PART 1: Cross-Tabulation and Chi-Square (35 points total)For PART 1, you will compose a cross-tabulation, and test a hypothesis with a chi-square and appropriate measures of association in SPSS. You w

SPSS How To Guide f or Project 4 - Toothman 1 ***Note*** This guide was written using SPSS Version 22 for Windows. The basic instructions to complete the statistical tests should be the same. Opening files may vary between versions and operating systems. Regardless, I suggest playing around with SPSS to learn it a bit on your own before to attempting to complete Project 4. Cross -Tabulation and Chi -Square : Background Once your dat a are open, click Analyze, then Descriptive Statistics, and finally Crosstabs to create your cross - tabulation and analyze your data using chi -square. Figure 1 This will open the following dialogue: Figure 2 Next, select the variables you will use to create your crosstab. You should select your independent variable to be your column variable , and the dependent variable to be your row variable. Select the variable and then click the arrow next to the appr opriate column or row box to move it to the appropriate section. SPSS How To Guide f or Project 4 - Toothman 2 In this example, I selected SEXORNT as my column variable. SEXORNT is a nominal level variable created from the question, “Which of the following best describes you?” with the following cate gories: “gay, lesbian, or homosexual,” “bisexual,” and “heterosexual or straight.” Respondents who reported “don’t know,” “refused,” or “not applicable” were coded as missing. For my dependent variable, I selected marhomo as my row variable. marhomo is an ordinal level variable created from responses to the statement, “homosexuals should have the right to marry.” Respondents reported the following valid responses: “strongly agree,” “agree,” “neither agree nor disagree,” “disagree,” and “strongly disa gree.” Respondents who reported “cannot choose” or “not applicable” were coded as missing. Figure 3 I will test the following hypotheses . The alpha has been set at 0.05. H0: Sexual orientation and attitudes toward same sex marriage are statistically independent. H1: Sexual orientation and attitudes toward same sex marriage are statistically dependent. Next, you will need to click on the box labeled Statistics to tell SPSS which statistics you will calculate for your cross -tabulation. The following dialogue will appear: SPSS How To Guide f or Project 4 - Toothman 3 Figure 4 Next, you will click on the checkbox next to each of the statistics you will calculate. At bare minimum, you will select the box for chi -square. You will also select a chec k-box to calculate an appropriate measure of association to test the strength of the relationship between your two variables. For our purposes, I will check the boxes for lambda and phi and Cramer’s V. Later in the guide, I will show you an example using t wo ordinal level variables so you can effectively read the output. Figure 5 Click Continue. Now you will return to this screen: SPSS How To Guide f or Project 4 - Toothman 4 Figure 6 Click Cells. The following cell display dialogue will appear. Figure 7 By default, only Observed should be checked. This will report the number of people who fall into each cell. In addition to observed, you should also check the box for column percentages . When you create your own table in Word or Excel, I only want to see the column percentages in your new table. SPSS How To Guide f or Project 4 - Toothman 5 Figure 8 Click Continue. This will return you to the crosstabs screen: Figure 9 Now you are ready to click OK. This will pr oduce the output. The output screen will show several boxes to you. Let’s go through them one by one. SPSS How To Guide f or Project 4 - Toothman 6 Output The first box simply shows you how many valid and missing cases you have. For your purposes, the Valid percent should be 100%, and missing should be 0%. Figure 10 The next box shows you the cross -tabulation. We’ll go through it one by one. Figure 11 First, just look at the table and make sure your data are displayed appropriately. Ours a re good! Notice the cells: SPSS How To Guide f or Project 4 - Toothman 7 Figure 12 Just from looking at the cells, it looks like people who identify as gay, lesbian, or homosexual seem more likely than bisexuals or heterosexuals to agree that LGBT people should be able to m arry. Bisexuals seem more divided, but lean more heavily on agreeing that they should be allow to marry. Heterosexuals seem even more divided: about half agreeing, 11.8% do not agree or disagree, and more than a third disagree. Take a look at the totals: Figure 13 By now you should also notice that the sample is disproportionately heterosexual. If we only looked at the raw totals, we would not have been able to infer much about the relationship between sexual orientation and SPSS How To Guide f or Project 4 - Toothman 8 att itudes toward same sex marriage. You will need to replicate this table on your own, using either Excel or Word to create the table for you. The next box shows you the chi -square statistics: Figure 14 We are interested in the inf ormation contained in the row labeled Pearson Chi -Square. Figure 15 Our obtained chi -square statistic is 22.355. We have eight degrees of freedom. The P -value (labeled asymp. sig. (2-sided) is 0.004. With this information, we can reject the null hypothesis. Sexual orientation and attitudes toward same sex marriage are statistically dependent. The next box shows us the directional measures. These are the first set of measures of association we calculat ed. SPSS How To Guide f or Project 4 - Toothman 9 Figure 16 In this box, we can find lambda. Since our dependent variable is marhomo , we need to refer to that section of the table. Figure 17 Lambda is zero! Why is that? lambda will always be zero when the mode for each category of the independent variable falls into the same category of the independent variable – even if other measures of association tell us that the two variables actually are related. If the two variables seem related, based on the chi -square statistic or observations of the differences in percentages, we need to try a different measure of association to measure the strength of the relationship. Lambda is not an adequate measure of association for our relation ship. So let’s take a look at the final table in our output: SPSS How To Guide f or Project 4 - Toothman 10 Figure 18 Here, we need to look at the row labeled Cramer’s V. Figure 19 Do not worry about information in the column labeled approx. sig. Our Cramer’ s V is 0.10. Interpret appropriately.  