*2.6. Statistical Analyses*

Di fferences in normalised mRNA counts with respect to the 12 genes of interest were tested using a mixed model analysis in SAS ® 9.4 (SAS Institute Inc. Cary, NC, USA). The employed model included the fixed e ffects of group (control versus meloxicam), time (0, 4, and 24 h), and their interaction, and the random e ffect of animals. An autoregression 1 (AR1) model [21] was used to account for the covariance between the repeated measures within the individuals. In addition, to account for minor di fferences in the baseline (0 h) mRNA counts within each group, baseline values were considered as a covariate in the mixed model. The normality of residuals of data was checked by Shapiro–Wilk and Anderson–Darling tests using the CAPABILITY Procedure in SAS ® 9.4 and the residuals were found to be normally distributed. Probability (*p*) values of ≤0.05 were considered statistically significant.

*A priori* power analysis could not be undertaken since there were no prior studies in cattle that used nCounter gene expression assay for pain-related cytokines. Hence, an indicative post-hoc power analysis was performed to estimate the power of detecting a significant di fference between the two groups at a given time point as well as between two time points within a group. Power was estimated for two genes (IL8 and PGHS2) that exhibited significant di fferential expression between groups at 4 and 24 h post-disbudding, respectively. Power was calculated using G\*Power software [22], assuming a simple t-test for di fferences between two independent means. The mean and standard deviation of mRNA counts, as well as sample size of the groups, were used as input values to estimate the realised power. The level of significance was set at 5%. Based on the observed e ffect size, the number of individuals required to achieve power values up to 1 were extrapolated for each of those two genes. Similarly, using the same software, the power of detecting a significant di fference in mRNA counts (compared to baseline values) of *IL8* and *PGHS2* genes at 4 and 24 h, respectively, was also determined. A paired t-test for di fferences between two dependent means (matched pairs) was assumed. The observed mean and standard deviation of mRNA counts at the two time points as well as sample size were inputted, and a correlation of 0.5 between the readings at the two time points was assumed.
