Reminder of how to do two-factor ANOVA in Excel: On the Schedule tab of Oncourse, find the Excel spreadsheet named TwoFactorANOVA.xls. On its second worksheet you'll find info about how to do two-factor ANOVA in Excel.

1. 10 pts. Page 331, #23. There are two significant results for which to describe the meaning. Also answer this: Where exactly do the values M=9.08 and M=7.46 come from, in terms of the four values in the bar graph?

2. 10 pts. An experimenter is interested in whether marking words with a color highlighter improves memory for those words. She is also interested in whether words are better remembered when they are accompanied by a picture. So she gives people a list of 24 words (which they studied for 50 seconds), and then has them recall (by writing) as many words as they can. Some people see the words in just black and white text, some in color highlighted text (with different words in different colors), some with black and white pictures next to the words, and some with color highlighted pictures and words. Here are the number of words correctly recalled for each group:
       no picture, no color: 22, 12, 20, 14, 14, 12
       no picture, with color: 14, 10, 19, 10, 15, 14
       with picture, no color: 11, 7, 11, 15, 16, 12
       with picture, with color: 9, 9, 16, 9, 9, 9
   Do an ANOVA in Excel. You'll need to enter the data in an array, and appropriately label the rows and columns. Print out the data table and results of the ANOVA. Next to the output table, clearly write answers to these questions:

   A. Is there a significant interaction between picture inclusion and coloring? Indicate exactly where in the output you find the answer to this question.

   B. What is the mean number of words recalled when there is no picture? What is the mean number of words recalled when there is a picture? Is there a significant main effect of picture inclusion? Indicate exactly where in the output you find the answers to these questions.

   C. What is the mean number of words recalled when there is no color? What is the mean number of words recalled when there is color? Is there a significant main effect of color? Indicate exactly where in the output you find the answers to these questions.

   (By the way, these data are real. My daughter wondered about this and so designed the experiment, with relatively little input from me, although she didn't do the ANOVA. The data are from her classmates at the time. They were in 5th grade.)

3. 10 pts. We want to know if the lengths of baby names have been changing over the years. Visit http://www.socialsecurity.gov/OACT/babynames and scroll to the section called Popular Names by Birth Year. Select "2003" for year of birth and "Top 50" for Popularity. When the table of results appears, select all 50 rows of the info (drag your cursor over it) and copy and paste it into an Excel spreadsheet, starting in cell B2. Your Excel spreadsheet should now have 50 rows and 5 columns, just like the website table. Go back to the website, and select "1990" for the year of birth (and still "top 50"). Get the data and put it into Excel below the previous data. To the right of those raw data, set up another table that will be used for the two factor ANOVA. It will have three columns: One for the row labels ("1990" or "2003"), one for "boy" and one for "girl". Under the boy and girl column labels, enter =len(**) with ** refering to the appropriate corresponding name in the raw data table.

   Print out the results of the ANOVA (but don't print out the data table; that would kill too many trees). Next to the output table, clearly write answers to these questions:

   A. Is there a significant interaction between year and gender? Indicate exactly where in the output you find the answer to this question.

   B. What is the mean name length for boys? For girls? Is there a significant main effect of gender? Indicate exactly where in the output you find the answers to these questions.

   C. What is the mean name length in 1990? In 2003? Is there a significant main effect of year? Indicate exactly where in the output you find the answers to these questions.

4. 10 pts. There are two purposes for this exercise. One is for you to see that random samples from the null hypothesis can exhibit main effects and interactions, just by chance. A second is for you to see what significant main effects and interactions look like in the presence of random data noise, unlike the perfect textbook examples you learn from. On the Schedule tab of Oncourse, find the Excel spreadsheet named TwoFactorANOVA.xls. On its third worksheet (with tab named "Random data from null hyp."), you will see data randomly sampled from a null hypothesis, with a two factor ANOVA conducted on the data. This was also shown in class.

   Press F9 a few times to see how cell means can change, just by chance, when sampled from the null hypothesis.

   A. Press F9 until the row effect is significant but the column and interaction effects are not significant. Stop! Print one page that shows the data, ANOVA output, and graph. You will need to print in landscape orientation, and you might need to squeeze the left columns and textbox so that the entire ANOVA output table fits on the page. Next to the graph, write in your own words how the graph depicts the row effect.

   B. Press F9 until the column effect is significant but the row and interaction effects are not significant. Stop! Print one page that shows the data, ANOVA output, and graph. You will need to print in landscape orientation, and you might need to squeeze the left columns and textbox so that the entire ANOVA output table fits on the page. Next to the graph, write in your own words how the graph depicts the column effect.

   C. Press F9 until the interaction effect is significant but the column and row effects are not significant. Stop! Print one page that shows the data, ANOVA output, and graph. You will need to print in landscape orientation, and you might need to squeeze the left columns and textbox so that the entire ANOVA output table fits on the page. Next to the graph, write in your own words how the graph depicts the interaction effect.