Extended Data Fig. 3: Statistical validations of the association between Veillonella gavage and mouse treadmill run time.

a, Density plot of maximum run times in the AB/BA crossover study. A two-sided Shapiro–Wilk normality test on the maximum run times for each mouse in each treatment group resulted in P = 0.67, with the null hypothesis that the distribution of data is normal (n = 64). b, 95% confidence intervals for the coefficient effect on treadmill run time in AB/BA crossover (Wald Z-tests, n = 64). Center values are the regression estimate for each coefficient. Error bars represent the 95% confidence interval. c, Histogram of P values for the treatment coefficient from LOOCV models predicting treadmill run time. The red line represents the P value for the model trained without any hold outs (Wald Z-tests, n = 64). d, Histogram of P values for the treatment coefficient from 1,000 label permutations in GLMM models predicting treadmill run time. The red line represents the P value for the model trained without any label permutation (Wald Z-tests, n = 64 per permutation).