Sensitivity Analysis on the Choice of the Metric on Cronbach’s \(\alpha \) Coefficient for Interval-Valued Data in Questionnaires

Interval-valuedGarcía-García, J.Gil, M.Á.Lubiano, M.A. scales have become an efficient alternative to conventional single-point scales for capturing richer information in questionnaires measuring imprecise human traits. Thus, new statistical techniques are being developed to analyze this type of data. In this respect, when items in a construct allow respondents to make use of interval-valued scales, the internal consistency reliability can be quantified by means of an extension of the well-known Cronbach \(\alpha \) coefficient based on the family of \(\theta \) -metrics between intervals. Since theoretical results are shown not to be informative enough, the impact of metric choice is discussed through a Monte Carlo study concerning different scenarios of a simulation procedure mimicking human rating.