Small samples

This paper proposes unit root tests for dynamic heterogeneous panels based on the mean of individual unit root statistics. In particular it proposes a standardized t-bar test statistic based on the (augmented) Dickey–Fuller statistics averaged across the groups. Under a general setting this statistic is shown to converge in probability to a standard normal variate sequentially with T (the time series dimension) →∞, followed by N (the cross sectional dimension) →∞. A diagonal convergence result with T and N→∞ while N/T→k,k being a finite non-negative constant, is also conjectured. In the special case where errors in individual Dickey–Fuller (DF) regressions are serially uncorrelated a modified version of the standardized t-bar statistic is shown to be distributed as standard normal as N→∞ for a fixed T, so long as T>5 in the case of DF regressions with intercepts and T>6 in the case of DF regressions with intercepts and linear time trends. An exact fixed N and T test is also developed using the simple average of the DF statistics. Monte Carlo results show that if a large enough lag order is selected for the underlying ADF regressions, then the small sample performances of the t-bar test is reasonably satisfactory and generally better than the test proposed by Levin and Lin (Unpublished manuscript, University of California, San Diego, 1993).

Text classification typically performs best with large training sets, but short texts are very common on the World Wide Web. Can we use resampling and data augmentation to construct larger texts using similar terms? Several current methods exist for working with short text that rely on using exte2rnal data and contexts, or workarounds.

Our focus is to test a new preprocessing approach that uses resampling, inspired by the bootstrap, combined with data augmentation, by treating each short text as a population and sampling similar words from a semantic space to create a longer text. We use blog post titles collected from the Technorati blog aggregator as experimental data with each title appearing in one of ten categories. We first test how well the raw short texts are classified using a variant of SVM designed specifically for short texts as well as a supervised topic model and an SVM model that uses semantic vectors as features. We then build a semantic space and augment each short text with related terms under a variety of experimental conditions. We test the classifiers on the augmented data and compare performance to the aforementioned baselines. The classifier performance on augmented test sets outperformed the baseline classifiers in most cases.

This article examines Q methodology as an empirical method for use in social work research. Q methodology applies statistical analysis to the qualitative study of human subjectivity such as attitudes, beliefs, feelings and opinions. Q methodology is effective for obtaining data from small samples, and it offers respondents a concise and valid way of expressing their viewpoints with minimal researcher interference. The article provides an overview of Q methodology and presents an actual example of a small‐scale Q study to facilitate a better understanding of the method. We conclude that Q methodology is especially suitable in social work research with respondents who may have difficulties in expressing themselves when more conventional research methods are used. Q methodology is an efficient tool in research involving the exploration and comparison of different points of view.

While policy-makers and educators have paid increasing attention to the importance of civic education, little is known about how teachers' knowledge and beliefs influence students' development in this area. Most research focuses either on teachers of civic-related subjects or on their students (not linking them) and is conducted in one country (often with small samples). This analysis uses survey data

... As part of a study to identify children with autism prospectively at 18 months of age (Baird and Baron), we assessed a small comparison group of typically developing infants on experimental tasks of joint attention, imitation, and play at 20 months (Charman; Charman and ...