MM570 Applied Statistics for Psychology Unit 9 Project: Descriptive Statistics This is a course level assessment assignment. MM570-3: Interpret correctly the output from SPSS analyses/statistical tests. Your Name: HINTS AND HELP Dataset: Stat_Grades.sav can be found in Doc Sharing under the Instructor Graded Projects category. Note: When asked to include the interpretation of the results and final conclusions, be sure to include all results, an interpretation of the meaning of the results, and final conclusions that a common person can understand. Make sure you use complete sentences, paragraph form (single spacing), proper grammar, and correct spelling. Minimal or incomplete responses can lose points. Include any SPSS results that you use, but do not include SPSS results that are not part of your solution. Hint: You are asked to determine \"appropriate\" tests and methods, and to make calculations. This means that you will have to determine which tests or methods are best and why. Remember to always show all of your work and each of your steps. For each question, follow the appropriate steps. 1) Write the hypothesis - Construct the null(s) and alternative(s) clearly and appropriately. 3) Run the appropriate SPSS test(s) and include the appropriate results 4) Explain and evaluate the SPSS results 5) Write a complete and paragraph form conclusion that can be understood by a normal non-statistical person. Use the Live Binder for further assistance. There is a link to the Live Binder under every Unit. 1 Point Possible A: 153 - 170 points Grading Criteria Student work demonstrates mastery of the objectives assessed by the Assignment. This is evidenced by at least the following: The selection of the statistical procedure(s) is/are the most appropriate ones for answering the questions; specifically, the correct ANOVA test method is selected for each question. The statistical procedure was calculated correctly using SPSS. The interpretation of the SPSS output is correct and complete, including applying the (Sig. in SPSS) p-value to determine null hypothesis rejection. The results of the statistical analyses are presented in easy to understand, non-statistical language that addresses the research question. SPSS output that is not needed in the solution is not included. Only appropriate SPSS output are included. Each step of the hypothesis testing procedure is included and Ho and Ha are clearly written. All aspects of the tests are included and explained, including the Post Hoc results and the interaction plot. Appropriate regression prediction equations are created and evaluated. Use alpha = .05 for this project. 1. Compare the different Year in School for students in the Stat_Grades.sav dataset to determine if there is a statistically significant difference in the average Final Exam Points between the different years (first year, sophomore, junior, senior). Be sure to state the hypothesis, state Ho and Ha, include and explain all SPSS results, and write final conclusions for the full results of the test. Include Post Hoc results and the plot. Be sure that your final conclusions are written in common terms for an average person to understand. (a) What is the hypothesis being tested? (b) What are Ho and Ha? 2 (c) What statistical test will you run - and include all the SPSS outputs (including the plot and post hoc)? (d) Explain the full results for the statistical test that you ran above. Was a post hoc actually needed in this case? Why or why not? Does the Post Hoc confirm your results, explain? What does the plot tell you about the interaction, explain? (e) Write a full conclusion for all results on this test in a way that can be understood by a nonstatistical person. This answer will be at least 100 words or more. 2. Extend the hypothesis from number one above. Compare the different ethnicities of the students in the Stat_Grades.sav dataset and the genders to determine if there is a statistically significant difference in the average Final Exam Points between the different ethnicities and different genders. Be sure to state the hypothesis, state all Ho and Ha, include and explain all SPSS results, and write final conclusions for the full results of the test. Include Post Hoc results, note any interactions and whether they are significant, and include and explain the plot. Be sure that your final conclusions are written in common terms for an average person to understand. (a) What is the hypothesis being tested? (b) What are the set of Ho's and Ha's? (c) What statistical test will you run - and include all the SPSS outputs (including the plot and post hoc)? (d) Explain the full results of the statistical test you have run. Was a post hoc actually needed in this case? Why or why not? Does the Post Hoc confirm your test results, explain? What does the plot tell you about the interaction, explain? 