In physics, datasets are often assumed to follow a Gaussian distribution. However, this may not always be justified. By constructing error distributions, or histograms of the number of standard deviations that a measurement deviates from a central estimate, the Gaussianity of datasets can be explored. This thesis applies statistical techniques used to test the Gaussianity of two datasets.

These techniques are first applied to a ⁷Li abundance dataset, where error distributions are constructed for 66 measurements (with error bars) used by [1] that give A(Li) = 2.21 ± 0.065 dex (median and 1σ symmetrized error). This error distribution is somewhat non-Gaussian, with large probability in the tails. Assuming Gaussianity, the observed A(Li) is 6.5σ away from that expected from standard Big Bang nucleosynthesis given by Planck observations. Accounting for the non-Gaussianity of the observed A(Li) error distribution reduces the discrepancy to 4.9σ, which is still significant.

Similar error distributions are constructed for a compilation of 232 Large Magellanic Cloud (LMC) distance moduli values from [2] that give an LMC distance modulus of (m − M)₀ = 18.49 ± 0.13 mag (median and 1σ symmetrized error). When using a weighted mean (median) central estimate, the error distribution has large (small) probability in the tails than what is expected for a Gaussian distribution. This may be the consequence of publication bias and/or correlations between measurements.