Analysing data from a questionnaire: Reliability and PCA

Topics Coding item scores Reliability of a straightforward scale Tests measuring more than one construct Presenting the results

Recoding negative items Masculinity questionnaire: I agree that blue is a lovely colour I agree that pink is a delicious colour Recode as (max + min) – score e.g. scale is 1—7 , recode as 8 – score Or scale is 0 – 7, recode as 7 – score

Reliability of a scale measuring one construct Split-half Cronbach's alpha

Warwick sweetness scale For example Warwick sweetness scale

Scale measuring more than one construct PCA Correlations among items Extraction / Rotation PCA / varimax Other extraction (FA) if components are correlated (e.g. anxiety & depression)

In action...

Note... Try different solutions, forcing the number of dimensions Eigenvalues v. scree plot Loadings; cut-off “Simple structure” is preferred

Component scores Give each person an”overall” score for Size or Smart: but how Chess + IQ + Alevel (?) Give more weight to the ones with biggest loadings

Check that it is1-D Calculate overall scores? PCA and scales with 1-d Check that it is1-D Calculate overall scores?

Do I need to check? -You must! Standardised tests Do I need to check? -You must!

Presentation of reliability analysis Method v. Results? Give value of coefficient p-value is generally irrelevant PCA – report Eigenvalues or % variance explained for each component Explain how you selected the solution you preferred Provide a table of loadings (use a cut-off to simplify)

Table of loadings C1 C2 Height .93 - Weight .94 - Shoe .94 - Chess - .89 IQ -.49 .85 Maths - .96

Further reading Dunbar (1998) Data analysis for psychology. London: Arnold. Ch6 pp85-88; Ch11 Klein, P. (1994) An easy guide to factor analysis. New York, Routledge. Vowles et al. (2008) The chronic pain acceptance questionnaire.... Pain, 140, 284-291