The Hubble Tension Survey: A Statistical Analysis of the 2012-2022 Measurements

In order to investigate the potential Hubble tension, we compile a catalogue of 216 measurements of the Hubble--Lema\^itre constant $H_0$ between 2012 and 2022, which includes 109 model-independent measurements and 107 $\Lambda$CDM model-based measurements. Statistical analyses of these measurements show that the deviations of the results with respect to the average $H_0$ are far larger than expected from their error bars if they follow a Gaussian distribution. We find that $x\sigma $ deviation is indeed equivalent in a Gaussian distribution to $x_{\rm eq}\sigma$ deviation in the frequency of values, where $x_{\rm eq}=0.72x^{0.88}$. Hence, a tension of 5$\sigma$, estimated between the Cepheid-calibrated type Ia supernovae and cosmic microwave background (CMB) data, is indeed a 3$\sigma$ tension in equivalent terms of a Gaussian distribution of frequencies. However, this recalibration should be independent of the data whose tension we want to test. If we adopt the previous analysis of data of 1976-2019, the equivalent tension is reduced to $2.25\sigma$. Covariance terms due to correlations of measurements do not significantly change the results. Nonetheless, the separation of the data into two blocks with $H_0<71$ and $H_0\ge 71$ km s$^{-1}$ Mpc$^{-1}$ finds compatibility with a Gaussian distribution for each of them without removing any outlier. These statistical results indicate that the underestimation of error bars for $H_0$ remains prevalent over the past decade, dominated by systematic errors in the methodologies of CMB and local distance ladder analyses.