the study of @Butler2009 of Politics & International Studies and found a similar correlation ($R^2 \approx 0.7$, $R \approx 0.85$). They correlated the proportion of publications in top journals with the proportion of publications that obtained four stars, which are both clearly size-independent measures.

In two publications, @Mryglod2013 [@Mryglod2013a] explicitly studied size-dependent correlations versus size-independent correlations in seven fields (Biology, Physics, Chemistry, Engineering, Geography & Environmental Science, Sociology, and History). They studied the average normalised citation score and the total normalised citation score and examined how they correlate with the RAE Grade (a weighted average of scores) and the RAE Score (the RAE Grade times the number of staff), respectively. They found size-independent correlations of only about $0.34$ for History and Engineering and up to about $0.6$ for Biology and Chemistry. The size-dependent correlations were substantially higher and reached about $0.9$ for all fields. We discuss this in more detail in Section \[sec:size\_dependent\].

In conclusion, most studies in the literature have found correlations on the order of $0.6$–$0.7$ for fields that seem to be amenable to bibliometric analysis. The conclusions that were drawn from such results nonetheless differed. Three types of conclusions can be distinguished. First, some authors concluded simply 