One Way ANOVA

This tutorial covers the steps for computing one-way ANOVA tests in StatCrunch. To begin, load the Telephone Holding Times data set, which will be used throughout this tutorial. This data set comes from "Statistics: The Art and Science of Learning from Data" by Alan Agresti and Christine Franklin. An airline has a toll-free phone number that they use for reservations where sometimes callers have to be placed on hold. The airline conducted a randomized experiment to determine if there was a significant difference in how long a caller would remain on hold depending on what is playing in the background. The airline randomly selected one out of every 1000 calls to be placed on hold with either a advertisement of current promotions, with muzak playing (elevator music), or with classical music playing. Each column contains the number of minutes that a random caller remained on the line until they hung up for each type of recorded message.

Performing an ANOVA test

To compute the appropriate ANOVA test results, choose the Stat > ANOVA > One Way menu option. Under Compare, there are options to compare Selected columns from the data table or to do the comparison based on Values in a single column. If Values in a single column is selected, all responses must be in the column selected for Responses in and the corresponding unique values of the column selected for Factors in will determine the response groups. In this case, use the default Selected columns option because the responses are stored in separate columns. Select the Advertisement, Muzak, and Classical columns to compare the mean hold times for the different types of recording played. Click Compute! to view the ANOVA test results. The results have a table displaying sample size for each column along with relevant summary statistics. At the bottom of the output, there is a standard ANOVA table with a F statistic and and a P-value for the test.

Computing Tukey intervals

Other statistical results can be added to the ANOVA output in StatCrunch. For this example, in the window containing the resulting ANOVA output above, choose Options > Edit to reopen the One Way ANOVA dialog window. Listed under the Options header are additional output options including Compute Tukey HSD and toTest homogeneity of variance. Select the Compute Tukey HSD to create simultaneous confidence intervals for the pairwise differnces between means. For the Level input, enter 0.90 to compute 90% confidence intervals and click Compute!. At the bottom of the resulting output shown below are the Tukey 90% simultaneous confidence intervals of the difference between mean wait times for each combination of recordings played.

Adding graphs to results

In the window containing the previous ANOVA results, choose Options > Edit to reopen the dialog window. Under Graphs, a list of optional graphs is provided for better understanding the differences between groups. Select Dotplot under Graphs and press Compute!. In the results window, press the > button at the bottom right to display the dotplot of the observations for each group. The plot shows the data for each group, and it has a red vertical line representing the overall grand mean computed by combining the data from all of the groups.

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