ratiolla

Ratiolla is a dimensionless statistical measure used to compare proportional changes between two related quantities across time or conditions. It is defined as the ratio of the proportional changes in two series A and B: ratiolla = (A1/A0) / (B1/B0), where A0 and B0 are baseline values and A1 and B1 are subsequent values. An alternative formulation uses logarithms: ratiolla = log(A1/A0) − log(B1/B0). In either form, a value of 1 indicates identical proportional change in A and B.

The term ratiolla is a coined word from ratio, with the suffix -olla, introduced by statistician Lina Fors in 2012 in a paper on comparative growth measures. The concept has not achieved widespread standardization and appears primarily in theoretical or methodological discussions.

Computation and properties: Ratiolla is dimensionless and remains invariant to the multiplication of both series by positive constants. It requires positive baseline values (A0 > 0 and B0 > 0) and nonzero subsequent values. The measure can be affected by small baseline values and outliers, and extreme ratios. For more than two series, a generalized ratiolla can be defined by taking the geometric mean of pairwise ratiollas.

Applications include economics, ecology, epidemiology, and data visualization, where researchers seek to compare relative growth or change between related indicators. Example: A rises from 100 to 150 (A1/A0 = 1.5); B rises from 200 to 250 (B1/B0 = 1.25); ratiolla = 1.5/1.25 = 1.2. This indicates that A's proportional change exceeded B's by 20%.

History and reception: Since its introduction, ratiolla has seen limited uptake in mainstream statistics, cited mainly in illustrative examples or niche methodological discussions. Critics note that interpretation depends on the choice of baselines and may be less intuitive than alternative measures such as growth rates or log returns.