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MATH1281 S2 2020: assignment 2 Page | 2 MATH1281/1282 Statistical Analysis 2 ASSIGNMENT 2 (Weighting: 45%) SUBMISSION: SUBMIT VIA ‘ASSIGNMENTS’ IN CANVAS. DUE DATE: BY MIDNIGHT, FRIDAY OCTOBER 30th, 2020. CAUTION: THIS ASSIGNMENT MUST BE YOUR OWN WORK. YOU ARE NOT ALLOWED TO CONSULT ANYONE ON ANY PART OF THE ASSIGNMENT. IF YOU NEED CLARIFICATION, EMAIL THE LECTURER. BY SUBMITTING THIS ASSIGNMENT ONLINE, YOU CONFIRM THAT YOU HAVE NOT CONSULTED ANYONE IN DOING THIS ASSIGNMENT AND THAT THIS ASSIGNMENT IS ENTIRELY YOUR OWN WORK. INSTRUCTIONS: 1. Before attempting this assignment, read all material covered in the lectures up to the 12th week. This includes all lecture slides, demo worksheets and solutions to demo worksheet questions, model answers to lab session questions, and any other relevant material on Canvas. 2. Attempt ALL questions. 3. An electronic WORD DOCUMENT copy of your assignment is to be submitted via ‘Assignments’ on Canvas. DO NOT SUBMIT AS A PDF DOCUMENT. 4. DO NOT USE THIS DOCUMENT TO WRITE YOUR ASSIGNMENT. OPEN YOUR OWN WORD DOCUMENT. YOU CAN THEN COPY AND PASTE THE QUESTIONS FROM THIS DOCUMENT INTO YOUR OWN DOCUMENT. Since ASSIGNMENT 2 is a take-home, open book Assessment, RMIT requires you to read and sign the DECLARATION below enclosing it as the FIRST PAGE OF ASSIGNMENT 2(COPY & PASTE THE DECLARATION BELOW TO FRONT PAGE OF YOUR ASSIGNMENT SUBMISSION) “The work I am submitting for this Assessment Task is entirely my own work. Nothing I submit is copied from another source -- either from another student or person, or from another resource. All written work is in my own words. I have not communicated with any other student during the period of this Assessment Task. I have not discussed the content of this Assessment with anyone else during the period of this Assessment Task.” NAME: STUDENT SNUMBER: SIGNATURE: MATH11281 SEMESTER 2, 2020 ASSIGNMENT 2 (weighted 45% of final mark) Attempt ALL Questions (Use your own words in responding to the questions. Copying and pasting from notes will be penalised). Section 1 (75 marks) 1. When performing a one-way ANOVA, the variability in the dependent variable is split into two categories: “variability between or explained variation” and “variability within or unexplained variation or error”. Elaborate on “explained” and “unexplained”. What do these two terms imply? No calculations required. (3 marks) 2. In a two-group situation where you have a treatment group and a placebo group, it is found that the treatment reduces blood sugar levels compared to placebo. Is a one-way ANOVA appropriate to assess for significant differences in blood sugar levels between the two groups? Explain your answer. (2 marks) 3. In the scenario described in (2) above, if we obtain a significant test result, is there a follow-up test that needs to be conducted? Explain your answer. (3 marks) 4. What are the underlying reasons for incorporating a second independent variable in a one-way ANOVA design so that it results in a two-way ANOVA design? In other words, why resort to a more complicated design. Illustrate your answer with your own example. Do not use examples from notes. No calculations required. (4 marks) 5. In a four-group experiment involving 4 different teaching methods in teaching basic calculus, the randomly assigned participants in each teaching method group are assessed for their Calculus knowledge at the end of the school term. Name the independent and dependent variables in this scenario. Name the statistical test you would use. If a statistically significant result is obtained, describe in detail what follow-up is necessary and why. (2 + 1 + 2 = 5 marks) 6. In the scenario described in (5) above, it is planned, in addition to assessing their Calculus knowledge, to assess the participants on their verbal skills, anxiety levels and self-confidence levels, at the end of the school term. How would you analyse the data in this new scenario? (1 + 3 = 4 marks) 7. As a High School Physical Education teacher, you have been given the responsibility by the Principal to evaluate the student experience of the physical education curriculum. One of the tools you would use is a student experience questionnaire. How would you go about designing this questionnaire? In your response explain how you would use factor analysis in developing the questionnaire. (2 + 3 = 5 marks) 8. Supposing the Questionnaire in (7) above contains 15 items or variables. The responses to the items are on a 5-point scale which ranges from ‘strongly disagree’ to ‘strongly agree’. Suggest three items that you would use in the Questionnaire. One of the items should be negatively phrased, while the other two must be positively phrased. When this questionnaire is administered to the students, some students do not provide responses to the three items. How are missing responses dealt with in SPSS factor analysis? (3 + 2 = 5 marks) 9. Prior to doing a factor analysis on the data from the Questionnaire in (8), what should be done about the negatively phrased item if all the other items on the questionnaire are positively phrased. Describe the process involved and why it is necessary. (1 + 3 = 4 marks) 10. Supposing that that the responses to each of the 15 items in (8) are standardised. Explain what is involved in the standardisation