With this recipe, we will look at the readability advertisement in different magazines. The data was collected from nine magazines covering different reader demographics. The responses include the number of words, number of sentences, and number of three plus-syllable words in the advertising copy. The first factor is the selected magazine. The second factor, group, is an educational level of the magazines readers, 1 being the highest and 3 being the lowest.
Magazines are randomly selected from a group of magazines at each readership educational level. The magazines in the study are nested under the group.
The data is from the magazine dataset at The Data and Story Library. Copy the data from the following link into Minitab:
http://lib.stat.cmu.edu/DASL/Datafiles/magadsdat.html
When copying the data in to Minitab, there is a blank line under the column headers. This can cause the column names to copy incorrectly. Copy just the Data section in to Minitab and then rename the columns. In the following instructions, the columns have been named Words, Sentences, 3+Syllables, Magazine, and Group.
- Navigate to Stat | ANOVA | General Linear Model and click on Fit General Linear Model.
- Enter
3+ Syllablesin the Responses field. - Enter
GroupandMagazineas the Factors, as shown in the following screenshot:
- Click on the Random/Nest button. In the Factor type: section, change Magazine to Random. Then, in the Nesting: section, enter
Groupin the row for Magazine. Click on OK. - Click on the Graphs button and choose Four in one residuals.
- Click on OK in each dialog to run the study.
The results of the nested design should show us that the main component of variation is the magazine rather than the group the magazine belongs to. This asks some interesting questions about the grouping by education level and what this means.
The Random/Nest… section of the General Linear Model menu allows us to define factors as either Fixed or Random and the nesting structure of the factors.
Magazine is defined as a random factor as the magazines are selected at random from a larger population of publications within each group.
The Fully Nested ANOVA tool can also be used to run the same results. The order of factors being entered into the model defines the nesting structure. For instance, A B would nest B within factor A. All factors within the Fully Nested ANOVA tool would be considered random.