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tokens: ways. They facilitate the comparative analysis of measurements in a pairwise fashion. One may use them with n measurements of a particular variable to generate n ( n −1)/2 comparisons for each pair of data. The benefits are twofold: (1) one can test how well each pair of data fits the models, and (2) assess how closely the published error bars fit a normal distribution, thereby providing some indication of possible contamination by correlated systematic uncertainties. Zheng et al. ( 2016 ) recently used such an approach to conclude that the stated errors in cosmic chronometer data are strongly non-Gaussian, suggesting that the quoted measurement uncertainties are almost certainly not based exclusively on statistical randomness (see also Leaf Melia 2017 ). As we shall see, the diagnostic Δμ( z i , z j ) is expected to be zero if the model being tested is the correct cosmology. To allow for possible non-Gaussianity in the published errors, we shall use both weighted-mean and median statistics to determine the degree to which each model's distribution of Δμ( z i , z j ) values is consistent with this null result. So while Wei, Wu Melia ( 2016 ) optimized the overall ΛCDM and R h = ct parametric fits to the H ii galaxy Hubble diagram, here we will test the consistency of each fit with individual pairs of data. We will begin with a brief description of the data in Section 2 , and then define and apply the diagnostic Δμ( z i , z j ) in Section 3 . The outcome of our analysis will be discussed in Section 4 , followed by our conclusions in Section 5 . 2 OBSERVATIONAL DATA AND METHODOLOGY We base our analysis on the methodology described in Chávez et al. ( 2012 , 2014 ) and Terlevich et al. ( 2015 ), using their total sample of 156 sources, including 107 local H ii galaxies, 24 GEHRs, and 25 high- z H ii galaxies. The correlation between the emission-line luminosity and the ionized gas velocity dispersion may be written as (Chávez et al. 2012 ; Chávez et al. 2014 ; Terlevich et al. 2015 ) where α is the slope and the constant κ represents the logarithmic luminosity at log σ(Hβ) = 0. As noted, previous applications of this relation have produced a very small scatter in the correlation for L (Hβ), making it a viable luminosity indicator for cosmology. But one cannot completely avoid its cosmology dependence because the Hβ luminosity is calculated using the expression where D L is the model-dependent luminosity distance at redshift z and F (Hβ) is the reddening corrected Hβ flux. From equation (1), we may then obtain the distance modulus of an H ii galaxy according to with an associated error in terms of σ log σ and σ log F , these being the 1σ uncertainties in log σ(Hβ) and log F (Hβ), respectively. This is to be compared with the theoretical distance modulus as a function of the cosmology-dependent luminosity distance D L . In ΛCDM, the luminosity distance may be written where p de = w de ρ de is the dark-energy equation of state; radiation is