We term this method empirical JTK_CYCLE with asymmetry search, and we compare its performance to JTK_CYCLE with Bonferroni and Benjamini-Hochberg multiple hypothesis testing correction, as well as to five other methods: cyclohedron test, address reduction, stable persistence, ANOVA , and F24.

We find that ANOVA , F24, and JTK_CYCLE consistently outperform the other three methods when data are limited and noisy; empirical JTK_CYCLE with asymmetry search gives the greatest sensitivity while controlling for the false discovery rate.

We test its performance for detecting way analysis of variance ( ANOVA ) [27].

In particular, ITK_CYCLE, F24, and ANOVA consistently outperform the other methods and offer distinct advantages for certain types of data.

The methods that we test are cyclohedron test [20, 21] , address reduction [22, 23], stable persistence [24, 25], F24 [31, 32], one-way analysis of variance ( ANOVA ) [27], and ITK_CYCLE [26].

Cyclohedron test, address reduction, stable persistence, and ANOVA seek to identify patterns without specifying the waveform a priori.

ANOVA compares the means of different time points with their variances to determine if differences are significant.

Permutational ANOVA and ANOSIM tests on the effect of the number of clades used in the calculation of the weighted UniFrac distance between Western (USA and Italy) and non-Western (Ma-show in Fig.

Permutational ANOVA and ANOSIM tests on the effect of the number of clades used in the calculation of the weighted UniFrac distance between young (below two years of age) and older (above two years of age) Western individuals (USA and Italy).

Permutational ANOVA and ANOSIM tests on the effect of the number of clades used in the calculation of the weighted UniFrac distance between young (below two years of age) and older

Permutational ANOVA (PERMANOVA) and ANOSIM tests were performed with 999 permutations.

R2 of the Permutational ANOVA obtained by partitioning the individuals into two samples using an increasing age threshold, and the pairwise weighted UniFrac distance.

Permutational ANOVA and ANOSIM tests on the effect of age.

The sample has been partitioned into two as function of an age threshold and the Permutational ANOVA and

Thus, if the ANOVA leads to a significant result the hypothesis for linear generalisation can be rejected.

The test performed was a one-way ANOVA with shape as the only factor.

We tested whether the linear hypothesis could be rejected by performing an ANOVA on the linear regression residuals for each participant.

These tests were again performed by testing for differences in the regression residuals using an ANOVA for each individual participant and correcting for multiple comparisons (Bonferroni).

This was confirmed by the ANOVA on the regression residuals for each participant.