[Determining the most unfavourable variance to calculate the Measurement Scale Imprecision Factor, and extension to...

The precision of estimates must be adequately reported in survey research, where ordinal and interval measurement scales are commonly used. Regarding mean estimate, absolute and relative errors exist as a function of the measurement scales. This manuscript discusses some assumptions underlying the development of the Measurement Scale Imprecision Factor--MSIF--, a tool to assess the degree of imprecision of estimates, regardless of the scale rank considered. Specifically, we propose a new method for determining the most unfavourable variance, which is consistent with the normal distribution assumption, unlike the original assumption based on the bimodal distribution. This method reduces the value of the most unfavourable variance, which is easily computed using the cumulative normal standard distribution function. In addition, we show the relationship between MSIF and other types of probabilistic sampling methods, such as stratified and cluster sampling.