Crandall, Sara R.2016-07-062016-07-062016-08-01http://hdl.handle.net/2097/32807In 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.en-US© the author. This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).http://rightsstatements.org/vocab/InC/1.0/AstrophysicsStatisticsThesis