review), where $n$ denotes the total size (e.g. number of publications or staff). The two size-dependent metrics would then be $x n$ and $y n$. Then, even if $x$ and $y$ are completely independent from each other, and hence show a correlation of $0$, the two size-dependent metrics $x n$ and $y n$ may show a quite high correlation. This is demonstrated in Fig. \[fig:spurious\], where $x$ and $y$ are two independent uniform variables and $n$ is a standard log-normal variable ($1000$ samples). In this example, the Pearson correlation between $x n$ and $y n$ may be as high as $0.7$–$0.8$. In other words, the fact that $x n$ and $y n$ may show a high correlation may be completely explained by the common factor $n$. A similar observation has already been made before in bibliometrics [@West2010], and related concerns were already raised by @Pearson1896 as early as 1896.

![ The correlation between two size-dependent metrics can be quite high even if the corresponding size-independent metrics are completely uncorrelated. The insets show the scatter plots of size-dependent and size-independent metrics. For the size-independent scatter plot logarithmic scales are used. []{data-label="fig:spurious"}](spurious){width="\linewidth"}

This complicates the interpretation of size-dependent correlations. A high size-dependent 