3 (e) Write a full conclusion for all results on this test in a way that can be understood by a nonstatistical person. This answer will be at least 100 words or more. 3. Prediction and Regression. If you recall from the Unit 3 Project, you looked at how to measure the relationship (correlation) between any two variables. You also learned that if two variables are strongly correlated (related) with each other, that one variable can be used to estimate or predict the other. The equation used to make this prediction is called a regression equation. Use the following SPSS outputs to answer the questions. The two variables in this case are Previous GPA and Final Course Percent. (a) What are the two variables that this question is investigating? Notice that the SPSS output above tells you that the r-value (called \"R\") is .440. Is this r-value strong enough to allow you to perform prediction between these two variables? Explain. (b) Using the \"Coefficients\" SPSS output above, create the prediction equation. Remember that your independent or \"x\" variable is Previous GPA and your dependent or \"y\" variable is Final Course Percent. Write the prediction equation here. 4 (c) Using the prediction equation that you created in part (b), predict the Final Course Percent for a student with a Previous GPA value of 2.79. Show all work. 4. From the Stat_Grades.sav dataset, use Quiz 2 and Quiz 5 to answer these questions. The question you will be considering here as you answer the questions below is \"Is the score on Quiz 2 highly correlated to the score on Quiz 5 and can one be used to estimate or predict the other?\" (a) What is the correlation or relationship (r-value) between Quiz 2 and Quiz 5? Is it weak, medium, or strong? Is it strong enough to use for prediction? (b) Use SPSS and run a regression analysis on Quiz 2 and Quiz 5. Place the SPSS \"Coefficients\" output (only) here. (c) Use the SPSS output to create the regression (prediction) equation. Remember, you are trying to predict how a student will perform on Quiz 5 based on how they do on Quiz 2. What is your dependent (y) variable? What is your independent (x) variable? Write the prediction equation here. (d) Use your prediction equation to predict how a student would perform on Quiz 5 if they got a 6.5 on Quiz 2. Show all work. Submitting your Project Make sure your name is on your project and saved to your computer. When you are ready to submit your completed project, click on the Dropbox and complete the steps below: Click the link that says \"Submit an Assignment.\" In the \"Submit to Basket\" menu, select Unit 9: Project. In the \"Comments\" field, include your name and Unit 9 Project. Click the \"Add Attachments\" button. Follow the steps listed to attach your Word document. You should revisit the Dropbox to view any helpful feedback your instructor has left for you. Make sure that you save a copy of your submitted and returned assignment. 5 $FL2@(#) IBM SPSS STATISTICS DATA FILE 64-bit MS Windows 19.0.1 ################i#########Y@18 Jul 1114:04:06 ###########################ID ########################GENDER ####Gender ########################ETHNICIT ###Ethnicity ########################YEAR ####Year in School ########################LOWUP ####Lower or Upper Division ########################SECTION ####Section of Class########################PREVGPA ###Previous GPA########################IQ ####Short Form IQ Test Score########################REVIEW ####ATTENDED REVIEW SESSIONS? ########################QUIZ1 ###Quiz 1 Points ########################QUIZ2 ###Quiz 2 Points ########################QUIZ3 ###Quiz 3 Points ########################QUIZ4 ###Quiz 4 Points ########################QUIZ5 ###Quiz 5 Points ########################FINAL ####Final Exam Points ########################TOTAL ###Total Points########################PERCENT ####Final Course Percent########################GRADE ###Numeric Grade ########################PASSFAIL ###Pass or Fail##############?#FEMALE #######@#MALE ##########################?#AMERICAN INDIAN#######@#ASIAN #######@AFROAMERICAN #######@ CAUCASIAN #######@#HISPANIC ##########################? 