Section 8.1: Analysis of Variance Activity: Anal'ysis of Variance Randomization Test Dominic Kelly and some friends in Australia wanted to see if ants cared about the sandwich lling in the sandwiches they were eating, so they decided to gather some data. They put out 8 bits of sandwich for each of three different types ofllings and. afterwaiting a few minutes. counted the number of ants on each of the 24 bits. The data are shown in the table below, with means and standard deviations. We wish to test to see if there is a difference in mean number of ants who approach a sandwich bit. depending on which lling is used. We'll do this using a randomization test. Vegemite Peanut Ham & Butter Pickles 18 43 44 29 59 34 42 22 36 42 25 49 31 36 54 21 47 65 38 19 59 25 21 53 Mean 30.75 34.0 49.25 Sthev. 9.25 14.63 10.79 3). Recall from Chapter 4 that to create a randomization sample. we use the data that we have while also assuming that the null hypothesis is true. In this case. the null hypothesis is that the three population means are equal. This means that the type of lling doesn't matter and any of the values could go with any of the llings. Explain how to use the 24 data values we have. and the fact that lling type doesn't matter. to create one simulated randomization sample. b). What randomization statistic should we compute for each randomization sample? We've seen that the F-statistic from an ANOVA table gives a measure of how different the group means are relative to the random variation within each group. This is a good measure for us to use! For each simulated randomization sample. we construct an ANOVA table and record the F-statistic for the sample. We denitely need to automate this part! cl. Use the "ANOVA for Difference in Means" option at the bottom of the main menu of StatKey. The Sandwich Ants data is the default dataset on this page. Click on the ANOVA table option next to the Original Sample. What is the F-statistic for the actual sample data? 77777777777 As in every randomization test. we want to see how extreme this F-statistic is if the null hypothesis is true. d). Using StatKey. generate one simulated sample. What are the group means for the simulated sample? Vegemite: __________ Peanut Butter: __________ Ham 8. Pickles: _________ Are these three means more spread out, less spread out, or about the same as the original three means? Select one: More spread out Less spread out About the same Click on the ANOVA table option next to the Randomization Sample. What is the F-statistic for this randomization sample? 7777777777 Is it larger or smaller than the F-statistic for the actual data?