Week 5 ANOVA Exercises Research Question: Is there a difference in the overall satisfaction of women based on the number of housing problems (no problems, 1 problem, 2 or more problems)? Using Polit2SetA dataset, run an ANOVA using Overall Satisfaction, Material Well-Being (satovrl) as the dependent variable and Housing Problems (hprobgrp) (this is the last variable in the dataset) as the Independent Variable. Follow these steps when using SPSS: 1. Open Polit2SetA dataset. 2. Click Analyze then click Compare Means, then One-way ANOVA. 3. Move the Dependent Variable (Overall Satisfaction “satovrl”) in the box labelled Dependent List by clicking the arrow button. The dependent variable is a continuous variable. 4. Move the Independent Variable (Housing Problems “Hprobgrp”) into the box labelled Factor. The hprobgrp is a categorical variable coded as (1= no hoursing problem, 2=one housing problem, 3=two or more housing problems). 5. Click the Options button (right side of box) and click on Descriptives and Homogeneity of Variance and then click continue. 6. Click on Post Hoc (right side of box). Click on Tukey and then click continue. 7. Click OK. 8. Check your answers against SPSS output provided. 9. Do not submit the SPSS tables/output as answers to the questions. Assignment: Through analysis of the data and use of the questions below, answer the questions on your findings from this ANOVA test. Answers should be short and do not need to be written as a sentence. No ciattion or APA is required. 1. 2. 3. 4. What is the total sample size? How many women were in each of the different hprobgrp groups? What are the mean and standrad deviation (SD) overall satisfaction scores for each group? Interpret the Levene’s statistic. (Hint: Is the assumption of homogeneity of variance met? Are equal variances assumed or not assumed?) 5. What is the value of the F-statistic, number of degrees of freedom and the p-value? 6. Is there a significant difference in the overall satisfaction level of women in each of the hprobgrp groups? 7. Interpret the post hoc test. When interpreting the post hoc test indicate the mean and standard deviation for each group and indicate which group was signifantly higher or lower from the other. If there is no difference between two groups indicate that as well. Week 5 t Test Exercises SPSS Output Independent t test Group Statistics Currently employed? CES-D Score N Mean Std. Deviation Std. Error Mean No 524 20.8965 12.46425 .54450 Yes 436 15.8239 10.13655 .48545 dimension1 Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means 95% Confidence Interval of the Sig. (2- CES-D Equal variances Score assumed Equal variances not assumed F Sig. t 23.615 .000 6.825 df tailed) Mean Std. Error Difference Difference Difference Lower Upper 958 .000 5.07264 .74326 3.61404 6.53124 6.954 957.514 .000 5.07264 .72949 3.64107 6.50421 Dependent t test Paired Samples Statistics Mean Pair 1 N Std. Deviation Std. Error Mean CES-D Score 18.5516 157 11.87462 .94770 CESD Score, Wave 1 17.8344 157 11.49908 .91773 Paired Samples Correlations N Pair 1 CES-D Score & CESD Correlation 157 Sig. .412 .000 Score, Wave 1 Paired Samples Test Paired Differences 95% Confidence Interval of Mean Pair 1 CES-D Score – CESD Score, Wave 1 .71718 Std. Std. Error Deviation Mean 12.67921 1.01191 the Difference Lower -1.28164 Upper 2.71599 Sig. (2t .709 df 156 tailed) .480 Independent t test with 3 outcome variables Group Statistics Educational attainment CES-D Score N Mean Std. Deviation Std. Error Mean No high school diploma 453 20.1408 11.49986 .54031 Diploma or GED 475 17.5931 11.72389 .53793 SF12: Physical Health No high school diploma 421 44.03546 10.781420 .525454 Component Score, Diploma or GED 440 46.27713 10.597265 .505205 SF12: Mental Health No high school diploma 421 45.70217 10.693544 .521171 Component Score, Diploma or GED 440 47.48328 10.895127 .519405 standardized standardized Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means 95% Confidence Interval of the F CES-D Score Equal variances .228 Sig. .633 t df Sig. (2- Mean Std. Error tailed) Difference Difference Difference Lower Upper 3.340 926 .001 2.54776 .76278 1.05078 4.04474 3.342 925.265 .001 2.54776 .76243 1.05146 4.04406 -3.076 859 .002 -2.241671 .728649 -3.671812 -.811529 -3.075 855.772 .002 -2.241671 .728927 -3.672364 -.810977 -2.420 859 .016 -1.781113 .736103 -3.225884 -.336341 -2.421 858.441 .016 -1.781113 .735800 -3.225290 -.336936 assumed Equal variances not assumed SF12: Physical Equal variances Health assumed Component Equal variances Score, not assumed 1.106 .293 standardized SF12: Mental Equal variances Health assumed Component Equal variances Score, not assumed standardized .174 .677 Week 5 Independent t Test Exercises Answer the questions below for Part I II and III. Make sure to create the table if asked and do not submit SPSS output as your answer. If you have any questions, please email your instructor. Don’t forget to save the document as instructed in the assignment submission directs. You do not have to submit a title page or reference list for this assignment. No citations are required for your submission. Part I The hypothesis being tested is: Women who are working will have a lower level of depression as compared to women who are not working. Using Polit2SetC SPSS dataset, which contains a number of mental health variables, determine if the above hypothesis is true. Follow these steps when using SPSS: 1. 