| Deriving statistical inferences based upon small sample has long been a concern of researchers. Resampling as a revolutionary methodology to deal with small-sample problems has been developed rapidly with the growth of modern computer techniques. However, existing resampling methods have inevitable limitations, such as dependent observations and sensitive to outliers. The present dissertation study attempts to reduce the limitations of the existing resampling methods by developing a new resampling method, the sample smoothing amplification resampling technique (S-SMART), to obtain an amplified sample which has large statistical power, conditional independence of observations, robustness to outliers, stable statistical behaviors, and an identical distribution with its small random proto-sample from any distributions. The amplified sample is a union of multiple resamples, each randomly generated from a Gaussian kernel distribution. The mean of each Gaussian kernel distribution is determined by the percentiles whose corresponding percentages equally divide the middle 95% percentage range of the small sample; and the random noise of the Gaussian kernel distribution is determined by the standard error of the original small sample. S-SMART is a robust technique because it includes a smoothing procedure using estimates of the evenly-paced middle 95% percentiles to produce S-SMART samples.; Through an evaluative simulation study, this dissertation provides numerical evidence for the reliability and validity of the amplified S-SMART samples. The amplified S-SMART samples were similar to its original small samples in terms of the statistical behaviors and distributions. Thus, it produces unbiased resamples from the original small sample while correcting influence of extreme values. Therefore, the new resampling method has the potential to help researchers improve the quality of research with small samples through increasing statistical power, resisting outlier influences, and making advanced statistical techniques applicable to research with small samples. |
