new_lab_7_correlation_chi_squared_worksheet

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CORRELATION & CHI SQUARED Lab 7 Name: Note: This worksheet is for lab 7. Be sure to read all of the instructions below. As you type, it may push things on subsequent questions to another page, be sure that you have completed ALL parts of each section. Purpose We’ve spent considerable time learning about experimental design & methods, it is now time to dig into SPSS and learn how to test our hypotheses! Before we can do that, we need to learn some SPSS fundamentals first. Lab 7: 1. The other worksheet walked us through how to enter data into SPSS, how to transform/recode that data as needed, and run some basic univariate statistics. 2. This worksheet will walk us through performing some simple hypothesis tests using correlations and chi- squared tests. In-Class: We will walk through a demonstration of the techniques for this assignment. Homework Assigned: The remainder of this worksheet (take-home) is assigned as homework and is due before our next lab meeting. Looking Forward These basic SPSS skills will be needed for all of the future SPSS assignments, especially the final project. It will be important to have a firm grasp of the recode/split/transform operations, as your final projects will likely require you to apply these in a unique way. Additionally, you will be guaranteed to need to do at least 2, if not 3, correlations for your final project. Materials (found under the lecture section on Canvas) 1) This worksheet 2) Corresponding handouts a. Pearson’s Correlation b. Scatterplots c. 2x2 Pearson’s Chi-Square 2) Dataset! a. Rather than enter our own data like earlier in the lab, we will use a much larger dataset that has already been prepared. Note: It is still a good idea to check the dataset to make sure that the variable view has been filled out completely! The dataset is ‘colsurv_new.sav’ – note that this can only be opened in SPSS. Use red font for this worksheet!!!

In-Class Use the colsurv_new.sav dataset to complete the in-class and take-home portions of this worksheet. We will use this dataset to run tests with two different statistical models, Pearson’s correlation, and Chi-squared. The In-Class portion is worth 10 points total (5 each for the correlation and Chi squared) and is based on full, correct completion. Correlation 1. Test the following research hypothesis: College students who report having more close friends tend to have a lower 1 st year GPA. (the logic is that more friends = more opportunities for socializing = less time for studying). 2. Considering the RH:  Does this research hypothesis suggest a positive, a negative, or no relationship between these variables? Negative hypothesis  Explain how you know this. Because one variable is increasing, and the other is decreasing 3. Examining the Scatterplot . Before we run a correlation, we need to make sure that the data appear linearly related, if not… it would be inappropriate to use a linear test on nonlinear data. Follow the scatterplot handout to get the scatterplot of these variables (put GPA on the Y axis).  Is the relationship clearly nonlinear? Yes  What would we do (or not do) of there was a nonlinear relationship? Run a Pearson’s correlation  Does the "direction" of the scatterplot seem to support the RH? Why or why not? I think it does because at the end of the graph, there seems to be a start of a negative, linear relationship 4. Statistical analysis . Follow the handout to get the Pearson's correlation between ”nfrnds” and “frgpa” & enter the results below. For the number of close friends mean = 5.93 std = 3.35 For the 1 st year GPA mean = 3.01 std = 1.07 N = 60 r = -0.215 df = 58 p = 0.099  State the H0 below: There is no linear relationship between the number of close friends and first-year GPA  Based on the results, do we retain or reject the H0? Retain the null  Is there support for the research hypothesis? No 5. Write-up with univariate stats . Follow the example in the handout. Include the means and std of each group in the text of the write-up. Univariate statistics are presented in Table 1. Pearson’s correlation between the number of close friends (M = 5.93, S = 3.35) and first year GPA (M = 3.01, S = 1.07) was r (58) = -0.215, p>0.05. There was no support to the research hypothesis that more closer friends the individual has the lower their first year GPA. We found that there was linear relationship between the number of close friends and first year GPA.