2. 3. 4. Open Polit2SetC dataset. Click Analyze then click Compare Means, then Independent Sample T-test. Move the Dependent Variable (CES_D Score “cesd”) in the area labelled Test Variable. Move the Independent Variable (Currently Employed “worknow”) into the area labelled Grouping Variable. The worknow variable is coded as (0= those women who do not work and 1= those women who are working). Click on Define Groups in group 1 box type 0 and in group 2 box type 1. Click Continue. 5. Click continue and then click OK. 6. Check your answers to the Week 5 t Test Excercises SPSS Output. Assignment: Through analysis of the data answer the questions below with your findings from this t-test. 1. 2. 3. 4. How many women were employed versus not employed in the sample? What is the total sample size? What are the mean and standard deviation for the CES-D scores for each group? Interpret the Levene’s statistic. (Hint: Is the assumption of homogeneity of variance met? Are equal variances assumed or not assumed?) Why? 5. What is the value of the t-statistic, number of degrees of freedom and the p-value? 6. Does the data support the hypothesis? Why or why not? Part II Hypothesis: Women who reported depression scores in wave 1 and wave 2 of the study did not have a significant difference in their level of depression. Using Polit2SetC SPSS dataset, determine if the above hypothesis is true. Follow these steps when using SPSS: 1. Open Polit2SetC dataset. 2. Click Analyze then click Compare Means, then Paired Samples T-test. 3. First click on CES-D Score (cesd) and move it into the box labelled Paired Variables (in the rectangle for Pair 1 of Variable 1 and then click on CESD Score, Wave 1 (cesdwav1) and move it into the Paired Variables box (in the rectangle next to CES-D Score, pair 1, variable 2). 4. Click continue and then click OK. 5. Check your answers to the Week 5 t Test Excercises SPSS Output Assignment: Through analysis of the data and answer the questions below for the findings from this ttest. 1. 2. 3. 4. 5. What is the total sample size? What are the mean and the standard deviation of the CES-D scores at wave 1 and wave 2? What is the mean difference between the two time periods? What is the value of the t-statistic, number of degrees of freedom and the p-value(sig)? Does the data support the hypothesis? Why or why not? Part III Using Polit2SetC dataset, run independent groups t-tests for three outcomes. The outcome variables are CES-D Score (cesd), SF12: Physical Health Component Score, standardized (sf12phys) and SF12: Mental Health Component Score, standardized (sf12ment). Follow these steps when using SPSS: 1. Open Polit2SetC dataset. 2. Click Analyze then click Compare Means, then Independent Sample T-test. 3. Move the Dependent Variables (CES_D Score “cesd”, SF12: Physical Health Component Score, standardized (sf12phys), and SF12: Mental Health Component Score, standardized (sf12ment) ) in the area labelled Test Variable. 4. Move the Independent Variable (Educational Attainment “educatn”) into the area labelled Grouping Variable. The educatn variable is coded as (1= no high school credential and 2=diploma or GED). Click on Define Groups in group 1 box type 1 and in group 2 box type 2. Click Continue. 5. Click continue and then click OK. 6. Check your answers to the Week 5 t Test Excercises SPSS Output Assignment: Create a table to present your results, use the table 6.3 in Chapter 6 in your book as a model. Write one or two paragraphs explaining and summarizing your results. Do not submit the SPSS output that is provided. Week 5 ANOVA Exercises SPSS Output Descriptives Overall satisfaction, material well-being 95% Confidence Interval for Mean N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum No Housing Problem 367 12.71 2.353 .123 12.47 12.95 4 16 One Housing Problem 264 11.97 2.588 .159 11.66 12.28 4 16 Two or More Housing 304 10.57 2.594 .149 10.28 10.86 4 16 935 11.80 2.658 .087 11.63 11.97 4 16 Problems Total Test of Homogeneity of Variances Overall satisfaction, material well-being Levene Statistic df1 2.109 df2 2 Sig. 932 .122 ANOVA Overall satisfaction, material well-being Sum of Squares Between Groups df Mean Square 771.072 2 385.536 Within Groups 5826.111 932 6.251 Total 6597.183 934 F Sig. 61.674 .000 Multiple Comparisons Overall satisfaction, material well-being Tukey HSD (I) Housing Problems (J) Housing Problems 95% Confidence Interval Mean Difference (I-J) No Housing Problem One Housing Problem Two or More Housing Std. Error Sig. Lower Bound Upper Bound .739* .202 .001 .27 1.21 * 2.139 .194 .000 1.68 2.59 -.739* .202 .001 -1.21 -.27 * 1.401 .210 .000 .91 1.89 -2.139* .194 .000 -2.59 -1.68 * .210 .000 -1.89 -.91 Problems One Housing Problem No Housing Problem Two or More Housing Problems Two or More Housing Problems No Housing Problem One Housing Problem *. The mean difference is significant at the 0.05 level. -1.401 Week 5 ANOVA Exercises Research Question: Is there a difference in the overall satisfaction of women based on the number of housing problems (no problems, 1 problem, 2 or more problems)? Using Polit2SetA dataset, run an ANOVA using Overall Satisfaction, Material Well-Being (satovrl) as the dependent variable and Housing Problems (hprobgrp) (this is the last variable in the dataset) as the Independent Variable. Follow these steps when using SPSS: 1. Open Polit2SetA dataset. 