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Compare the different Year in School for students in the Stat_Grades.sav dataset to determine if there is a statistically significant difference in the average Final Exam Points between the different years (first year, sophomore, junior, senior). Be sure to state the hypothesis, state Ho and Ha, include and explain all SPSS results, and write final conclusions for the full results of the test. Include Post Hoc results and the plot. Be sure that your final conclusions are written in common terms for an average person to understand. (a) What is the hypothesis being tested? The hypothesis being tested is \"Is there is a statistically significant difference in the average Final Exam Points between the different years (first year, sophomore, junior, senior).\" (b) What are Ho and Ha? H0: 1 = 2 = 3 = 4 Ha: At least one schooling year differs significantly in the average Final Exam Points with others. (c) What statistical test will you run - and include all the SPSS outputs (including the plot and post hoc)? The one-way ANOVA is the appropriate statistical test for this analysis. ANOVA Final Exam Points Sum of Squares Between Groups Within Groups Total Post Hoc Tests 37.165 6525.025 6562.190 df Mean Square 3 101 104 12.388 64.604 F .192 Sig. .902 Multiple Comparisons Final Exam Points Tukey HSD Mean Difference (IJ) Std. Error (I) Year in School (J) Year in School FIRST-YEAR SOPHOMORE -3.088 4.993 .926 JUNIOR -2.135 4.748 .970 SENIOR SOPHOMORE FIRST-YEAR JUNIOR SENIOR JUNIOR FIRST-YEAR SOPHOMORE SENIOR SENIOR FIRST-YEAR -1.561 3.088 .952 1.526 2.135 -.952 .574 1.561 4.993 4.993 2.100 2.608 4.748 2.100 2.100 4.993 .989 .926 .969 .936 .970 .969 .993 .989 SOPHOMORE -1.526 2.608 .936 -.574 2.100 .993 JUNIOR Sig. Multiple Comparisons Final Exam Points Tukey HSD (J) Year in (I) Year in School School FIRST-YEAR SOPHOMORE JUNIOR SENIOR Means Plots 95% Confidence Interval Lower Bound Upper Bound SOPHOMORE -16.13 9.96 JUNIOR -14.54 10.27 SENIOR FIRST-YEAR JUNIOR SENIOR FIRST-YEAR SOPHOMORE SENIOR FIRST-YEAR -14.61 -9.96 -4.53 -5.29 -10.27 -6.44 -4.91 -11.48 11.48 16.13 6.44 8.34 14.54 4.53 6.06 14.61 SOPHOMORE -8.34 5.29 JUNIOR -6.06 4.91 (d) Explain the full results for the statistical test that you ran above. Was a post hoc actually needed in this case? Why or why not? Does the Post Hoc confirm your results, explain? What does the plot tell you about the interaction, explain? The test statistic, F = 0.192 Degrees of freedom = (3, 101) P-value = 0.902 Since P-value > = .05, do not reject the null hypothesis. Since the null hypothesis in the above one-way ANOVA is not rejected, there is no need to perform the post hoc tests, to identify which pairs of schooling years differ significantly in the average Final Exam Points. The means plot also indicates the same conclusion as specified above. (e) Write a full conclusion for all results on this test in a way that can be understood by a nonstatistical person. This answer will be at least 100 words or more. The results provide no sufficient evidence to support the claim that there is a statistically significant difference in the average Final Exam Points between the different years (first year, sophomore, junior, senior), F (3, 101) = .192, p = .902 > .05, First-Year [M = 59.33, SD = 5.859], Sophomore [M = 62.42, SD = 6.628], Junior [M = 61.47, SD = 8.478], and Senior [M = 60.89, SD = 7.951]. Therefore, the average Final Exam Points are same on the average for all the 4 years in school. Since the result of the ANOVA is not significant, no further analysis on the pair-wise mean differences, i.e. post hoc tests are not necessary for this data. 2. Extend the hypothesis from number one above. Compare the different ethnicities of the students in the Stat_Grades.sav dataset and the genders to determine if there is a statistically significant difference in the average Final Exam Points between the different ethnicities and different genders. Be sure to state the hypothesis, state all Ho and Ha, include and explain all SPSS results, and write final conclusions for the full results of the test. Include Post Hoc results, note any interactions and whether they are significant, and include and explain the plot. Be sure that your final conclusions are written in common terms for an average person to understand. (a) What is the hypothesis being tested? The hypotheses being tested is \"Is there a statistically significant difference in the average Final Exam Points between the different ethnicities and different genders?\" and \"Is the interaction between Ethnicity and Gender is significant on Final Exam Points?