procedure. If you had to sum the variances of the responses to all the standardised items, what would you obtain? If you summed the mean responses to all the standardised responses, what would you obtain? (3 + 1 +1= 5 marks) 11. Using the same questionnaire as in (8) above, you obtain after a factor analysis, one of the factors having the same loading of 0.6 for each of the 15 items. What is the eigenvalue for this factor? Interpret or explain what this eigenvalue denotes. What percentage of the total variability in the responses to all the items is explained by this factor? (1+2+2=5 marks) 12. Using the same questionnaire as (8) above, you extract 5 factors through a factor analysis. For the first item of the questionnaire, the loadings of this item across the 5 factors are 0.4, 0.3, 0.7, 0.2 and 0.2. What is the communality for this item? Explain what information does the communality convey to you. (1+2 = 3 marks) 13. Hyperactive children are often treated with a stimulant such as Ritalin to improve their attention spans. In one test of this drug treatment, hyperactive children were given a boring task to work on. A psychologist recorded the amount of time in seconds each time the child worked on the task before becoming distracted. Each child was assessed before receiving the drug and thrice more 1, 2 and 3 hours after the drug was administered. The data are tabled below. CHILD BEFORE DRUG 1 HOUR AFTER DRUG 2 HOURS AFTER DRUG 3 HOURS AFTER DRUG 1 28 135 140 149 2 15 309 315 320 3 83 150 160 245 4 44 248 267 284 5 78 345 360 380 6 31 343 355 367 7 88 210 230 239 8 72 215 228 234 a. Can the data in the table be treated as repeated measures? Explain your answer. Indicate the type of design. (2 + 1 = 3 marks) b. Would there be a ‘carry-over’ effect? Explain. (1 + 2 = 3 marks) c. Name and explain an important assumption, other than normality, that needs to be tested using the data. (1 + 3 = 4 marks) d. If the assumption in (c) is violated, what are your options? (3 marks) e. Enter the data into SPSS, perform a suitable analysis using a significance level of 0.01 to produce contrasts involving repeated comparisons. Present an APA report of the analysis. (8 marks) f. Repeat (e) above and obtain Helmert contrasts. Explain what these contrasts involve. No APA report required and only present the SPSS output table of the contrast test results with your comments. (1 + 1 + 3 = 5 marks) g. Explain what is involved in DEVIATION contrasts. No need to do any analysis. (1 mark) Section 2 (45 marks) Question 1(15 marks) Suppose we are interested in comparing the effectiveness of three different teaching methods in a Research methods Psychology/Exercise Science course. In a research study, students in the course were randomly assigned to one of the three teaching method groups. Each group was taught the course by one of the three teaching methods for a whole semester. At the end of the semester, the were assessed on the content taught and obtained a course score. They were also assessed on their motivation via a rating scale questionnaire whereby their responses were converted into a motivation score for each of the students. The data are contained in the SPSS file motivate.sav which can be accessed via the Assignment 2 Report Folder in Canvas. Suggest and implement the MOST suitable analysis for the data. Think carefully why the motivation data was included in the research design and the part it would play in the analysis. Set up research questions you want to answer through the analysis. Present your findings in an APA Report. (15 marks) Question 2 (8 marks) Use the above SPSS Table output to answer the questions below. a. Name the statistical analysis that the above table is part of. (1 mark) b. Name the dependent variable used in the analysis. (1 mark) c. Name the two factors that are part of the analysis. (1 mark) d. Summarise in detail the statistical analysis findings provided by the table. (5 marks) Question 3 (22 marks) Every academic year, RMIT asks postgraduate students who graduate to evaluate their postgraduate experience via a Questionnaire. A copy of this Questionnaire is available in the Assignment 2 Folder in Canvas. The data set for the student evaluations via the Questionnaire for the academic year 2008 is also available in the same folder. You are asked to answer the following questions: a. Do an intuitive factor analysis via the wording of the Questionnaire items. Present in table form, giving each factor a suitable name. b. Check the Questionnaire items for negatively/positively phrased statements and accordingly, decide which items should be reverse-scaled. Implement the re-scaling on the data set via SPSS. Mention this in your report below. c. Perform a factor analysis on the data using Principal component extraction and Varimax rotation. In the process, make sure missing values are appropriately taken care of. d. Summarise your factors with suitable names in a table. e. Compare your Intuitive Factor analysis with SPSS factor analysis. f. Write a brief report that summarises assumption testing results and your responses to (d) and (e) above. END OF ASSIGNMENT ON-GOING POSTGRADUATE RESEARCH EXPERIENCE SURVEY 2007 ON-GOING POSTGRADUATE RESEARCH EXPERIENCE SURVEY 2008 ABOUT THIS SURVEY RMIT University is committed to improving the experience of its research degree