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  • Composite Score: Quartile Ranking to Z-Score

    Greetings Statalist Community,

    I am working on a study and I plan to use an index (ALPHA - efficiency index) among other factors. Unlike my other variables, ALPHA is ranked for each organization individually, but there is a quartile ranking as well:

    These quartiles indicate the department’s performance relative to other departments in the organization without requiring direct comparison of individual department ranks. Each organization's ALPHA rankings are divided into four equal-sized groups (quartiles), ranging from the least efficient to the most efficient departments. A department ranked first is in the most efficient quartile.

    Since the quartile ranking follows the same pattern for all organizations in the study, I plan to include it in my final scoring - acknowledging in the research shortcoming that although not precise but the only possible way for me to include this index in my study.

    I have two questions:
    1. What is the methodological flaw for this approach?
    2. How it is possible for me to include this index as described into my final scoring? My other indices in the final calculation converted into z-scores. What is a correct way to convert a quartile to a z-score?
    I appreciate your advice please.

    Thanks,
    Eliot
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