The problem of comparing two sociometric matrices, as originally discussed by Katz and Powell in the early 1950’s, is reconsidered and generalized using a different inference model. In particular, the proposed indices of conformity are justified by a regression argument similar to the one used by Somers in presenting his well-known measures of asymmetric ordinal association. A permutation distribution and an associated significance test are developed for the specific hypothesis of “no conformity” reinterpreted as a random matching of the rows and (simultaneously) the columns of one sociometric matrix to the rows and columns of a second. The approximate significance tests that are presented and illustrated with a simple numerical example are based on the first two moments of the permutation distribution, or alternatively, on a random sample from the complete distribution.

Equal parameter estimates across subgroups is a substantial requirement of statistical tests. Ignoring subgroup differences poses a threat to study replicability, model specification, and theory development. Structural change tests are a powerful statistical technique to assess parameter invariance. A core element of those tests is the empirical fluctuation process. In the case of parameter invariance, the fluctuation process asymptotically follows a Brownian bridge. This asymptotic assumption further provides the basis for inference. However, the empirical fluctuation process does not follow a Brownian bridge in small samples, and this situation is amplified in large psychometric models. Therefore, common methods of obtaining the sampling distribution are invalid and the structural change test becomes conservative. We discuss an alternative solution to obtaining the sampling distribution—permutation approaches. Permutation approaches estimate the sampling distribution through resampling of the dataset, avoiding distributional assumptions. Hereby, the tests power are improved. We conclude that the permutation alternative is superior to standard asymptotic approximations of the sampling distribution.

Differential item functioning (DIF), referring to between-group variation in item characteristics above and beyond the group-level disparity in the latent variable of interest, has long been regarded as an important item-level diagnostic. The presence of DIF impairs the fit of the single-group item response model being used, and calls for either model modification or item deletion in practice, depending on the mode of analysis. Methods for testing DIF with continuous covariates, rather than categorical grouping variables, have been developed; however, they are restrictive in parametric forms, and thus are not sufficiently flexible to describe complex interaction among latent variables and covariates. In the current study, we formulate the probability of endorsing each test item as a general bivariate function of a unidimensional latent trait and a single covariate, which is then approximated by a two-dimensional smoothing spline. The accuracy and precision of the proposed procedure is evaluated via Monte Carlo simulations. If anchor items are available, we proposed an extended model that simultaneously estimates item characteristic functions (ICFs) for anchor items, ICFs conditional on the covariate for non-anchor items, and the latent variable density conditional on the covariate—all using regression splines. A permutation DIF test is developed, and its performance is compared to the conventional parametric approach in a simulation study. We also illustrate the proposed semiparametric DIF testing procedure with an empirical example.

Randomization tests are often recommended when parametric assumptions may be violated because they require no distributional or random sampling assumptions in order to be valid. In addition to being exact, a randomization test may also be more powerful than its parametric counterpart. This was demonstrated in a simulation study which examined the conditional power of three nondirectional tests: the randomization t test, the Wilcoxon–Mann–Whitney (WMW) test, and the parametric t test. When the treatment effect was skewed, with degree of skewness correlated with the size of the effect, the randomization t test was systematically more powerful than the parametric t test. The relative power of the WMW test under the skewed treatment effect condition depended on the sample size ratio.

The values of the signal-to-noise ratio are determined, at which the method of processing X-ray diffraction data reveals reflections with intensity less than the noise component of the background. The possibilities of the method are demonstrated on weak reflections of α-quartz. The method of processing X-ray diffraction data makes it possible to increase the possibilities of X-ray phase analysis in determining the qualitative phase composition of multiphase materials with a small (down to 0.1 wt.%) content of several (up to eight) phases.

This paper develops tests of independence and stationarity in choice data collected with small samples. The method builds on the approach of Smith and Batchelder (2008). The technique is intended to distinguish cases where a person is systematically changing “true” preferences (from one group of trials to another) from cases in which a person is following a random preference mixture model with independently and identically distributed sampling in each trial. Preference reversals are counted between all pairs of repetitions. The variance of these preference reversals between all pairs of repetitions is then calculated. The distribution of this statistic is simulated by a Monte Carlo procedure in which the data are randomly permuted and the statistic is recalculated in each simulated sample. A second test computes the correlation between the mean number of preference reversals and the difference between replicates, which is also simulated by Monte Carlo. Data of Regenwetter, Dana, and Davis-Stober (2011) are reanalyzed by this method. Eight of 18 subjects showed significant deviations from the independence assumptions by one or both of these tests, which is significantly more than expected by chance.

In this paper, we present the results of our analysis of the 110-item basic wordlists for four reconstructed and one ancient languages, the linguistic ancestors of five language families which are hypothesized to constitute the Altaic (a.k.a. Transeurasian) macrofamily: Proto-Turkic, Proto-Mongolic, Proto-Tungusic, Middle Korean and Proto-Japonic wordlists. Protolanguage wordlists were reconstructed according to strict criteria of semantic reconstruction, based on accurate semantic glossing of forms in daughter languages. Each involved form was encoded into a bi-consonantal CC-shaped sequence using the consonant class method, after which a recently developed weighted permutation test was applied. In a typical situation, our algorithm makes a small number of type 1 errors (false positive), but the number of type 2 errors (false negative) can be substantial. Our main finding is that pairs between the Nuclear Altaic taxa – Turkic, Mongolic and Tungusic – as well as the Turkic-Japonic and Tungusic-Japonic pairs demonstrate significant p-values. In some cases, this can be attributed to either ancient contacts or genealogical relationships, but at least for the Turkic–Japonic pair, a contact scenario is unlikely owing to geographical remoteness.

This paper presents a unilevel and multilevel approach for the analysis and meta-analysis of single-case experiments (SCEs). We propose a definition of SCEs and derive the specific features of SCEs’ data that have to be taken into account when analysing and meta-analysing SCEs. We discuss multilevel models of increasing complexity and propose alternative and complementary techniques based on probability combining and randomisation test wrapping. The proposed techniques are demonstrated with real-life data and corresponding R code.