Rating scale analysis

In many research studies, respondents' beliefs and opinions about various concepts are often measured by means of five, six and seven point scales. The widely used five point scale is commonly known as a Likert scale (Likert, (1932) "A technique for the measurement of attitudes", Archives of Psychology, 22, No. 140). In such situations, it is desirable to have a test statistic that provides a measure of the amount of agreement or disagreement in the sample, that is, whether or not a particular item 'pole' is characteristic of the respondents. This is preferable to making arbitrary decisions about the extremeness or otherwise of the sample responses. A suitable test for this purpose was designed by Cooper (1976), "An exact probability test for use with Likert-type scales, Educational and Psychological Measurement, 36, pp. 647-655. (Cooper z), with modifications suggested by Whitney (1978), "An alternative test for use with Likert-type scales", Educational and Psychological Measurement, 38, pp. 15-19 (Whitney t). Cooper showed that for large samples, the Cooper z statistic has a sample distribution that is approximately normal. The alternative Whitney t statistic has a sample distribution that is approximately t with (n-1) degrees of freedom and is suitable for small samples. Between them, these two statistics, although rarely used, provide a quick and straightforward way of analysing rating scales in an objective way. This presentation will describe the Stata syntax used to calculate the Cooper z and Whitney t statistics and create the related bar graphs. An illustrative example will be used to demonstrate their use in a survey.