The Student’s t Test. A very common problem in statistics is to estimate the population mean of a probability distribution given a sample, the subject of sections 7.1 and 7.2 of the statistics textbook. As explained there, this relates directly to the so-called t test. For large samples we may assume, due to the central limit theorem, that the sample mean is normally distributed; one often cons...

The comparison of parasite numbers or intensities between different samples of hosts is a common and important question in most parasitological studies. The main question is whether the values in one sample tend to be higher (or lower) than the values of the other sample. We argue that it is more appropriate to test a null hypothesis about the probability that an individual host from one sample...

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 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-...