Chi -Square and Measures of Association for Two Ordinal Level Variables If you select two ordinal level variables to complete this portion of the assignment, you will need to select a different measure of association. For this next test, I will continue to use marhomo as the dependent variable. The variable fund16 is the indep endent variable. Fund16 is an ordinal level variable that reports the “fundamentalism/liberalism of religion [the] respondent was raised in.” The categories “fundamentalist” (1) means the religion was categorized as a very conservative denomination. “Moder ate” (2) means the religion was categorized as being a more moderate religion. “Liberal” (3) means the religion was considered to be a liberal religious group. We can think of this as a continuum. Higher scores indicate more liberal religious beliefs at 16 ; lower scores indicate more conservative religious beliefs. We will test the following hypotheses: H0: Religious fundamentalism at 16 and attitudes toward same sex marriage are statistically independent. H1: Religious fundamentalism at 16 and attitudes t oward same sex marriage are statistically dependent. SPSS How To Guide f or Project 4 - Toothman 11 Figure 20 We set up our chi -square test similarly to the previous example, until we get to the statistics box. We will still select a chi -square test to test the significance of the relationship, but with respect to the association, we need to select gamma and either Kendall’s tau -b or Kendall’s tau -c. Since there are five categories on our dependent variable, and only three for our column variable, we should select Kendall’s t au -c in addition to gamma. This is because we use Kendall’s tau -c when the cross -tabulation is a rectangle. If we had the same number of categories on both variables, we would use Kendall’s tau -b. Figure 21 SPSS How To Guide f or Project 4 - Toothman 12 Output Let’s take a look at the cross -tabulation: Figure 22 It seems that something may be going on here. A little over one -third of people raised in fundamentalist religions agree that same -sex couples should be allowed to marry. Twelve and a half percent do not agree or disagree, while over half disagree with the statement that same -sex couples should be allowed to marry. Over one -half of those raised in moderate and liberal denominations agreed that same -sex couples should be allowed to marry. So there might be something going on here. Keep in mind that on the fund16 variable, lower scores = more conservative beliefs; higher scores = more liberal beliefs . On our marhomo variable, lower scores = agreement that same -sex couples should be allowed to marry and higher scores = disagreement that same -sex couples should be allowed to marry. With this in mind, and with the evidence presented above, it seems that if the two variables are st atistically dependent, we are likely to have a negative relationship. As the independent variable score increases, the dependent variable score decreases. The chi -square test suggests that we should reject our null hypothesis. Religious fundamentalism and attitudes toward same -sex marriage are statistically dependent. SPSS How To Guide f or Project 4 - Toothman 13 Figure 23 Now we can examine the box labeled symmetric measures. Here we can find our gamma and the Kendall’s tau - c.

Figure 24 We are onl y interested in the information contained in the value column. Our Kendall’s tau -c is -0.143 and our gamma is -0.193. Interpret appropriately.  SPSS How To Guide f or Project 4 - Toothman 14 Regression and Correlation To begin, click Analyze, then Regression, and finally linear to complete the regr ession and correlation portion of Project 4. Figure 25 The following linear regression dialogue will appear: Figure 26 SPSS How To Guide f or Project 4 - Toothman 15 You will need to select two appropriate variables to obtain your regression line equation. Remember, your independent variable is the one you think will predict a change in the dependent variable. In this example, weekswrk is an interval -ratio level variable reporting the number of weeks a respondent worked last year. It is the independent variable. VISLIB is an interval -ratio level variable reporting the number of times a respondent visited a public library last year. Figure 27 All we need to do to get the information to report our linear regression equation, the correlation coefficient, and the coefficient of determination, is click OK. Your output will appear! I’ll go through each box one by one. Figure 28 The first box just shows the variables in the equation and the method used to enter them (you don’t need to worry about this). Double check that the variables entered matches your independent variable and the dependent variable below the box matches what you intended to do. We’re all good! SPSS How To Guide f or Project 4 - Toothman 16 The Model Summary box reports Pearson’s correlation coefficient ( R) and the coefficient of determination ( R2). Figure 29 Hold off on interpreting the correlation coefficient for now. We c an also see that our regression equation demonstrates that only 0.1% of the variation in visits to the library last year is explained by how many weeks worked last year. The next box shows us ANOVA. ANOVA and regression are related! For this portion of th e assignment, do not worry about this box. This box shows us if there is a significant relationship in our regression (we did not cover this in our class – we can conduct hypothesis tests with regression, too!). In short: there isn’t a statistically signif icant relationship. Figure 30 The final box, labeled coefficients, contains the information you need to report