  In early dark energy (EDE) resolution of Hubble tension, the spectral index
$n_s$ of primordial scalar perturbation follows a scaling relation ${\delta
n_s}\simeq 0.4\frac{\delta H_0}{H_0}$, where $H_0$ is the Hubble constant.
However, this $n_s-H_0$ relation was obtained based on the datasets including
Planck cosmic microwave background (CMB) data. In this paper, we investigate
this scaling relation with Planck-independent CMB data, i.e. ACT and SPT-3G
combined with WMAP(+BAO+Pantheon), respectively. Our results show that the
WMAP+SPT-3G dataset also follows this scaling relation, while the WMAP+ACT
dataset seems to favor smaller $n_s$, which is related to the fact that the
critical redshift $z_c$, at which EDE is excited, favored by the WMAP+ACT
dataset is lower and closer to the recombination time.
