Statistical Analysis of Rat Behavioral Data

The recorded data (1 min bins) and derived parameters, Vt/Ti and Response Area (cumulative percent changes from pre-values) were taken for statistical analyses. The pre-drug 1 min bins excluded occasional marked deviations from resting due to movements or scratching by the rats. These exclusions ensured accurate determinations of baseline parameters. The data are presented as mean ± SEM. All data unless otherwise stated (see immediately below) were analyzed by one-way or two-way analysis of variance followed by Student's modified t test with Bonferroni corrections for multiple comparisons between means using the error mean square terms from each ANOVA^{40 –43 (link)}. A value of P < 0.05 denoted the initial level of statistical significance that was modified according to the number of comparisons between means as detailed by Wallenstein et al. (1980)^{41 (link)}. The modified t-statistic is t = (mean group 1—mean group 2)/[s × (1/n₁ + 1/n₂)^1/2] where s² = the mean square within groups term from the ANOVA (the square root of this value is used in the modified t-statistic formula) and n₁ and n₂ are the number of rats in each group under comparison. Based on an elementary inequality called Bonferroni's inequality, a conservative critical value for the modified t-statistics taken from tables of t-distribution using a significance level of P/m, where m is the number of comparisons between groups to be performed. The degrees of freedom are those for the mean square for within group variation from the ANOVA table. In most cases, the critical Bonferroni value cannot be obtained from conventional tables of the t- distribution but may be approximated from widely available tables of the normal curve by t* = z + (z + z³)/4n, with n being the degrees of freedom and z being the critical normal curve value for P/m^{40 –43 (link)}. Wallenstein et al.^{41 (link)} first demonstrated that the Bonferroni procedure is preferable for general use since it is easiest to apply, has the widest range of applications, and gives critical values that will be lower than those of other procedures if the investigator is able to limit the number of comparisons, and that will be only slightly larger than those of other procedures if many comparisons are made. The practical application of the Bonferroni procedure first demonstrated by Wallenstein et al.^{41 (link)} has been supported and expanded upon by Ludbrook^{42 (link)} and by McHugh^{43 (link)}. A value of P < 0.05 was taken as the initial level of statistical significance^{40 ,41 (link)}. With respect to Supplemental Figures S4–S7, the data were analyzed by one-way ANOVA and Tukey’s least significance difference (LSD) test, with statistical differences taken as P < 0.05^{40 ,41 (link)}.