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The aim of this analysis was to determine whether or not the given error barstruly represented the dispersion of values in a historical compilation of twocosmological parameters: the amplitude of mass fluctuations ($\sigma_8$) andHubble's constant ($H_0$) parameters in the standard cosmological model. Forthis analysis, a chi-squared test was executed on a compiled list of pastmeasurements. It was found through analysis of the chi-squared ($\chi^2$)values of the data that for $\sigma_8$ (60 data points measured between 1993and 2019 and $\chi^2$ between 182.4 and 189.0) the associated probability Q isextremely low, with $Q = 1.6 \times 10^{-15}$ for the weighted average and $Q =8.8 \times 10^{-15}$ for the best linear fit of the data. This was also thecase for the $\chi^2$ values of $H_0$ (163 data points measured between 1976and 2019 and $\chi^2$ between 480.1 and 575.7), where $Q = 1.8 \times 10^{-33}$for the linear fit of the data and $Q = 1.0 \times 10^{-47}$ for the weightedaverage of the data. The general conclusion was that the statistical error barsassociated with the observed parameter measurements have been underestimated orthe systematic errors were not properly taken into account in at least 20\% ofthe measurements. The~fact that the underestimation of error bars for $H_0$ isso common might explain the apparent 4.4$\sigma$ discrepancy formally knowntoday as the Hubble tension.

A Chi-Squared Analysis of the Measurements of Two Cosmological Parameters Over Time