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This assignment makes use of a scale introduced to study idealisation (agree with positive statements concerning one’s interpretation of world events; 8 questions) and self-perception (higher scores reflecting lower quality of self-value; 16 questions). Questions will be asked concerning the qualitative and quantitative information about the scale, which was administered upon n = 179 University of Manitoba undergraduates in 1993 in an Introduction to Psychology course. The assignment will not actually require that you computationally perform any results, merely to interpret the results provided for you. The scales were recorded using 1 – 9-point ordinal items, and all items have been positively recoded to reflect greater amounts of the respective measured contents. It is hypothesised that each scale is unidimensional, and that there exists a negative correlation between the two latent factors. This would reflect the hypothesis that believing the world is a ideal and fair place is similar to one’s self-
perception as a capable human being. This is supported by the correlation between the two sum scores which was found to be r = .55, 95% CI = ( .44, .64).

1. Describe the assumptions of the Pearson Correlation, and explain how the Pearson correlation applies to Psychometric investigations.

2. In Table2and Table3, correlation matrices from a replication of the two scales are provided. Visually inspecting the items, does it appear that the scale structure is compliant with the theorised latent structures? Why or why not?

3. Tables3,4,5, and6provide the respective item analyses of the two Scales, as well as Cronbach’s alpha, and the response patterns to the item levels. Given the correlations provided in Table8, does it appear that the total scores are measuring either behaviour as desired? Why or why not?

4. Provided in Figure1is a histogram of the total, or sum score, for each respondent on the two Scales. Considering the purpose of the scale, explain whether these distributions seem to conform to what we are looking to measure?

5. Using Figure1, along with the other observed score characteristics, what criticisms concerning the psychometric properties of the scales would be appropriate as currently constructed?

6. A pair of Confirmatory Factor Analysis with IRT were conducted, and the fit statistics from said model were provided as well in Table7. Please interpret this respective goodness of fits, and how it reflects upon the quality of the scale. What would be your next suggested procedure for an applied model which performed with these results?

7. The first model fitted was a Rasch model, while the second was a 2-parameter model. From both theoretical and empirical perspectives, why would one type of measurement be preferred over the other? Be sure to consider the results found in Table9in constructing this recommendation.

8. Define the IRT difficulty parameter. If a sample question has a high, positive value (say 3.5), roughly how frequently would one expect a sample select this response?

9. Recall the relationship between discrimination and test information. Would it be more ideal for a scale which measures suicidal depression to possess 10 questions which are highly discriminating, or 10 questions which are very difficult for most people to endorse?

10. How does Cronbach’s α relate to test reliability from a latent variable perspective? What circumstances would make it an invalid measure of the either scale’s reliability?

11. Figure2contains the information estimates for both latent traits. Based off of these estimates, can either scale be considered a reliable measure?

12. Our next step is to improve the measurement characteristics by including 6 more items, to make a total of 30 items. What would the respective difficulty and discrimination parameters be for your selected items, and how many would you include for either scale?

13. Report the quantitatively selected three items for each scale which are most important to the overall measurement scale characteristics. Why are these items ‘the best?’

14. In Table9, are the loading patterns amongst the set of items observed in the two scales, for both the 1PL and 2PL IRT models. The observed correlation between the two latent traits are ρ = .403 forb either model. Given these empirical results, which model is better suited for each scale as an applied measure of the latent trait. In other words, which parametrisation would you recommend a Developmental Psychologist utilise for their research?

15. Does the hypothesised latent structure support the research question? Explain why or why not.

 

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  • Posted on : December 23rd, 2018

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