Using Tukey-Kramer versus the ANOVA F-test as the omnibus test of the Hayter-Fisher procedure for comparing all pairs of normally distributed means, when sample sizes are unequal, is investigated. Simulation results suggest that using Tukey-Kramer leads to as much or more any-pairs power compared to using the F-test for certain patterns of mean differences, and equivalent per-pair and all-pairs...

1) Be able to perform the key steps to hypothesis testing 2) Understand the concept and use of the alpha value 3) Understand in general terms how the p value is derived 4) Correctly interpret the p value 5) Distinguish between type I and type II error 6) Understand the relationships among sample size, power, type I and type II error 7) Have a general notion of the concept of power as it relates...

In order to circumvent the influence of correlation in paired-samples and repeated measures experimental designs, researchers typically perform a one-sample Student t test on difference scores. That procedure entails some loss of power, because it employs N – 1 degrees of freedom instead of the 2N – 2 degrees of freedom of the independent-samples t test. In the case of non-normal distributions,...

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 ...