In this paper, we propose an explicit closed-form Bayes factor for the problem of two-sample hypothesis testing. The proposed approach can be regarded as a Bayesian version of the pooled-variance t-statistic and has various appealing properties in practical applications. It relies on data only through the t-statistic and can thus be calculated by using an Excel spreadsheet or a pocket calculator. It avoids several undesirable paradoxes, which may be encountered by the previous Bayesian approach of Gönen et al. (2005). Specifically, the proposed approach can be easily taught in an introductory statistics course with an emphasis on Bayesian thinking. Simulated and real data examples are provided for illustrative purposes.

Electrospinning of fibrous tissue engineering scaffolds has been traditionally conducted using positive voltages. In the current study, positive voltage (PV) electrospinning and negative voltage (NV) electrospinning were investigated for forming fibrous membranes of poly(hydroxybutyrate-co-hydroxyvalerate) (PHBV). In both PV-electrospinning and NV-electrospinning, the fiber diameter generally increased with increasing needle inner diameter and PHBV concentration but decreased with increasing working distance. The use of a conductivity-enhancing surfactant, benzyl triethylammonium chloride (BTEAC), significantly reduced PHBV fiber diameters from the micron scale to the sub-micron scale. Interestingly, with increasing applied voltage, the fiber diameter increased for PV-electrospinning but decreased for NV-electrospinning. The PV-electrospun fibrous membranes from solutions without BTEAC (PVEfm) and with BTEAC (PVEfm-B) and NV-electrospun membranes from solutions without BTEAC (NVEfm) and with BTEAC (NVEfm-B) were characterized in terms of their structure, wettability, thermal properties and tensile properties. Both PVEfm and NVEfm exhibited similar water contact angles (∼104°) but the contact angle of PVEfm-B or NVEfm-B was not measurable. The elongation at break of PVEfm-B or NVEfm-B was significantly higher than that of PVEfm or NVEfm. Using NV-electrospinning or a combination of NV- and PV-electrospinning may be very useful for developing suitable scaffolds for tissue engineering applications.

When the experimental data set is contaminated, we usually employ robust alternatives to common location and scale estimators, such as the sample median and Hodges-Lehmann estimators for location and the sample median absolute deviation and Shamos estimators for scale. It is well-known that these estimators have high positive asymptotic breakdown points and are normally consistent as the sample size tends to infinity.To our knowledge, the finite-sample properties of these estimators depending on the sample size have not well been studied in the literature.In this paper, we fill this gap by providing their closed-form finite-sample breakdown points and calculating the unbiasing factors and relative efficiencies of the robust estimators through the extensive Monte Carlo simulations up to the sample size 100. The numerical study shows that the unbiasing factor improves the finite-sample performance significantly. In addition, we also provide the predicted values for the unbiasing factors which are obtained by using the least squares method which can be used for the case of sample size more than 100.

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The nanostructured Au cocatalyst modification of BiVO4 photocatalyst, as a prospective method, can significantly promote its photocatalytic H2O2 production performance. However, the contact between Au and BiVO4 causes a strong built-in field, which impedes the photogenerated-electron transfer and the accumulation of negative charge density for Au, which reduces its catalytic activity of two-electron O2 reduction, thus limiting the enhanced H2O2 production performance of the Au/BiVO4 photocatalyst. To solve the above problems, here, a Cu@Au core-shell nanostructured cocatalyst is designed to selectively modify on the electron-enriched (010) facet of a single-crystal BiVO4 microparticle by facile photodeposition and subsequently galvanic displacement. In this case, ohmic contact between the Cu nanoparticle and (010) facet of BiVO4 can effectively transfer the photogenerated electrons to the Au cocatalyst and simultaneously facilitate the catalytic activity improvement of two-electron O2 reduction for the Au cocatalyst due to its low negative charge accumulation. As a result, the optimized BiVO4 photocatalyst with Cu@Au core-shell nanostructured modification exhibits obviously improved photocatalytic performance of H2O2 formation (91.1 μmol L–1) compared with Au/BiVO4 (62.5 μmol L–1). The present strategy of a bimetal cocatalyst with a core-shell nanostructure opens up an insight to explore effective photocatalytic materials for the application of H2O2 production.