University of Warwick, Department of Sociology, 2014/15 SO 201: SSAASS (Surveys and Statistics) (Richard Lampard) Index Construction (Week 13)

Scale/Index Construction Researchers sometimes want to measure some latent characteristic of their respondents, e.g. whether they have a ‘traditional’ or a ‘modern’ viewpoint on couple relationships. This is often done by asking a number of questions which each tap that characteristic and, when aggregated, collectively do so in more reliable way.

Some issues... How does one know that a measure constructed by aggregating various items to give a scale is measuring the ‘right’ quantity, i.e. is a valid measure? How does one ensure that what a measure is measuring is unidimensional, i.e. that it is not a composite of measures of two or more underlying concepts? How does one assess which items need to be included to maximise the reliability of the measure? And how does one assess the overall reliability of the scale?

Some answers... For a discussion of assessing various forms of validity, see Oppenheim (1992). Unidimensionality can be assessed using a technique called factor analysis, see DeVellis (2003). Reliability can be assessed using a measure called Cronbach’s alpha (see De Vaus, 2001; DeVellis, 2003).

Factor analysis Factor analysis generates a set of underlying factors which successively maximise the amount of (remaining) variation in the items that they can explain. If a scale is working properly unidimensionally, then the first factor will explain a high proportion of the variation, and the subsequent factors similar, small amounts.

Cronbach’s alpha According to DeVellis (2003: 95), “Alpha is an indication of the proportion of variance in the scale scores that is attributable to the true score”. Items are chosen for inclusion so as to maximise that proportion, and if they have relatively high correlations with the rest of the items within the scale (viewed collectively). De Vaus (2001) suggests that a value of at least 0.7 is preferable.

Some additional issues... Should all the items in the scale be treated as of equal importance? Or should their values be added in such a way as to increase/ decrease the relative importance of some items? Are the gaps between the values that a variable can take uniform in meaning?

Some examples... Masculinity/Femininity: The Bem Sex-Role Inventory Psycho-social well-being: The General Health Questionnaire (GHQ) The Warwick-Edinburgh Mental Well-being Scale (WEMWBS): see http://www.hqlo.com/content/5/1/63

Another example... BSA left-right scale (used since 1986) See Park et al. (2012) British Social Attitudes 28. London: Sage/NatCen. http://ir2.flife.de/data/natcen-social-research/igb_html/pdf/1000001_e.pdf Can be found in the BSA 2006 dataset...