Prior Expected Frequencies or Values Another question we might ask is: Does the distribution of frequencies of my observations fit well with another distribution I am thinking of that comes from prior observations? For example, if we compared the distribution of preferences for Philadelphia sports teams: Eagles, Phillies and Flyers. Does this year's distribution of preferences look like last year's distribution? This would also be a Goodness of Fit problem. This time, however, we would be comparing a presently observed set of frequencies to a distribution we have in mind, last years observed frequencies, not a chance or equal distribution. * PROBLEM 1 * Our first question is: Is there a difference in the Covid vaccination status numbers when comparing Republicans to Democrats? A recent Gallop Poll (September, 2021) reported the following results for Republicans. Vaccinated* Plan to be Don't plan to Vaccinated be Vaccinated Republicans 56 4 40 *Fully or partially vaccinated The same survey reported the following for Democrats? Vaccinated* Plan to be Don't plan to Vaccinated be Vaccinated Republicans 92 4 3 *Fully or partially vaccinated While the difference between Republicans and Democrats seems obvious, we want to test this with a Goodness of Fit Chi Square. Is the 56-4-40 distribution for Republicans sufficiently different from the 92-3-3 distribution for Democrats, that we can conclude that it is a real difference and not one due simply to chance? Creating the Data file using Weight Cases for this problem Data entry, using the WEIGHT CASES function for Chi Square problems is not like data entry for other kinds of statistical analysis in SPSS. For this problem, the variable being studied is Vaccination Status which has four categories ( Vaccinated, Plan to be Vaccinated, and Don't Plan to be Vaccinated). In setting up our data, these categories will be treated as a variable and placed in a single column. A second variable, "freq" (short for frequencies), will be created and contain the frequency of each category. In addition, it is best to use nominal data in working with categories. In our case:Vaccinated" has been added. Finally, type a "3" in the Value cell, and type "Do Not Plan to be Vaccinated" in the Label cell, and then select "ADD." You will see the Value Label "3 - Do Not Plan to be Vaccinated" has been added. SELECT OK. This takes you back to the Variable View Window. SELECT the Data View tab at the bottom of the screen. This will take you back to the Data View. (It is a good idea to SAVE your data: FILE - SAVE AS ... as you would save any file.) "Weighting the data" We need to complete one more step before we can execute a Chi Square. We need to Weight the data so it accurately reflects that there are 56 Republicans that are vaccinated, 3 that plan to be vaccinated and so on. From the Tool Bar at the top Select DATA and then at the bottom of the drop-down menu, WEIGHT CASES. This produces the Weight Cases window. Select the "Weight Cases by" button, and then select "freq" and move it into the "Frequency Variable" slot. Select OK. This will bring up an Output Window. You do not have to return to the Data View Window but you can, if you want, by selecting the "Go to Data" icon on the tool bar (It is the icon with the Big Red Star). Executing the Chi Square We can now do the Goodness of Fit Chi Square to answer our question: Is there a difference in the Covid vaccination status numbers when comparing Republicans to Democrats? Select ANALYZE-NONPARAMETRIC-LEGACY DIALOGS-CHI SQUARE. In the Chi-Square sub-menu, you can see the variables listed down the left side of the screen and an empty box on the right side labeled, "Test Variable List". Move the variable, Party from the list to the "Test Variable List" box using the arrow that sits between them. Problem Notice in the "Expected Values" section of the sub-menu the "All categories equal" button is selected. This is by default. In our case, however, we have another distribution we want to compare to the 56-3-40 distribution for Republicans. We want to compare this distribution for the distribution for Democrats: 92-4-3. Consequently, we Select the "Values" button and enter the three numbers 92, 4, and 3 one at a time. 92 ADD, then 4 ADD, and finally, 3 ADD. (Note: you might have to clear out the "Values" slot to enter the subsequent entries.) Select OK. The resulting analysis will come up in the Output View. You will see two tables: Test Statistics and the Party Frequencies with expected values and residuals. PROBLEM 1: Concerning the comparison of distribution for Republicans and Democrats: What do you conclude? Do the Republican and Democrat distributions match or are they different. If different, how so? Describe what you have found and what conclusions you are drawing and how you justify them.NPar Tests [DataSet0] C: \\Users\\galvi\\Downloads\\Problem 1. sav Chi-Square Test Frequencies Party Observed N Expected N Residual Vaccinated 56 92.0 36.C Plan to be Vaccinated 3 4.0 -1.0 Do Not Plan to be 40 3.0 37.0 Vaccinated Total 99 Test Statistics Party Chi-Square 470.670 df 2 Asymp. Sig. <.001 a. cells have expected frequencies less than the minimum cell frequency is page>