Revisiting the Evidence for a Cardinal Treatment of Ordinal Variables

Abstract

Well‐being (i.e., satisfaction, happiness) is a latent variable, impossible to observe directly. Hence, questionnaires ask people to grade their well‐being in different life domains. The most common practice - comparing well‐being by means of descriptive analysis or linear regressions - ignores that the underlying collected well‐being information is ordinal. If the well‐being function is ordinal, then monotonic transformations are allowed. We demonstrate that treating ordinal data by methods intended to be used for cardinal data may give an incorrect impression of a robust result. Particularly, we derive the conditions under which the use of cardinal method to an ordinal variable gives an illusionary sense of robustness, while in fact one can reverse the conclusion reached by using an alternative cardinal assumption. The paper provides empirical applications.