Every day, researchers work with complex samples selected from finite populations of interest to make inferences about population parameters. However, in many situations these samples are assumed as SRS samples. Serious consequences have been reported in the complex survey data literature; when this assumption is considered.
I invite you to find out a little more about some relevant contributions to the development of the Psychometry under complex sampling designs, as highlighted in this e-book.
Keywords: Mokken scaling, Mokken scale analysis, complex data, Complex Mokken, design effect, clustering, sampling weights, stratification, clustered samples, variance estimation, point estimation, large-scale educational surveys, Jackknife resampling technique, Non Parametric Item Response Theory.