Boosting statistical power in ethology: continuous data are superior to ordinal and binomial data

It is common practice among applied ethologists to score gradations in behavioural expressions or animal welfare measures using ordinal scales (OS) with a few (usually 2-5) categories. Several scholars have advocated, however, to use tagged visual analogue scales (tVAS) instead of OS whenever the variable truly varies in severity along a continuum. One of the main arguments is that this would increase the statistical power and hence reduce the sample size required to confirm or reject research hypotheses. This is the first study in which this assumption has been tested using 10,000 stochastic simulations based on 3 real datasets with tVAS data: sow gait scores (0-150mm scale with tags at 30mm intervals), pig heat stress scores (0-150mm scale with tags at 30mm intervals), and cow panting scores (0-50mm scale with tags at 10mm intervals). We compared the sample size required to achieve 80% power when the data were analysed as binomial (BI), 5-point ordinal categories (5P), or tVAS data for detecting i) a difference between fictitious treatment X vs Y, and ii) for detecting an association between the welfare scores and a related variable (resp. feeding interval duration, rectal T°, and the Heat Load Index). The mean scores, as well as the difference between the treatments (δ) and the strength of the associated variables (ϐ) were simulated to vary, in order to broaden the possible scenarios and investigate the degree to which findings can be generalized. The outcomes of the tests of treatment differences revealed that the sample size required was consistently lowest for tVAS data and on average 17.7% (range 10 – 30%) and 90.7% (range 50 – 360%) higher for 5P and BI data respectively. For the regression analyses, the sample size required was also consistently lowest for tVAS data and on average 74.3% (range 61 – 211%) higher for 5P (regression analyses were not performed on BI data). These simulations confirm that the statistical power is higher when continuous variables are scored using a continuous tVAS instead of an ordinal or binomial scale. Choosing and designing an appropriate scale for collecting data is an important, but often neglected, consideration for reducing the number of animals required for hypothesis testing.