Two-Factor ANOVA Method

We are interesting in examining the effects on the response variable of two factors simultaneously. - How do price and advertising simultaneously affect sales? - How do gender and type of advertisement affect sales? - How do type of support and level of technician expertise affect customer satisfaction rating? - How do marketing level and price levels affect product perception? - Advertising web effectiveness rating based on media type and sound level.

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′ n = the number of replicates, the number of observations receiving an AB combination or treatment

r = the number of levels of factor A

c = the number of levels of factor B

Example: Comparing lifetime number of jobs by education level and gender.

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′ n = 10

r = the number of levels of factor education level, 4

c = the number of levels of factor gender, 2

Example: Comparing lifetime number of jobs by education level and gender.

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H0 : The effect of education level on the number of jobs is not dependent on gender and vice - versa.

H1 : The effect of education level on the number of jobs is dependent on gender and vice - versa.

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H0 : The means of all levels of factor A are equal. μ1 = μ2 = μ3 = μ4

H1 : At least 2 means differ.

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H0 : The means of all levels of factor B are equal. μm = μF

H1 : At least 2 means differ.

Example: Analyzing whiteness based on the effects of temperature and detergent brand.

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′ n =

r = the number of levels of temperature

c = the number of levels of detergent

Two-Way ANOVA Summary

Source df SS MS F

A r-1 SSA MSA F*=MSA/MSE

B c-1 SSB MSB F*=MSB/MSE

AB (r-1)(c-1) SSAB MSAB F*=MSAB/MSE

Error Rc(n’-1) SSE MSE

Total n-1 SST

•Test regarding the effect of 2 factors simultaneously on a response variable.•Equal variance assumption.

Homework Ice Cream Ratings

This experiment sought to understand how branding affects consumer preferences. Specifically, in this study a taste test was conducted utilizing three different brands of vanilla ice cream. Premium (Ben and Jerry’s), midrange (Blue Bell), and store (Tom Thumb) brands of ice cream were utilized. All of the brands were the vanilla flavor. The experimental units were a group of 72 undergraduate college students in two introductory business courses (intro to management information systems and intro to statistics). Students were excluded from the study if could not eat ice cream or had a particular aversion to vanilla.

Each of the subjects tasted one of the ice creams and rated it. Half of the students tasted an ice cream without knowing its brand and half of the students tasted an ice cream knowing its brand. Students were randomly assigned to one of the six tasting groups (treatments) for each class. From each of the two classes, 36 students tasted ice cream brands, half of which were unaware of the brand they were tasting. There were 6 replications for each treatment, i.e. awareness, brand combination.

Students rated taste on a 1 to 5 scale with 1 being a poor rating and 5 being the best possible rating.

Run a two-factor analysis of variance and interpret your results.

For those tasting a certain brand of ice cream, is their rating significantly different depending on whether they are aware of the brand or not?

Are there significant differences in ratings based on brand?

Are there significant differences based on awareness?

Try to find the slightly interesting significant result of this study and interpret appropriately.

Use the data set IceCreamRatings. Where Awareness=1, yes the student knows the brand he/she is tasting, and Awareness=2, no the student does not know the brand he/she is tasting. Where Brand 1 (premium), Brand 2 (midrange), and Brand 3 (store labeled).

© This study and data property of David Weltman, University of Texas at Arlington

Homework IRS

The data file IRS contains the amount of time (in minutes) that it took for a random sample of people in 3 different income brackets (1=low, 2=medium, and 3=high) to complete a type of new tax form. The IRS is considering introducing one type of these forms. Based on the results of this analysis, the IRS will introduce a new form or forms to taxpayers.

Using form completion time as the primary criteria, what would you recommend to the IRS in regards to introducing one or more of these new forms?