\" (b) What are the set of Ho's and Ha's? For Interaction effect between Ethnicity and Gender: H0: There is no significant interaction between the two factors Ethnicity and Gender. Ha: There is a significant interaction between the two factors Ethnicity and Gender. For Main effect of Ethnicity: H0: There is no significant effect of the levels of Ethnicity on the Final Exam Points. Ha: There is a significant effect of the levels of Ethnicity on the Final Exam Points. For Main effect of Gender: H0: There is no significant effect of the levels of Gender on the Final Exam Points. Ha: There is a significant effect of the levels of Gender on the Final Exam Points. (c) What statistical test will you run - and include all the SPSS outputs (including the plot and post hoc)? The two-way ANOVA is the appropriate statistical test for this analysis. Tests of Between-Subjects Effects Dependent Variable: Final Exam Points Source Corrected Model Intercept ethnicit gender ethnicit * gender Error Total Corrected Total Type III Sum of Squares df a 725.414 167153.102 293.065 370.266 387.279 5836.776 403391.000 6562.190 Mean Square 9 1 4 1 4 95 105 104 80.602 1.312 167153.102 2720.602 73.266 1.192 370.266 6.026 96.820 1.576 61.440 a. R Squared = .111 (Adjusted R Squared = .026) Post Hoc Tests Ethnicity F Sig. .241 .000 .319 .016 .187 Partial Eta Squared .111 .966 .048 .060 .062 Multiple Comparisons Final Exam Points Tukey HSD Mean Difference (IJ) Std. Error (I) Ethnicity (J) Ethnicity AMERICAN INDIAN ASIAN -3.05 3.919 .936 AFROAMERICAN -2.16 3.853 .980 CAUCASIAN -1.87 3.695 .987 HISPANIC AMERICAN INDIAN AFROAMERICAN CAUCASIAN HISPANIC AMERICAN INDIAN ASIAN CAUCASIAN HISPANIC AMERICAN INDIAN ASIAN AFROAMERICAN HISPANIC AMERICAN INDIAN 1.89 3.05 4.228 3.919 .992 .936 .89 2.373 .996 1.18 4.94 2.16 2.106 2.942 3.853 .980 .452 .980 -.89 .29 4.05 1.87 2.373 1.981 2.854 3.695 .996 1.000 .617 .987 -1.18 -.29 2.106 1.981 .980 1.000 3.76 -1.89 2.636 4.228 .613 .992 ASIAN -4.94 2.942 .452 AFROAMERICAN -4.05 2.854 .617 CAUCASIAN -3.76 2.636 .613 ASIAN AFROAMERICAN CAUCASIAN HISPANIC Based on observed means. The error term is Mean Square (Error) = 61.440. Sig. Multiple Comparisons Final Exam Points Tukey HSD 95% Confidence Interval (I) Ethnicity (J) Ethnicity AMERICAN INDIAN ASIAN -13.95 7.85 AFROAMERICAN -12.87 8.56 CAUCASIAN -12.14 8.41 HISPANIC AMERICAN INDIAN AFROAMERICAN CAUCASIAN HISPANIC AMERICAN INDIAN ASIAN CAUCASIAN HISPANIC AMERICAN INDIAN ASIAN AFROAMERICAN HISPANIC AMERICAN INDIAN -9.87 -7.85 13.65 13.95 -5.71 7.49 -4.67 -3.24 -8.56 7.04 13.12 12.87 -7.49 -5.22 -3.89 -8.41 5.71 5.80 11.99 12.14 -7.04 -5.80 4.67 5.22 -3.57 -13.65 11.09 9.87 ASIAN -13.12 3.24 AFROAMERICAN -11.99 3.89 CAUCASIAN -11.09 3.57 ASIAN AFROAMERICAN CAUCASIAN HISPANIC Lower Bound Upper Bound Based on observed means. The error term is Mean Square (Error) = 61.440. Profile (Interaction) Plot (d) Explain the full results of the statistical test you have run. Was a post hoc actually needed in this case? Why or why not? Does the Post Hoc confirm your test results, explain? What does the plot tell you about the interaction, explain? For Interaction effect between Ethnicity and Gender The test statistic, F = 1.576 Degrees of freedom = (4, 95) P-value = 0.187 Since P-value > = .05, do not reject the null hypothesis. For main effect of Ethnicity The test statistic, F = 1.192 Degrees of freedom = (4, 95) P-value = 0.319 Since P-value > = .05, do not reject the null hypothesis. For main effect of Gender The test statistic, F = 6.026 Degrees of freedom = (1, 95) P-value = 0.016 Since P-value < = .05, reject the null hypothesis. Since the null hypothesis for the main effect of Ethnicity is not rejected, there is no need to perform the post hoc tests, to identify which pairs of Ethnicity differ significantly in the average Final Exam Points. Though, the null hypothesis for the main effect of Gender is rejected, there is no need to perform the post hoc tests, to identify which pairs of Ethnicity differ significantly in the average Final Exam Points, because there are only 2 levels of comparison for the factor Gender. The interaction plot also indicates the same conclusion as specified above, because all the other ethnicities showing same pattern for males and females, i.e. larger average final exam points for females and smaller average final exam points for males, except one ethnicity \"Caucasian\". Since at least one pattern differs, interaction is not significant. (e) Write a full conclusion for all results on this test in a way that can be understood