A straightforward method is developed to assess and determine the level of measurement of shortened summated rating scales. Like calibrating measurement, assessing measurement scale properties can only be done in the presence of a gold standard. In the case of summated rating scales, commonly known as Likert scales, measurement at ordinal level is assumed rather than inferred. Because the assumption that Likert scales are measured at ordinal level is uncontested in the literature, shortened summated rating scales can be assessed for nominal or ordinal measurement level by using the (complete) Likert scale as gold standard. Moreover, if we (unjustifiably) assume the Likert scale is measured at interval scale, the shortened scales can be tested for interval and ratio measurement as well. The method is applied in a well-known summated rating scale, the CESD scale for depression. It was found that subscales consisting of less than 60% of the items of the original scale have lost all metrological properties of that scale, including ordinality as measured by Kendall’s tau. This result justifies concern about the robustness of measurement scale properties of shortened SRS’s.
Keywords: Summated rating scale; Likert scale; ordinal; measurement level; metrology; CESD; depression
The summated rating scale (SRS) is one of the most frequently used tools in the social sciences. Its conception is attributed to Rensis Likert (1932), which is why it is often called “Likert scale”, a scale consisting of the sum of ordinal scaled (“Likert-type”) items. Among the documented reasons for use of the Likert scale are that a well-developed SRS can have good reliability and validity (i.e. psychometric properties), the SRS is relatively cheap and easy to develop, and an SRS is usually quick and easy for respondents to complete and typically does not induce complaints from them (Spector, 1996). However, while Likert scales are perhaps easy to develop and present low burdens for respondents, the analysis of such scales is problematic. Controversy regards their level of measurement. Following Stevens (1951), measurements can have different measurement scales. If we denote a given attribute by X, a measurement of the attribute by M, and consider two objects i and j, the following definitions apply:
- Nominal scale: If xi = xj then mi = mj and when xi ≠ xj then mi ≠ mj
- Ordinal scale: If xi < xj then mi < mj
- Interval scale: xi – xj = β(mi – mj) for some β>0
- Ratio scale: xi ⁄ xj = mi ⁄ mj
Nominal and ordinal scales are also known as categorical or “qualitative” measurement scales, while interval and ratio scales are known as metric or “quantitative” measurement scales. Different measurement scales require different means of data analysis. For instance, association of variables measured at metric level is usually done by Pearson correlations (parametric analysis); analysis of associations of categorical variables is appropriately done by Pearson chi-square for independence (non-parametric analysis). With respect to the analysis of Likert scales, the divide is between those claiming that parametric analysis of such data is “illegal” because the Likert scale is