Abstract
OBJECTIVE: The purpose of this study were to establish a model of quantitative evaluation that uses the population mean as a baseline of variations and describe variations derived from different types and systems using new concepts. METHODS: The observed datasets, including measurement data and relative data, were transformed to 0-1.0 using the population mean. Datasets derived from different types (same category of dataset, different categories of datasets, and datasets with the same baseline) were transformed using different methods. The 'middle compared index' (MCI) was used to describe the change in magnitude as follows: [a/(a+b)+(1-b)/(2-a-b)-1](1.7), where 'a' represents the number after the magnitude change and 'b' represents the number before the magnitude change. Actual data were used to observe the MCI's ability to evaluate variations quantitatively. RESULTS: When the value before the magnitude change was equal to that after the magnitude change, the MCI was equal to 0; when the value before the magnitude change was equal to 0 and that after the magnitude change was equal to 1, the MCI was equal to 1. This implies the MCI is valid. When the value before the magnitude change was 0 and that after the magnitude change was 0.5, or when the value before the magnitude change was 0.5 and that after the magnitude change was 1.0, each MCI was approximately equal to 0.5. The values derived from the absolute, ratio, and MCI methods were different, indicating that the MCI is an independent index. CONCLUSION: The MCI perfectly performs as an evaluation model using the population mean as the baseline, and it may be more a reasonable index than the ratio or absolute methods. The MCI increases our understanding of quantitative variations in evaluation measures of association using new concepts.