  We introduce a new diagnostic for the null test of dynamical dark energy.
This diagnostic is useful, especially when we include anisotropic baryon
acoustic oscillation (BAO) data in an analysis, to quantify the deviations from
the standard $\Lambda$CDM model. This null test is independent of any late-time
cosmological model or parametrization. With this, we study the evidence for
dynamical dark energy in light of Dark Energy Spectroscopic Instrument (DESI)
2024 data combined with cosmic microwave background (CMB) observations of the
Planck 2018 mission and local $H_0$ measurements. We find low (around
0.6$\sigma$) to moderate (around 1$\sigma$) evidence for dynamical dark energy
which is not that significant. Although we get individual deviations at around
2$\sigma$ at the effective redshift 0.51 of the DESI 2024 data, the average
deviations combining all redshift points are almost independent of the
inclusion or exclusion of the data at effective redshift 0.51 (the differences
are only around 0.3$\sigma$). We get almost similar results for other non-DESI
BAO data. The evidences are almost independent of the early-time physics and
these evidences have very low dependence on $H_0$ values. The evidence of
dynamical dark energy, obtained in this analysis, is not consistent with the
DESI key paper results with the $w_0w_a$CDM model, but interestingly, these are
almost consistent with the DESI's results with $z_pw_p$CDM model.
