Civil Society and Its Institutional Context in CEE

VOLUNTAS: International Journal of Voluntary and Nonprofit Organizations - Although civil societies in Central and Eastern Europe are often portrayed as similar, united by a shared communist past,...     

The two-sample <Emphasis Type="Italic">t</Emphasis> test: pre-testing its assumptions does not pay off

Traditionally, when applying the two-sample t test, some pre-testing occurs. That is, the theory-based assumptions of normal distributions as well as of homogeneity of the variances are often tested in applied sciences in advance of the tried-for t test. But this paper shows that such pre-testing leads to unknown final type-I- and type-II-risks if the respective statistical tests are performed using the same set of observations. In order to get an impression of the extension of the resulting misinterpreted risks, some theoretical deductions are given and, in particular, a systematic simulation study is done. As a result, we propose that it is preferable to apply no pre-tests for the t test and no t test at all, but instead to use the Welch-test as a standard test: its power comes close to that of the t test when the variances are homogeneous, and for unequal variances and skewness values |γ ₁| < 3, it keeps the so called 20% robustness whereas the t test as well as Wilcoxon’s U test cannot be recommended for most cases.     

Tests of additivity in mixed and fixed effect two-way ANOVA models with single sub-class numbers

In variety testing as well as in psychological assessment, the situation occurs that in a two-way ANOVA-type model with only one replication per cell, analysis is done under the assumption of no interaction between the two factors. Tests for this situation are known only for fixed factors and normally distributed outcomes. In the following we will present five additivity tests and apply them to fixed and mixed models and to quantitative as well as to Bernoulli distributed data. We consider their performance via simulation studies with respect to the type-I-risk and power. Furthermore, two new approaches will be presented, one being a modification of Tukey’s test and the other being a new experimental design to test for interactions.