6. Write-up without univariate stats. Follow the example in the handout. Instead of including the means & std in the text of the write-up, refer the reader to the table for the relevant data. Univariate statistics are presented in Table 1. Pearson’s correlation between the number of close friends and first year GPA was r (58) = -0.215, p>0.05. There was no support to the research hypothesis that more closer friends the individual has the lower their first year GPA. We found that there was linear relationship between the number of close friends and first year GPA. 7. Compose a “Table 1” showing the mean and std for each variable in the correlation. You should replace anything in brackets “[ ]” with your own title, name, or values. Table 1 Univariate statistics of number of close friends and first years Variable Mean Std Number of Close Friends 5.93 3.35 First Year GPA 3.01 1.07 8. Grab a screenshot of the homework checker screen, showing all of your input answers in green (correct). Paste it below this step. Your TA will not grade the assignment without this. *** continued below

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Chi-Squared 1. Test the following research hypothesis: Among college students, students from urban neighborhoods are equally likely to be Greek or Independents, whereas students from rural neighborhoods are more likely to be members of a Greek organization than to be an Independent. 2. Considering the RH: a. Label the contingency table on the right to depict the RH, by changing each “?” to “<”, “>”, or “=”. b. Does this research hypothesis suggest a symmetrical pattern of relationship, asymmetrical pattern of relationship or no relationship between these variables? Independent Greek Urban 12 = 14 Rural 14 < 20 Asymmetrical 2. Examining the Contingency Table. Follow the handout to get the cross-tabulation & fill in the values above.  Does the "pattern" in the table seem to support the RH? Maybe  Why or why not? for rural, Greek > Independent, for urban – we don’t know if 12 and 14 are significantly different 3. Statistical analysis . Follow the handout to get the Pearson's X² between these variables. Number of Greeks in the sample 34 number of Independents 26 Number from urban neighborhood 26 number rural neighborhood 34 X² = 0.149 df = 1 p = 0.70 State the H0 below: No pattern of relationship between Greek membership and neighborhood type. Based on the results, do we retain or reject the H0? Retain Is there support for the research hypothesis? No support for RH 4. Write-up. Follow the example in the handout. Refer to a Table 1 that contains the contingency table. Table 1 shows the contingency table for these variables. There were larger number of individuals in rural neighborhoods than urban, and more in Greek than independent. From the contingency table, there seems to be support in that those in rural neighborhoods were more likely to be Greek affiliated than as independent, and potentially equally divided between Greek and independent for those in urban neighborhoods. However, the chi- squared test revealed that there was no pattern or relationship between Greek membership and neighborhood type, X 2 (1) = 0.146, 9 = 0.70. Thus, there was no support to the RH and null hypothesis was retained.

5. Compose a Table 1 that holds the contingency table for the analysis. (add lines as necessary to ensure that the table is not split across pages) Table 1 Contingency table for neighborhood type and Greek membership Greek Membership Neighborhood Type Independent Greek Total Urban 12 14 26 Rural 14 20 34 Total 26 34 60 6. Grab a screenshot of the homework checker screen, showing all of your input answers in green (correct). Paste it below this step. Your TA will not grade the assignment without this. *** Take-Home below

Take-Home The points for the Take-Home section are marked for each step in parentheses, the total for correlation and chi- squared are 20 points each. Correlation 1. Test the following research hypothesis: College students who report having more close friends tend to spend more evenings during socializing with friends during the semester. 2. Considering the RH (1):  Does this research hypothesis suggest a positive, a negative, or no relationship between these variables? Positive relationship  Explain how you know this. Because both are increasing 3. Examining the Scatterplot (2). Before we run a correlation, we need to make sure that the data appear linearly related, if not… it would be inappropriate to use a linear test on nonlinear data. Follow the scatterplot handout to get the scatterplot of these variables (put GPA on the Y axis).  Is the relationship clearly nonlinear? Yes  What would we do (or not do) of there was a nonlinear relationship? Run a Pearson’s correlation  Does the "direction" of the scatterplot seem to support the RH? Why or why not? Yes because there seems to be a start of a positive, linear relationship 4. Statistical analysis (5). Follow the handout to get the Pearson's correlation between ”frnds” and “clsevngs” & enter the results below. For the number of close friends mean = 5.93 std = 3.35 For the nights socializing during the semester mean = 2.52 std = 1.19 N = 60 r = 0.466 df = 58 p = 0  State the H0 below: There is no relationship between the number of close friends and number of nights socializing  Based on the results, do we retain or reject the H0? Reject  Is there support for the research hypothesis? Yes 5. Write-up with univariate stats (5) . Follow the example in the handout. Include the means and std of each group in the text of the write-up. Univariate statistics are presented in Table 1. Pearson’s correlation between the number of close friend (M=5.93, S=3.35) and number of nights socializing (M=2.52, S=1,19) was r(58) = 0.466, p=0. There was support for the research hypothesis that more closer friends leads to more night spent socializing. We found that there was a nonlinear relationship between the number of close friends and number of nights spent socializing.

