Statistical Analysis of Fears of Contracting COVID-19 in Singapore

Joshua wants to know whether people’s fears of contracting COVID-19 changed over Singapore’s circuit breaker period, which lasted from 7 th April to 1 st June 2020. He recruited 10 people at the start of the circuit breaker period and asked them to report how concerned they were about contracting COVID-19 (from 1 = not at all concerned to 7 = extremely concerned) on 20 th April, 11 th May, and 1 st June 2020. The results of his study are presented in the table below:

(a) Identify the design Joshua used in this study. What feature(s) lead you to conclude that that’s the design he used? Why do you think Joshua chose to use this design to answer his research question? What might be a potential problem with such a design?

(b) What parametric statistical test would you recommend Joshua use to analyse these data? Provide a justification for choosing this test. 

(c) Write the statistical model in mathematical form, and name each of the terms in the model. 

(d) State any two assumptions of the statistical test you identified in (1b). Test those assumptions (using SPSS or another suitable package such as R, Jamovi, JASP, MAtlab or other). Interpret the output and say whether the assumptions have been met. 

(e) Assuming all assumptions are met and there are no concerns about small sample size, conduct the statistical test you identified in (1b) using a statistical package. Can Jason conclude that people’s fears of contracting COVID-19 changed over Singapore’s circuit breaker period? Why or why not? Use an alpha level of .05. 

(f) Given the results of the statistical test, would you recommend additional analyses? If so, state the analyses and why you recommend conducting them. Then, conduct and report the results of those analyses. If not, state why it is not necessary to conduct additional analyses. You do not need to conduct any analyses if you don’t recommend additional ones. 

Joshua thinks that the effect of time on people’s fears of contracting COVID-19 might depend on whether they are essential workers. So, he re-contacted the 10 participants and (after profuse apologies) asked them to identify themselves as essential workers or non-essential workers. The original table has been updated to reflect whether the participant identified as essential worker.

(a) What parametric statistical test would you recommend Joshua use to analyse these data? Provide a justification for choosing this test. 

(b) Write the statistical model in mathematical form, and name each of the terms in the model. 

(c) State all the null and alternate hypotheses that you are testing in mathematical symbols and words.

(d) Conduct the statistical test you identified in (2a) using a statistical package. Report the findings in APA format. Use an alpha level of .05.

(e) Given the results of the analysis, would you recommend any additional analyses? If so, state the analyses and why you recommend conducting them. If not, state why it is not necessary to conduct additional analyses. Whether you recommend additional analyses, you do not need to conduct the analyses. No additional marks will be awarded for doing so.