by a nonstatistical person. This answer will be at least 100 words or more. The results of two-way ANOVA indicated that, there is no significant interaction between the factors Ethnicity and Gender, F (4, 95) = 1.576, p = .187 > .05, = .062. Since the interaction is not significant, it indicates that Ethnicity and Gender has no combined effect on the Final Exam Points. The results of two-way ANOVA to test for main effect due to the factor Ethnicity indicated that it has no significant effect on the Final Exam Points, F (4, 95) = 1.192, p = .319 > 0.05, = .048. The results of two-way ANOVA to test for main effect due to gender indicated that it has a significant effect on the Final Exam Points, F (1, 95) = 6.026, p = .016 < 0.05, = .060. 3. Prediction and Regression. If you recall from the Unit 3 Project, you looked at how to measure the relationship (correlation) between any two variables. You also learned that if two variables are strongly correlated (related) with each other, that one variable can be used to estimate or predict the other. The equation used to make this prediction is called a regression equation. Use the following SPSS outputs to answer the questions. The two variables in this case are Previous GPA and Final Course Percent. (a) What are the two variables that this question is investigating? Notice that the SPSS output above tells you that the r-value (called \"R\") is .440. Is this r-value strong enough to allow you to perform prediction between these two variables? Explain. The dependent (y) variable in this case is Final Course Percent and the independent (x) variable is Previous GPA. The r-value between Previous GPA and Final Course Percent lies in between, 0.3 < r = 0.440 < 0.7, the relationship between the two variables is considered as medium. The results indicate sufficient evidence to support the claim that the relationship between the two variables is strong enough to perform prediction, r = 0.440, p = 0.000 < .001. (b) Using the \"Coefficients\" SPSS output above, create the prediction equation. Remember that your independent or \"x\" variable is Previous GPA and your dependent or \"y\" variable is Final Course Percent. Write the prediction equation here. The fitted regression equation is, ^y =60.926+ 6.987 x . (c) Using the prediction equation that you created in part (b), predict the Final Course Percent for a student with a Previous GPA value of 2.79. Show all work. The predicted Final Course Percent for a student with a Previous GPA value of 2.79 is, ^y =60.926+ 6.987 2.79=80.42 4. From the Stat_Grades.sav dataset, use Quiz 2 and Quiz 5 to answer these questions. The question you will be considering here as you answer the questions below is \"Is the score on Quiz 2 highly correlated to the score on Quiz 5 and can one be used to estimate or predict the other?\" Correlations Quiz 5 Points Quiz 2 Points Pearson Correlation Quiz 5 Points 1.000 .700 Quiz 2 Points Quiz 5 Points Quiz 2 Points Quiz 5 Points .700 . .000 105 1.000 .000 . 105 Quiz 2 Points 105 105 Sig. (1-tailed) N (a) What is the correlation or relationship (r-value) between Quiz 2 and Quiz 5? Is it weak, medium, or strong? Is it strong enough to use for prediction? The correlation or relationship (r-value) between Quiz 2 and Quiz 5 is 0.7. Since it is at least 0.7, the relationship between the two variables is considered as strong. The results indicate sufficient evidence to support the claim that the relationship between the two variables is strong enough to use for prediction, r (103) = 0.7, p = 0.000 < .001. (b) Use SPSS and run a regression analysis on Quiz 2 and Quiz 5. Place the SPSS \"Coefficients\" output (only) here. Coefficientsa Unstandardized Coefficients Model 1 B (Constant) Quiz 2 Points Standardized Coefficients Std. Error 1.786 .623 .762 .076 Beta t .700 Sig. 2.867 .005 9.961 .000 a. Dependent Variable: Quiz 5 Points (c) Use the SPSS output to create the regression (prediction) equation. Remember, you are trying to predict how a student will perform on Quiz 5 based on how they do on Quiz 2. What is your dependent (y) variable? What is your independent (x) variable? Write the prediction equation here. The dependent (y) variable in this case is Quiz 5 Points and the independent (x) variable is Quiz 2 Points. The fitted regression equation is, ^y =1.786+ 0.762 x . (d) Use your prediction equation to predict how a student would perform on Quiz 5 if they got a 6.5 on Quiz 2. Show all work. The predicted score on Quiz 5 if a student got a 6.5 on Quiz 2 is, ^y =1.786+ 0.762 6.5=6.739