Statisticians may be most useful when there are no statistics. Yes, you read that correctly. One such example is a case of alleged age discrimination. Statistics on rates of promotion by age and rank in an organization can typically be calculated from data routinely collected for personnel administration. By contrast, data on merit used in promotions are often absent, or measured with substantial error.
As long as early promotion is credited with a positive correlation to ability, a simple model of promotion shows that - given no age discrimination - rates of promotion in every rank must be greater for younger officers. Further, raw rates of promotion by age do not estimate any parameter reasonably describing age discrimination.
Statisticians at Analysis & Inference used several statistical methodologies to highlight this point. Application of the work was made to legal cases involving alleged age discrimination.
