Consider inference with a small number of potentially heterogeneous clusters. Suppose estimating the model on each cluster yields q asymptotically unbiased, independent Gaussian estimators with potentially heterogeneous variances. Following Ibragimov and Müller (2010), one can then conduct asymptotically valid inference with a standard t-test based on the q cluster estimators, since at conventi...

In statistic tests, the probability distribution of the statistics is important. When samples are drawn from population N (µ, σ(2)) with a sample size of n, the distribution of the sample mean X̄ should be a normal distribution N (µ, σ(2)/n). Under the null hypothesis µ = µ0, the distribution of statistics [Formula: see text] should be standardized as a normal distribution. When the variance of ...

Brownian motion is a stochastic process (Wt, t ≥ 0) such that • W0 = 0. • (Wt2 −Wt1) and (Wt4 −Wt3) are independent, for any t1 < t2 ≤ t3 < t4. • (Wt2 −Wt1) ∼ N(0, t2 − t1). • For almost all ω, the sample function t 7→Wt(ω) is continuous. Since Wt has stationary independent increments, we already know that EWt = 0 and that the covariance function is r(t, s) = t∧ s. Thus the covariance matrix of...

OBJECTIVE To provide a practical guidance for the analysis of N-of-1 trials by comparing four commonly used models. METHODS The four models, paired t-test, mixed effects model of difference, mixed effects model and meta-analysis of summary data were compared using a simulation study. The assumed 3-cycles and 4-cycles N-of-1 trials were set with sample sizes of 1, 3, 5, 10, 20 and 30 respectiv...

The Kids and Communities Count Farm Safety Lesson is a follow-up to our Kids Count Lesson that used the North American Guidelines for Children's Agricultural Tasks (NAGCAT) and was previously delivered to nearly 2,000 fifth-grade students in Hillsborough County, Florida. This year, the lesson was administered in two migrant schools and included a parent survey and a presentation of the lesson i...

Materials and Methods: This Randomized Control Trial consists of two experimental and control groups. The experimental group received intervention based on Health Action Model. Control group did not receive any intervention except participating in the current safety courses of company. The sample size was 270 worker who were randomly selected and divided into two experimental (n=135) and contro...

The importance of sample size evaluation in clinical trials is reviewed and a general method is presented from which specific equations are derived for sample size determination or the analysis of power for a wide variety os statistical procedures. The method is discussed and illustrated in relation to the t test, tests for proportions, tests of survival time, and tests for correlations as they...