH 5003)

This video demonstrates how to conduct an ANOVA test and a post hoc test inSPSS.

StatsLectures.com.(2010). One-way ANOVA[Video file]. Retrieved from http://www.youtube.com/watch?v=51QZa7b0Ozk

This video steps through a one-way ANOVA test. This video includes calculationsof degrees of freedom and test statistics.

OptionalResources

StatisticsLectures.com.(2012b). Post-hoc test forone-way ANOVA [Video file].  Retrieved from http://statisticslectures.com/topics/posthoconewayanova/#video

Note: Theapproximate length of this media piece is 6 minutes.

This video steps through Tukey and Scheffe post hoc tests by hand.