Table 7: Mean stellar population gradients and their errors for HDEGs. $\sigma $: standard deviation about the mean; N: number of galaxies averaged; $N_{\rm eff}$: effective number of points; t: t-statistic to verify the hypothesis "mean = 0''; $\sigma _{\rm exp}$: standard deviation expected from the errors; $\alpha $: significance level to reject the hypothesis "$\sigma $ = $\sigma _{\rm exp}$'' in a $\chi ^2$ test. Column 9 shows the t-statistic to confirm whether the gradients obtained with individual indicators are the same as the metallicity gradients obtained with a combination of ten different indicators. As a reference, the 10th column shows the mean gradients obtained for the LDEGs from Sect. 4 (see Table 3). The final column of the table shows the t-statistic, to verify if the mean gradients are the same for both samples of galaxies, LDEGs and HDEGs. A high value of t indicates significant differences.
  Mean $\sigma $ N $N_{\rm eff}$ t $\sigma _{\rm exp}$ $\alpha $ t LDEGs t'
grad log age $ 0.027\pm 0.067$ 0.258 15 9.79 0.34 0.138 0.0003   $ 0.082\pm 0.015$ 0.8
grad [M/H] $-0.328\pm 0.064$ 0.247 15 11.85 5.59 0.157 0.0017   $-0.206\pm 0.019$ 1.8
grad [M/H] (CN2-H$\beta $) $-0.643\pm 0.111$ 0.432 15 10.86 5.60 0.236 0.0003 2.10 $-0.582\pm 0.032$ 0.5
grad [M/H] (C4668-H$\beta $) $-0.599\pm 0.092$ 0.358 15 9.18 5.71 0.185 4.2E-06 1.96 $-0.459\pm 0.028$ 1.4
grad [M/H] (Fe4383-H$\beta $) $-0.168\pm 0.118$ 0.456 15 8.95 1.47 0.275 0.0014 0.95 $-0.197\pm 0.025$ 0.2
grad [M/H] (Mgb-H$\beta $) $-0.537\pm 0.158$ 0.611 15 10.23 2.85 0.337 4.2E-05 1.02 $-0.407\pm 0.039$ 0.8
grad [M/H] (Ca4227-H$\beta $) $-0.168\pm 0.214$ 0.831 15 11.16 0.70 0.434 1.7E-06 0.61 $-0.238\pm 0.034$ 0.3

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