PSYC 326 Design and Analysis Assignment Report 2

PSYC 326 INSTRUCTIONS:

This assignment is graded out of 30 marks and is worth 30% of the overall grade for the subject. It is to be submitted on FRI 26 SEP, before 11.59p.m.

Submit this document via Turnitin with your answers. For questions requiring hand calculations, you may type the answer using the Equation function in Word. Alternatively, you may write the answer on a piece of paper, take a picture of the answer and paste it below the question. Make sure your answer is legible. PLEASE DO NOT USE PENCIL OR LIGHT COLOURED PENS. Those tend to be very difficult to read. I cannot award you the marks if I cannot read the answers. Show all working to gain the full marks. Use 4 decimal places for intermediate working and round to the nearest 2 decimal places for final answers. Copy and paste the relevant output from any statistical package of your choice below the respective question. Marks will be deducted for including irrelevant output. Write all answers in the context of the questions. Unless otherwise stated, use an alpha of .05.

Do not try to submit anyone else’s version of the assignment. Plagiarism can be detected and has led to students being expelled from the University.

Finally, it is highly preferable that your answers (with working) are presented in a neat and orderly fashion. Marks may be deducted for messy work. 

Problem Scenario 1

(7 questions, 15 marks in total)

The Human Resources (HR) director of a company wanted to determine whether employees with young children (defined as having at least one child aged 10 or younger) preferred to work from home more days per week than employees without young children, while controlling for tenure. To investigate this, he surveyed employees from five departments (i.e., Human Resources, Finance & Accounting, IT, Sales & Marketing, and Customer Service), asking them how many days per week they would ideally like to work from home. Employees with children were also asked to report the age of their youngest child.

The data from the survey are collated in PSYC326_Report2_PS1.csv, available on Moodle. The variables are coded as follows:

• RESPONDENT – respondent identification number;
• DEPARTMENT – the respondent’s department (i.e., Human Resources, Finance & Accounting, IT, Sales & Marketing, or Customer Service);
• AGE – age of youngest child; -9 if employee had no children;
• TENURE – length of time respondent has worked for the company (in years)
• PREFERENCE – Preferred number of work-from-home (WFH) days per week
  Based on the scenario above, answer the following questions.

(a) In the context of this study, explain why the HR director might want to perform a linear mixed model for these data. Provide two reasons. Be as clear and specific as possible. (0.5 mark)

(b) The HR director wanted to know whether employees with young children prefer to have more WFH days per week than employees without young children, while controlling for tenure. Assuming he is not interested in any interactions between the variables, state the mathematical model, including definitions of all the parameters. For this question, use the GLM and not the ANOVA notation. (4.5 marks)

(c) Using a statistical package (e.g., SPSS, jamovi, R), conduct the analysis testing the statistical model you stated in (1b) using restricted likelihood method of estimation. Ensure that your data are correctly transformed such that you can determine from the output whether there is a difference in the preferred number of WFH days per week between two groups of people: employees with young children and those without. (Recall that “employees with young children” was defined in the problem scenario earlier as someone who has “at least one child aged 10 or younger”.) Report the results of the analysis in APA format. At minimum, you should discuss whether the parameters in the model are significant, including both fixed and random effects, and what the results mean. (3.25 marks)

Hint: To transform the data, you can use the IF function within your statistical software of choice. Alternatively, you can apply the IF function in Excel to transform the data first and then import the modified file into the statistical package.

(d) Copy-and-paste all the output you referred to for the APA report in (1c) below. Highlight the values you used for the APA report in the output (e.g., putting a box around the values, circling the values). Only include relevant output; marks will be deducted for including irrelevant output. (3 marks)

(e) What is the preferred number of WFH days per week for a person who worked at the company for 2 years and is a parent of at least one young child? Show all (0.75 mark)

(f) What is the intra-class correlation (ICC) value for the analysis conducted in (1c)? Explain what this value means in the context of the problem scenario. Finally, explain what would cause this ICC value to be high. (1.5 marks)

(g) The HR director wants to know whether he should control for the effect of tenure in his analysis. Using a statistical package (e.g., SPSS, jamovi, R), conduct the appropriate linear mixed model analysis to compare a model that includes and one that excludes tenure. Copy-and-paste the relevant tables in your answer. Decide which model is a better fit for the data and explain why. (1.5 marks)

Problem Scenario 2

(7 questions, 15 marks in total)

A team of medical researchers in the United States conducted a study to investigate whether the number of comorbidities a patient had, along with the presence of metastatic cancer, could predict the 6-month survival of critically ill patients. They were also interested in determining whether the predictions from their statistical model were more accurate than those made by physicians. This research is particularly important given the aging population and increasing concerns about the suffering experienced near the end of life. If the model proved more accurate than physicians’ estimates, it could help patients and their families make more informed decisions about end-of-life care.

The researchers collected medical data from 9,105 critically ill patients from five medical centers across the U.S. They then asked the patients’ physicians whether they expected the patient to survive after six months. Patients were followed until death or the end of six months, whichever came first.

The data relevant to this study are in the file PSYC326_Report2_PS2.csv, which is on Moodle. The variables in the dataset are coded as follows:

• PATIENT_ID– patient identification number;
• COMORBIDITIES– number of simultaneous diseases (or comorbidities) exhibited by the patient;
• CANCER – equal to 1 if the patient had non-metastatic cancer, 2 if they had metastatic cancer; 3 if they did not have cancer;
• PROGNOSIS_6M – equal to 1 if doctor predicted the patient would survive after 6 months; 0 otherwise;
• SURVIVED_6M – equal to 1 if the patient survived after 6 months; 0 otherwise
  Based on the scenario above, answer the following questions.

(a) What statistical test should the medical researchers use to investigate whether the number of comorbidities a patient had and the presence of metastatic cancer predicted their 6-month survival? Provide a justification for choosing this test in the context of this study. (0.5 mark)

(b) Using a statistical package (e.g., SPSS, jamovi, R), conduct the statistical test you identified above. Assuming the researchers are not interested in any interactions between the variables. Set the baseline category for CANCER to the second category (i.e., had metastatic cancer). You should also test for multi-collinearity. Report the results of your analyses in APA format. At minimum, you should discuss whether multi-collinearity is an issue, whether the model is a good fit to the data, whether the parameters in the model are significant, and what the results mean. (5.25 marks)

(c) Copy-and-paste all the output you referred to for the APA report in (2b) below. Highlight the values you used for the APA report in the output (e.g., putting a box around the values, circling the values). Only include relevant output; marks will be deducted for including irrelevant output. (1.5 marks)

(d) Based on your analysis, write the formula for the probability that a patient would survive after six months. You must include the actual values of the parameter estimates and define all terms in the formula. (2 marks)

(e) What is the probability of a patient with non-metastatic cancer and 3 comorbidities surviving after six months? Show all (1 mark)

(f) What is the model’s overall accuracy rate, the accuracy rate for survival and the accuracy rate for death? Show all working and/or copy-and-paste all relevant output to substantiate your answer. Then, interpret the values in the context of this problem scenario. Finally, explain whether the model is more “optimistic” or more “pessimistic” about patients’ six-month survival. (1.75 marks)

(g) If you had to choose, would you rely on the predictions made by the statistical model or those made by the physicians? Explain your answer fully. Show all working and/or copy-and-paste all relevant output to substantiate your answer. (3 marks)