Objective: This study was aimed to propose an alternate method of scoring the intensity of disability in a patient, which will facilitate ranking and classifying a group of patients in mutually exclusive classes along with the quantification of progress made by a patient or the effect of interventions and also tracking the path of improvement of a patient and estimating the survival curve for drawing useful conclusions. Method: A nonparametric measure of disability intensity in terms of Cos θi for the ith patient is proposed to avoid limitations of the usual scoring of modified Rankin scale and satisfies many desired properties. Two measures of interrater agreement in terms of standard error of measurement and coefficient of variation are also proposed and their relationships with Cos θi are detailed. Illustration with hypothetical data involving 30 patients and 10 raters was undertaken. Results: Distribution of Cos θ was close to normal. Principal component analysis of Cos θ resulted in one factor explaining 64% of variance. Inconsistent raters were identified. Coefficient of variation appears to perform better than the standard error of measurement. Split-half reliability of raters in terms of angular association was higher. Similarly, split-half reliability of disability intensity (Cos θ) was higher. Average disability intensity [Formula: see text] showed similar empirical results with rigorous method of most preferred direction of a finite number of angles. Conclusions: The proposed simple measures will help the researchers and practitioners to make meaningful analysis and draw meaningful conclusions. Future studies may be undertaken to rescale Likert data to scales having properties of interval-level measurement and study the proposed measures in detail.
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.
This article addresses limitations of Logistics Performance Index (LPI) and suggests remedies. Reliability of the instrument used in LPI may be better found by Angular Association method or Bhattacharyya’s measure, using only the frequencies or probabilities of item–response categories without involving assumptions of continuous nature or linearity or normality for the observed variables or the underlying variable being measured. The suggested methods also avoid test of uni-dimensionality, assumption of normality, bivariate normality. The problems of outlying observations and linear assumptions in principal component analysis for finding reliability theta are also avoided in each proposed method. Geometric mean approach provides a better alternative to compute LPI scores avoiding scaling and calculation of weights satisfies many desired properties and reduces level of substitutability between components, facilitates statistical test of equality of two geometric means and identifies critical areas for corrective measures. Such identifications are important from a policy point of view. The graph of LPI for a country over a long period of time reflects pattern of growth of LPI for the country. The method helps to rank and benchmark the countries, if the target vector is taken as LPI score of the best performing country. JEL Codes: C43, C54
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