On some properties of medians, percentiles, baselines, and thresholds in empirical bibliometric analysis

Abstract: One of the most useful and correct methodological approaches in bibliometrics is ranking. In the context of highly skewed bibliometric distributions and severe distortions caused by outliers, it is often the preferable way of analysis. Ranking methodology strictly implies that "oranges should be compared with oranges, apples with apples". We should make a "like with like" comparison. Ranks in different fields show how a unit under study is compared to others in its field. But do we always apply an "apples approach" appropriately? Is median really a 50%, quartile a 25%, 10th percentile a 10%? The paper considers theoretical definitions of such terms compared to their real sense in the course of bibliometric research. It is found that in many empirical cases quartiles are not quarters, medians are not halves, world baselines are not unity, and integer thresholds lead to inequality of performance evaluation in different science fields.