Central limit theorem does not apply unless each experiment is independent. This is not true of the concepts which psychometrician operationally define includin

Central limit theorem does not apply unless each experiment is independent. This is not true of the concepts which psychometrician operationally define including personality factors and intelligence. As an example: Human height is not normally distributed. It is multi-modal based on geographical location, socioeconomic status and sex. There are genetic and environmental factors that makes it so that each childbirth is not an independent event marking a new height. The same holds for personality traits (if they exists) and intelligence (if it exists as described by IQ tests). The field of psychometrics has a problem with assigning normal distribution to everything even though there is reason to belief things are not normally distributed.