ARMS: Statistics Exam type questions

Part A (45 marks)

This question was inspired by L. J. Frewer et als’ (1996) paper entitled “What Determines Trust in Information About Food-Related Risks? Underlying Psychological Constructs”

The purpose of the research was to ascertain the level of trust individuals had in the safety and hazard information provided to them by providers of food items.

Participants were asked to what extent they agreed with the following statements.  .

The responses were coded on the following scale

When the question asked about ‘the extent’ in relation to the question then 0 indicated a very low extent/ not at all up to 5 which indicated very strongly/large extent

The data can be found in the FoodHazards.csv.

1. Undertake a PCA analysis and report your findings following the APA guidelines              .                                                                                            (25 Marks)

Results of the analysis are in the JASP file. To report a PCA you can have a look at the answers to the supplementary exercises I gave you for lecture 4 in term 2. If I were to write it down, I’d do something like (but please, try to write it up with your own words, do not copy-paste this):

A principal components analysis (PCA) was conducted on the 13 items with orthogonal rotation (varimax).  

The case to variable ratio is equal to 390:13 = 30:1, more than the ideal value of 10:1 so we have sufficient cases to proceed with analysis. Reviewing the zero-order correlation matrix, there are significant patterns of correlations in the data set. The component loading table revealed that all items have uniqueness values below 0.80 except for ‘freedom’ (1.00), therefore this item was removed from the analysis.

There are 3 factors with an eigenvalue superior to the criteria of 1, taken together they explain 63.8% of the variance in the dataset. Factor 1 has an eigenvalue of 3.79 and after rotation explains 31.5% of the variance in the data. Factor 2 has an eigenvalue of 3.49 and after rotation explains 29.1% of the variance in the data. Factor 3 has an eigenvalue of 1.02 and after rotation explains 0.78% of the variance in the data. Factor 1 and Factor 2 have both 6 items solutions, whilst factor 3 has only one item solution (Freedom). The scree plot also suggests an elbow at factor 2, with the first 2 factors lying above the line and one factor on the line (Factor 3). This would suggest that a 2 factor solution may be more appropriate. Results of the parallel Analysis confirmed a 2 factors solution.

Looking at the rotated component matrix (see Table 1), all items have loading values above .5 therefore all items were retained in the analysis. A total of 6 items loaded onto the first factor. These were items relating to people’s belief that people providing food related information were untrustworthy or unaccountable, and was labelled ‘distrust in the food people’. The most important item was accountability with a factor loading of -.91 and the less important item was sensationalization with a loading of .67. For the second component, 6 items loaded onto this factor.  These related to people’s beliefs regarding the accuracy of food related information, this factor was labelled ‘bias of the food people’. The most important item was accuracy with a factor loading of -.86 and the less important item was distortion with a loading of .64.

Table 1.

Summary of the Principal Component Analysis results for the food related questionnaire (N = 390).

1. What would you name each of the factors extracted in this analysis?

.                                                                                                   (5 Marks)

No right of wrong answer here – I’ve decided to name them ‘distrust’ and ‘bias but any other name would do as long as they are meaningful.

Before submitting your work to a scientific journal for publication, you want to make sure that the scales you used have good enough internal consistency.

1. Using the same data file, conduct the appropriate analysis                                                                                                                                                                (10 Marks)

Again the results are in the file – here you should have performed a cronbach alpha. To write up the results you can look at the answer to the practice exercises of lecture 15.. A way to write it up would be:

For Factor 1, the Cronbach’s alpha is .879, indicating a good level of internal consistency/reliability. For Factor 2, the Cronbach’s alpha is .854, indicating a good level of reliability as well.

1. . What would you conclude about the different factors identified?                                                                                                           (5 Marks)

Here the conclusion is that not only the PCA analysis gives you accurate number of factors, but it is confirmed by the PCA. An you can be confident your items measure the same thing as their internal consistency is very good.

1. Part B (15 marks)

1. Briefly describe the difference between a systematic review and a meta-analysis                                                                                                                                 (5 marks)

Here your answers should be in the lines of

Systematic review = identify, select, appraise, and synthesize results from similar but separate studies

Meta-analysis = statistical analysis of a large collection of results from individual studies is an optional component of a systematic review

Again, these are the definition I gave in the lecture (look at lecture 17) but you should write something along these lines with your own words.

1. Briefly described what is p-hacking and why it is considered as bad practice in science.                                         .                                                                 (5 marks)

p-hacking is a bad practice, it is everything that relates to manipulation of the data analysis so that you’ll get a significant results (or ns, depending on what you predict). There is a lot of things you can say here – have a look back at lecture 19 to revise this.

1. Briefly describe what a type 2 error is and what we can do to avoid it.                                                                                                                                                   (5 marks)

Another easy way to grab 5 marks here – have look back at lecture 16, where I explained it in details, as well as power.

ARMS: Statistics Exam type questions

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