## Location

Hilton Hawaiian Village, Honolulu, Hawaii

## Event Website

https://hicss.hawaii.edu/

## Start Date

3-1-2024 12:00 AM

## End Date

6-1-2024 12:00 AM

## Description

Bipolar Likert scales are commonly used in psychometrics. Improved psychometric profiling can help to reduce costs, optimize resource usage, increase patient welfare and reduce mental health risks. In health economics grant funding depends on quality-adjusted life years (QALY) index values associated with the effect size of a therapeutic intervention. Increasing the statistical power corresponds to increasing effect sizes and, thus, increased grant funding and incentives. Recently, the compositional structure (i.e., the Simplex) of bipolar scales data was revealed. While the isometric log-ratio (ilr) transformation converts compositional data towards the interval scale the central limit theorem of statistics (CLT) postulates that sample means of ilr transformed and means of untransformed item response data, both, are approximately normally distributed. The larger the convergence towards normality the more reliable are the results of procedures based on approximate normal distribution, e.g., correlation analyses and partial least squares path modeling. Via simulation we show that the null-hypothesis of normality is rejected less often when using means of ilr transformed item responses. That is, the ilr transformation causes a shift towards normality. As a result, the statistical power of procedures based on approximate normal distribution increases.

## Recommended Citation

Lehmann, Rene and Vogt, Bodo, "Shifting psychometric bipolar scales data towards the normal distribution" (2024). *Hawaii International Conference on System Sciences 2024 (HICSS-57)*. 5.

https://aisel.aisnet.org/hicss-57/hc/process/5

Shifting psychometric bipolar scales data towards the normal distribution

Hilton Hawaiian Village, Honolulu, Hawaii

Bipolar Likert scales are commonly used in psychometrics. Improved psychometric profiling can help to reduce costs, optimize resource usage, increase patient welfare and reduce mental health risks. In health economics grant funding depends on quality-adjusted life years (QALY) index values associated with the effect size of a therapeutic intervention. Increasing the statistical power corresponds to increasing effect sizes and, thus, increased grant funding and incentives. Recently, the compositional structure (i.e., the Simplex) of bipolar scales data was revealed. While the isometric log-ratio (ilr) transformation converts compositional data towards the interval scale the central limit theorem of statistics (CLT) postulates that sample means of ilr transformed and means of untransformed item response data, both, are approximately normally distributed. The larger the convergence towards normality the more reliable are the results of procedures based on approximate normal distribution, e.g., correlation analyses and partial least squares path modeling. Via simulation we show that the null-hypothesis of normality is rejected less often when using means of ilr transformed item responses. That is, the ilr transformation causes a shift towards normality. As a result, the statistical power of procedures based on approximate normal distribution increases.

https://aisel.aisnet.org/hicss-57/hc/process/5