The a priori procedure (APP) provides minimum sample sizes to meet specifications for precision and confidence that, in turn, can enhance trust that the sample statistics to be obtained provide good estimates of corresponding population parameters. A recent advance by Chen et al.3 showed how to perform the APP with respect to Cohen’s [Formula: see text], which is the most popular effect size measure in the social sciences. However, a limitation is that Chen et al.3 assumed normal distributions that compose only a subset of the much larger family of skew normal distributions, which are used as distributions of random errors in many economical models such as stochastic frontier models that are popular and useful models to investigate production efficiency in microeconomics, see Hung.5 Therefore, it would be useful to generalize to skew normal distributions. We perform the mathematical derivations for the generalization and support them with simulations and worked examples. Finally, we provide a free and user-friendly computer program by which researchers can perform the APP to determine minimum sample sizes necessary to meet specifications for precision and confidence, with respect to Cohen’s [Formula: see text], for a matched sample under the large umbrella of skew normal distributions.

The design and fabrication of a compact and low-cost 4×25-Gb/s transmitter optical sub-assembly (TOSA) and receiver optical sub-assembly (ROSA) using a hybrid integrated technique are reported. TOSA and ROSA are developed without thermoelectric cooler for coarse wavelength division multiplexing applications. Physical dimension of the packaged optical subassembly is limited to 11.5 mm×5.4 mm×5.4 mm. The design of TOSA and ROSA is employed using a silica-based arrayed waveguide grating chip to select the specific channel wavelength at O-band. In TOSA, the wavelength of four 1.3-µm discrete directly modulated laser chips is well controlled based on the reconstruction equivalent chirp technique. In the back-to-back transmission test, bit error rates for all lanes of cascade of the TOSA and ROSA are small. A clear opening eye diagram is obtained.