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Understanding Normality of Distribution, Linearity, and Missing Data

Section A:
1) When we talked on the phone, you mentioned how it is important to check something called ‘normality of distribution’? You specifically mentioned the possibility of the mental health variables being ‘left skewed’ in this sample. Can you explain what is meant by these two terms (in italics), using one of our study variables as an example? [200 words]

2) You also mentioned ‘linearity’ and said this also important to check in relation to some of our planned statistical analyses. Can you explain what this is, which statistical analyses it is relevant to, and why this is important to check? [200 words]
Section B: Missing data [total word count = 400 words]
After visiting the prison you were asked to email your proposal in writing (above), to the governors, and they have responded by email and asked you to explain something in relation to missing data. Read the email below from the governors and write a reply that answers their questions. Use plain English and layman’s terms again where possible as the aim is again to demonstrate your understanding and ability to clearly communicate this understanding. You should reference at least two empirical studies (i.e., evidence) to support your answer.

Dear Chris,

Thank you for your study proposal, which was very useful. We shared the proposal with our prison staff, and we would like you to explain and elaborate on your proposed 8 methods for handling data with missing questionnaire responses. Our specific questions are below:

1) We have googled ‘listwise’ deletion to better understand what this entails, and we have concerns that this will lead to a significant loss of participant data from the study. We are particularly concerned that we could lose some prisoners from the data file who may have inadvertently missed the odd question out (due to poor attention span perhaps), but who we know have significant mental health difficulties and might therefore provide us with really useful data. Yet, we can also see from your proposal that listwise deletion might not actually be used. Please can you explain the conditions that would lead you to select listwise deletion, and reassure us that if used, the technique will not adversely impact our study.

2) The second alternative method of handling missing data you propose to use is “Multiple Imputation”. We also googled this and whist we feel this technique could be valuable (because unlike listwise deletion we do not lose any participants from the data file), we found the descriptions online to be quite confusing to say the least. Can you therefore help us better understand by outlining what Multiple Imputation is, and why you are recommending this specific technique over and above all other missing data estimation methods.

Quite crucially, can you explain all this in layman’s terms please, so that we can understand?
Kind regards,
Charlie and Jo
Charlie Smith, Prison Governor, HMP Duckvill
Jo Warburton, Prison Governor, HMP Goosevill
Section C: Interpreting SPSS output [total word count = 400 words].
Imagine that you now have approval from both governors to run your study, and that you have collected and entered all data into SPSS. The first thing you must do is to screen your data, and you will find some of the SPSS output below in Appendix 1. Specifically, you will find the results of the resilience variable examined separately for males and females. Answer the questions below and where required perform the relevant additional statistical tests. Tip: the word count is less useful here as a guide to mark allocation. Overall Section C carries the most marks because some questions have marks awarded separately for each correct statistical value/p value etc, and then interpretation.

Questions 1-4 should be answered within 200 words; question 5 is an additional 200 words.

1. What does the stem-and-leaf plot tell you about the distribution of resilience scores in male prisoners?

2. Describe the normal QQ plot for resilience in females and what it suggests

3. Describe the ‘detrended’ normal QQ plot for resilience in males and what it suggests. Next, does the result of the Kolmogorov-Smirnov test support/not support this? [report the KS test values]

4. Looking at the boxplot for females, what impact are these outliers having on the distribution?

5. Using the SPSS data file on Blackboard, conduct the same normality tests (i.e., KS tests and all plots etc) for the whole group i.e., males and females combined (just as in the workshop), on all variables: emotional resilience, anxiety, depression and wellbeing. Note that you do not need to deal with missing data first; the only tests you need to run are the ones shown in Appendix I but for the whole sample. Include the output as an appendix section in your report. Next, looking at the output for the Resilience variable only report the correct skewness and kurtosis values AND z skewness and z kurtosis values (you have to calculate the Z values yourself – see lecture slides and workshop handout) and based on these values and the histogram describe the distribution/shape of the resilience variable. [200 words].
Section D: Critiquing data screening and/or transformation [total word count = 300 words]
Imagine that you have now completed all phases of your study and have written up the results for publication and submitted it to the Journal of Clinical Psychology for review. Given the journal word limit, some sections of your report you have written have had to be brief, and the “Data Screening Results” section (below) is one of them.