we develop a two phase sampling procedure to determine the sample size necessary to estimatethe population mean of a normally distributed random variable and show that the resulting estimator has preassigned variance and is unbiased under a regular condition. we present a necessary and sufficient condition under which the final sample mean is an unbiased estimator for the population mean.

BACKGROUND In this article, we discuss the purpose of sample size calculation in clinical trials, the need for it, and the methods by which it is accomplished. Study samples that are either too small or too large are unacceptable, for clinical, methodological, and ethical reasons. The physicians participating in clinical trials should be directly involved in sample size planning, because their ...

Testing linear combinations of normal group means with unequal variances and possibly unequal samples sizes using a t-statistic is a well known problem for which the effective degrees of freedom are unknown. ? and ? set forth their approximations based on the ratio of combinations of fourth moments, and their methodology remains the de facto standard. We propose a new approach that extends thei...

Virzi (1992), Nielsen and Landauer (1993), and Lewis (1994) have published influential articles on the topic of sample size in usability testing. In these articles, the authors presented a mathematical model of problem discovery rates in usability testing. Using the problem discovery rate model, they showed that it was possible to determine the sample size needed to uncover a given proportion o...

We propose a framework for analyzing and comparing distributions, which we use to construct statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS), and is called the maximum mean discrepancy (MMD). We present two distributionfre...

The experimental result of hypothesis test for hip roof model with = 3:0 is shown in gure 3,where the x axis represents the statistic used in the test and the y axis represents 10, where is the signicance level. Figure 3 shows the result of test mean and covari-ance simultaneously. sample density sample distribution null distribution function null density function Figure 3: Test mean and covari...

The goal of the two-sample test (a.k.a. the homogeneity test) is, given two sets of samples, to judge whether the probability distributions behind the samples are the same or not. In this paper, we propose a novel non-parametric method of two-sample test based on a least-squares density ratio estimator. Through various experiments, we show that the proposed method overall produces smaller type-...