Sample size calculation for Mann-Whitney U test with five methods

<p><strong>Background: </strong>Precise sample size estimation plays a vital role in the planning of a study specifically for medical treatment expenses that are expensive and studies that are of high risk.</p><p><strong>Methods: </strong>Among a variety of sample size calculation methods for the nonparametric Mann-Whitney U test, five potential methods are selected for evaluation in this article. The evaluation of method performance is based on the results obtained from high precision Monte Carlo simulations.</p><p><strong>Results: </strong>The sample size deviations (from the simulation ones) are performance indicators. The sum of the squared deviations over all scenarios is used as the criterion for ranking the five methods. For power comparisons, the percentage errors (relative to the simulated powers) are used. The effect size and target power both have large impacts on the minimum required sample sizes.</p><p><strong>Conclusions: </strong>Based on the ranking criterion, Shieh's method has the best performance. Noether's method always overestimates the minimum required sample sizes but not too severe.</p>

Fractional Entropy-Based Test of Uniformity with Power Comparisons

In the present paper, we use the fractional and weighted cumulative residual entropy measures to test the uniformity. The limit distribution and an approximation of the distribution of the test statistic based on the fractional cumulative residual entropy are derived. Moreover, for this test statistic, percentage points and power against seven alternatives are reported. Finally, a simulation study is carried out to compare the power of the proposed tests and other tests of uniformity.

Smooth Break Detection and De-Trending in Unit Root Testing

This study explores the methods to de-trend the smooth structural break processes while conducting the unit root tests. The two most commonly applied approaches for modelling smooth structural breaks namely the smooth transition and the Fourier functions are considered. We perform a sequence of power comparisons among alternative unit root tests that accommodate smooth or sharp structural breaks. The power experiments demonstrate that the unit root tests utilizing the Fourier function lead to unexpected results. Furthermore, through simulation studies, we investigate the source of such unexpected outcomes. Moreover, we provide the asymptotic distribution of two recently proposed unit root tests, namely Fourier-Augmented Dickey–Fuller (FADF) and Fourier-Kapetanios, Shin and Shell (FKSS), which are not given in the original studies. Lastly, we find that the selection of de-trending function is pivotal for unit root testing with structural breaks.

Goodness-of-fit test for skew normality based on energy statistics

In this paper, we propose a goodness-of-fit test based on the energy statistic for skew normality. Simulations indicate that the Type-I error of the proposed test can be controlled reasonably well for given nominal levels. Power comparisons to other existing methods under different settings show the advantage of the proposed test. Such a test is applied to two real data sets to illustrate the testing procedure.

Power Comparisons of Five Most Commonly Used Autocorrelation Tests

In regression analysis, autocorrelation of the error terms violates the ordinary least squares assumption that the error terms are uncorrelated. The consequence is that the estimates of coefficients and their standard errors will be wrong if the autocorrelation is ignored. There are many tests for autocorrelation, we want to know which test is more powerful. We use Monte Carlo methods to compare the power of five most commonly used tests for autocorrlation, namely Durbin-Watson, Breusch-Godfrey, Box–Pierce, Ljung Box, and Runs tests in two different linear regression models. The results indicate the Durbin-Watson test performs better in the regression model without lagged dependent variable, although the advantage over the other tests reduce with increasing autocorrelation and sample sizes. For the model with lagged dependent variable, the Breusch-Godfrey test is generally superior to the other tests.R code for Power Comparison of the Five Autocorrelation Tests is provided.

Social Dominance Theory and Power Comparison

This chapter extends classic social comparison research to explain how people think about group-based hierarchies and how they act within them. People spontaneously compare themselves to others in terms of relative status and power, not only as individuals but also as members of groups relative to other groups. Using a social dominance framework, the authors discuss the impact of such comparisons on socio-political attitudes and behavior. Social dominance theory describes how certain attitudes, values, and social practices enhance group hierarchies, whereas other attitudes, values, and social practices are hierarchy-attenuating. Power differentials within any type of group hierarchy are given by the balance between these forces that play out at three levels of analysis: in societal institutions (macro level), in intergroup relations (meso level), and among different individuals (micro level). The authors discuss not only how social comparisons shape hierarchy-enhancing and hierarchy-attenuating outcomes at each level but also how these outcomes, in turn, can mute the natural consequences of group-based power comparisons.