Background Scales for evaluating insomnia differ in number of items, response format, and result in different scores distributions and score ranges and may not facilitate meaningful comparisons. Objectives Transform ordinal item-scores of three scales of insomnia to continuous, equidistant, monotonic, normally distributed scores, avoiding limitations of summative scoring of Likert scales. Methods Equidistant item-scores by weighted sum using data-driven weights to different levels of different items, considering cell frequencies of Item-Levels matrix, followed by normalization and conversion to [1, 10]. Equivalent test-scores (as sum of transformed item- scores) for a pair of scales were found by Normal Probability curves. Empirical illustration given. Results Transformed test-scores are continuous, monotonic and followed Normal distribution with no outliers and tied scores. Such test-scores facilitate ranking, better classification and meaningful comparison of scales of different lengths and formats and finding equivalent score combinations of two scales. For a given value of transformed test-score of a scale, easy alternate method avoiding integration proposed to find equivalent scores of another scales. Equivalent scores of scales help to relate various cut-off scores of different scales and uniformity in interpretations. Integration of various scales of insomnia is achieved by finding one-to-one correspondence among the equivalent score of various scales with correlation over 0.99 Conclusion Resultant test-scores facilitated undertaking analysis in parametric set up. Considering the theoretical advantages including meaningfulness of operations, better comparison, use of such method of transforming scores of Likert items/test is recommended test and items, Future studies were suggested.
Calculation of Univariate and Bivariate Normal Probability Functions