your regression line equation. Figure 31 The information contained under the column label ed B shows us both the slope ( b) and the y-intercept (a). The row labeled (Constant) shows us the constant of the regression line. This is different language than you are already familiar. The number in the cell where B and (Constant) meet is the y-intercept. SPSS How To Guide f or Project 4 - Toothman 17 The row labeled WEEKS R WORKED LAST YEAR shows us various statistics relevant to how the independent variable is related to the dependent variable. In the cell where B and WEEKS R WORKED LAST YEAR meet, we are shown the slope of the line (b). For each unit increase in the number of weeks someone worked last year, we expect a decrease in the number of library visits last year of 0.019. Let’s return to the correlation box I showed you earlier. Figure 32 The correlatio n coefficient presented here is only going to show a positive figure (this is what you should expect; the explanation is beyond the scope of this class). However, based on the slope of our regression line, we know that we actually have a negative relations hip – as X increases, Y decreases. When you report your correlation coefficient, make sure you report the appropriate sign. In this case, we know we have a very weak negative relationship (R = -0.036). Just to confirm, you can but do not have to calculate the bivariate correlation (click Analyze, then Correlation , and then Bivariate Correlation ). Take a look at what we find: Figure 33 There it is! We can see there is a negative correlation of -0.36! SPSS How To Guide f or Project 4 - Toothman 18 ANOVA To begin our ANOVA, you will first click Analyze, then Compare Means, and finally One -way ANOVA. Figure 34 The following One -way ANOVA dialogue will appear: Figure 35 Under dependent list, you will select your dependent variable. For our purposes, I’ll use our weekswrk variable from earlier. Under factor, you will select your grouping variable . I’m selecting marital, which is a nominal level variable reporting respondents’ marital status: ma rried, widowed, divorced, separated, or never married . This is the variable you will use to see if there are differences in the mean number of weeks worked last year by marital status . I’ll test the following hypotheses: H0: There are no differences in mean weeks worked last year by marital status. H1: There is at least one difference in the mean number of weeks worked last year by marital status. SPSS How To Guide f or Project 4 - Toothman 19 Figure 36 From here, click on the box that says Post Hoc. Your book doesn’t d iscuss post -hoc tests, but they are very useful in figuring out which groups differ and which do not. The following Post Hoc Multiple Comparisons dialogue will appear: Figure 37 There are lots of different tests we can use to see which groups differ. Click the box labeled simply Tukey. Then click Continue. SPSS How To Guide f or Project 4 - Toothman 20 Figure 38 This will bring you back to the One -Way ANOVA dialogue. Click OK. Figure 39 Now your output will appear. We’ll go through it one by one. The first box shows you the sum of squares, mean squares, degrees of freedom, the obtained F -statistic, and the p -value. Everything you need and are already comfortable with calcu lating by hand.  Figure 40 SPSS How To Guide f or Project 4 - Toothman 21 In Project 4, I’ve asked you to report dfb, df w, MSB, MSW, the obtained F-statistic, and the p-value. It’s all right here! We can reject the null hypothesis because our ANOVA demonstrates there is at least one difference in mean number of weeks worked last year. If you did not find a significant relationship, you’re pretty much done. If you did find a significant relationship, you need to take a look at the next bit of output. The Post Hoc Tests output comes next. Figure 41 The first column shows us all five relationship status categories. Notice that it is labeled (I) MARITAL STATUS. The next column shows us each of the other four relationship status categories, relative to the category reported in the first column. It is labeled (J) MARITAL STATUS. The third column labeled Mean Differences (I -J) shows us the mean difference in weeks worked last year, subtract ing the mean number of weeks worked for the first category (labeled I) from the mean number of weeks worked for the second category (labeled J). Let’s examine the first row: SPSS How To Guide f or Project 4 - Toothman 22 Figure 42 First, we are looking at the mean difference in the number of weeks worked last year between married respondents and widowed respondents. The value reported in the first cell under the Mean Difference (I -J) column is calculated using the following formula: − = In this equation, I = Married and J = Widowed. The mean difference is 23.317 weeks. This means that married respondents worked an average of 23.317 more weeks than widowed respondents did last year. Now take a look at the value under the sig. column. This is the P -value! The P -value is 0.000. This means that at the alpha = 0.05 level, we can confirm that married respondents worked significantly more weeks last year than widowed respondents. You need to do this for each row. Notice there is repeated information in the table. Let’s look at the row where I = WIDOWED and J = MARRIED. SPSS How To Guide f or Project 4 - Toothman 23 Figure 43 From this, we can see that widowed respondents worked significantly fewer weeks last year than m arried respondents did. They worked 23.317 weeks fewer, on average. Hey! That’s the reciprocal value!  Let’s identify each set that significantly differed: SPSS How To Guide f or Project 4 - Toothman 24 Figure 44 Notice anything? Widowed respondents worked significantly fewer weeks last year than married, divorced, separated, and never married respondents. Perhaps even more interesting, the only significant differences involved widowed respondents. What might expla in this? It is probable that most of the widowed respondents are elderly, and thus at retirement age already. Make sure you report all significant differences appropriately.  Good luck on Project 4! I hope this guide was helpful.