Normally distributed Health Related Quality of Life Measures

Background: Non-normal distributions of Health Related Quality of Life (HRQoL) measures violate basic assumption of parametric statistical analysis. Testing normality of the data is a pre-requisite for selection of statistical tests and techniques. Different methods of testing normality give contrasting results. Objective: Avoiding the problems of discrepancies of tests of normality, the paper describes methods of transforming ordinal item scores of HRQoL tools to equidistant scores facilitating meaningful addition and further linear transform to proposed scores which can be added to get dimension scores and test scores, each following normal distribution, parameters of which can be estimated from the data. Results: Distribution of HRQoL scores as convolution of normally distributed item scores facilitates meaningful arithmetic aggregation and provides platform to perform parametric analysis with desired properties like plotting of progress/decline of HRQoL across time, statistical test of hypothesis, identification of critical indicators, finding equivalent scores of two or more HRQoL tools, etc. Conclusions: The proposed methods of HRQoL scores with normality and wide application areas with better measures of reliability, validity in terms of largest eigenvalue is recommended