2. Click Analyze then click Compare Means, then One-way ANOVA. 3. Move the Dependent Variable (Overall Satisfaction “satovrl”) in the box labelled Dependent List by clicking the arrow button. The dependent variable is a continuous variable. 4. Move the Independent Variable (Housing Problems “Hprobgrp”) into the box labelled Factor. The hprobgrp is a categorical variable coded as (1= no hoursing problem, 2=one housing problem, 3=two or more housing problems). 5. Click the Options button (right side of box) and click on Descriptives and Homogeneity of Variance and then click continue. 6. Click on Post Hoc (right side of box). Click on Tukey and then click continue. 7. Click OK. 8. Check your answers against SPSS output provided. 9. Do not submit the SPSS tables/output as answers to the questions. Assignment: Through analysis of the data and use of the questions below, answer the questions on your findings from this ANOVA test. Answers should be short and do not need to be written as a sentence. No ciattion or APA is required. 1. What is the total sample size? 2. How many women were in each of the different hprobgrp groups? 3. What are the mean and standrad deviation (SD) overall satisfaction scores for each group? 4. Interpret the Levene’s statistic. (Hint: Is the assumption of homogeneity of variance met? Are equal variances assumed or not assumed?) 5. What is the value of the F-statistic, number of degrees of freedom and the p-value? 6. Is there a significant difference in the overall satisfaction level of women in each of the hprobgrp groups? 7. Interpret the post hoc test. When interpreting the post hoc test indicate the mean and standard deviation for each group and indicate which group was signifantly higher or lower from the other. If there is no difference between two groups indicate that as well. Answer 1: What is the total sample size? We are considering a data of 935 individuals and take a sample of size is 935. Answer 2: How many women were in each of the different hprobgrp groups? From 935 sample size, 367, 264 and 304 respectively fall in the groups of no Housing Problem, One Housing Problem and Two or More Housing Problems. Answer 3: What are the mean (SD) overall satisfaction scores for each group? The above result shows that the mean (sd), by the overall satisfaction scores are mean 12.71 sd 2.353, mean 11.97 sd 2.588 and mean 10.57 sd 2.594 respectively for the groups No Housing Problem, One Housing Problem and Two or More Housing Problems. The overall mean satisfaction scores is 11.80 while sd satisfaction scores is 2.658. Answer 4: Interpret the Levene’s statistic. (Hint: Is the assumption of homogeneity of variance met? Are equal variances assumed or not assumed?) We use Levene’s test is used to test whether the variances of the groups are same or significantly different. The null hypothesis is that the variances are not significantly different. The obtained output indicated that the test statistic is 2.109 with associated p-value of 0.122. As the p-value is larger than the significance level of 0.05. Hence the null hypothesis was not rejected as the variances are not significantly different across the groups thus the assumption of homogeneity of variance are met. Answer 5: What is the value of the F-statistic, number of degrees of freedom and the p-value? The result shows that the test statistic is 61.974 with associated p-value 0.000. Answer 6: Is there a significant difference in the overall satisfaction level of women in each of the hprobgrp groups? As the p-value is lower compared to the significance level 0.05, thus null hypothesis may not be rejected. Therefore, the result above result to the assumption that, the variances are not significantly distinct across the groups. In addition, the homogeneity assumption of variance is met. By the ANOVA test, we see that F-statistic value is 61.674 with df of between groups, 2 and that of within groups 932 .Similarly, the related p-value is 0.000. We clearly see that the Ftest p-value is lower compared to the significance level of 0.05 thereby we reject the null hypothesis. In addition, we finalize that there is a major difference in the whole satisfaction level of women in every of the hprobgrp groups. Answer 7: Interpret the post hoc test. When interpreting the post hoc test indicate the mean and standard deviation for each group and indicate which group was signifantly higher or lower from the other. If there is no difference between two groups indicate that as well. The post hoc analysis is utilized for the analysis. As there is major group’s differences, we have to recognize the specific group that varies. The output display that p-values of the post hoc test for every pair is much smaller compared to the significance level of 0.05. Therefore, every group means are significantly distinct. Therefore, every group has significantly dissimilar mean. The descriptive statistics shows that the group of No Housing Problem has the higher mean. In addition, the group with Two or More Housing Problems has lower mean.
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