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6. Write-up without univariate stats (5). Follow the example in the handout. Instead of including the means & std in the text of the write-up, refer the reader to the table for the relevant data. Univariate statistics are presented in Table 1. Pearson’s correlation between the number of close friends and the number of nights spent socializing was r(58)=0.466, p=0. There was support for the research hypothesis that more closer friends leads to more night spent socializing in the semester. We found that there was a nonlinear relationship between the number of close friends and number of nights spent socializing. 7. Compose a “Table 1” showing the mean and std for each variable in the correlation (2). You should replace anything in brackets “[ ]” with your own title, name, or values. Table 1 Univariate statistics for number of close friends and number of nights spent socializing Variable Mean Std Number of Close Friends 5.93 3.35 Number of Nights 2.52 1.19 8. Grab a screenshot of the homework checker screen, showing all of your input answers in green (correct). Paste it below this step. Your TA will not grade the assignment without this. *** continued below

Chi-Squared 1. Test the following research hypothesis: among college students, Greeks tended to have voted in the last ASUN election whereas Independents tend to have not voted. 2. Considering the RH (4): a. Label the contingency table on the right to depict the RH, by changing each “?” to “<”, “>”, or “=”. b. Does this research hypothesis suggest a symmetrical pattern of relationship, asymmetrical pattern of relationship or no relationship between these variables? Independent Greek Voted 10 < 27 No Vote 16 > 7 Symmetrical 3. Examining the Contingency Table (4). Follow the handout to get the cross-tabulation & fill in the values above.  Does the "pattern" in the table seem to support the RH? Maybe  Why or why not? They all seem to be statistically different, but we cannot be sure 4. Statistical analysis (5) . Follow the handout to get the Pearson's X² between these variables. Number of Greeks in the sample 34 Number of Independents 26 Number who voted 37 Number NOT voted 23 X² = 10.45 df = 1 p = 0 State the H0 below: There is no relationship between whether or not they are in a Greek house and if they voted in the ASUN election Based on the results, do we retain or reject the H0? Reject Is there support for the research hypothesis? Yes 5. Write-up (5). Follow the example in the handout. Refer to a Table 1 that contains the contingency table. Table 1 shows the contingency table for these variables. There were a larger number of individuals in Greek life than independent, and more who voted than not voted. From the contingency table, there seems to be support in that those who are Greek are more likely to vote in the ASUN election. The chi-squared test revealed that there was a pattern or relationship between Greek members and if they voted, X 2 (1) =10.45, p=0. Thus, there was full support to the RH and null hypothesis was rejected.

*** continue to step 6 below 6. Compose a Table 1 that holds the contingency table for the analysis (2). (add lines as necessary to ensure that the table is not split across pages) Table 1 Contingency table for Greek membership and if voted Voted in last ASUN election Greek Membership Didn’t Vote Did Vote Total Independent 16 10 26 Greek 7 27 34 Total 23 37 60 7. Grab a screenshot of the homework checker screen, showing all of your input answers in green (correct). Paste it below this step. Your TA will not grade the assignment without this.

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