Assigning and combining probabilities in single-case studies

There is currently a considerable diversity of quantitative measures available for summarizing the results in single-case studies. Given that the interpretation of some of them is difficult due to the lack of established benchmarks, the current paper proposes an approach for obtaining further numerical evidence on the importance of the results, complementing the substantive criteria, visual analysis, and primary summary measures. This additional evidence consists of obtaining the statistical significance of the outcome when referred to the corresponding sampling distribution. This sampling distribution is formed by the values of the outcomes (expressed as data nonoverlap, R-squared, etc.) in case the intervention is ineffective. The approach proposed here is intended to offer the outcome"s probability of being as extreme when there is no treatment effect without the need for some assumptions that cannot be checked with guarantees. Following this approach, researchers would compare their outcomes to reference values rather than constructing the sampling distributions themselves. The integration of single-case studies is problematic, when different metrics are used across primary studies and not all raw data are available. Via the approach for assigning p values it is possible to combine the results of similar studies regardless of the primary effect size indicator. The alternatives for combining probabilities are discussed in the context of single-case studies pointing out two potentially useful methods one based on a weighted average and the other on the binomial test.

Choosing among techniques for quantifying single-case intervention effectiveness

If single case experimental designs are to be used to establish guidelines for evidence-based interventions in clinical and educational settings, numerical values that reflect treatment effect sizes are required. The present study compares four recently developed procedures for quantifying the magnitude of intervention effect using data with known characteristics. Monte Carlo methods were used to generate AB designs data with potential confounding variables (serial dependence, linear and curvilinear trend, and heteroscedasticity between phases) and two types of treatment effect (level and slope change). The results suggest that data features are important for choosing the appropriate procedure and, thus, inspecting the graphed data visually is a necessary initial stage. In the presence of serial dependence or a change in data variability, the Nonoverlap of All Pairs (NAP) and the Slope and Level Change (SLC) were the only techniques of the four examined that performed adequately. Introducing a data correction step in NAP renders it unaffected by linear trend, as is also the case for the Percentage of Nonoverlapping Corrected Data and SLC. The performance of these techniques indicates that professionals" judgments concerning treatment effectiveness can be readily complemented by both visual and statistical analyses. A flowchart to guide selection of techniques according to the data characteristics identified by visual inspection is provided.

Effects of adult dysthyroidism on the morphology of hippocampal neurons.

This study investigates the effect of thyroid hormones on the morphology of hippocampal neurons in adult rats. Hypo- and hyperthyroidism were induced by adding 0.02% methimazole and 1% l-thyroxine, in drinking water from 40 days of age, respectively. When the rats were 89 days old their brains were removed and stained by a modified Golgi method and blood samples were collected in order to measure T4 serum levels. Neurons were selected and drawn using a camera lucida. Our results show that methimazole administration reduces the dendritic branching of the apical shafts of CA3 and CA1 pyramidal neurons mainly by increasing the distance to the first branch point in both types of neurons, and reducing branch points in the radius of 50 μm from the soma in CA1 neurons. Nevertheless, it was observed an increase of apical spine density in CA3 neurons from this group. Thyroxine reduces apical and basal tree of CA3 pyramidal neurons increasing the distance to the first branch point, reducing branch points in the radius of 50 μm from the soma and increases their apical and basal spine density. In CA1 field, thyroxine reduces the number of basal branch points. Both treatments seems to provoke alterations in the same direction reducing the dendritic branching and increasing spine density, although no significances appeared in some of the parameters analyzed. The effects are more evident in thyroxine than methimazole group; and in CA3 neurons than in CA1 neurons. In discussion it is pointed that the increase of spine density could be a mechanism to compensate the functionality reduction that can be provoke by the treatment effect on dendritic branching.

Regression-based techniques for statistical decision making in single-case designs

The present study evaluates the performance of four methods for estimating regression coefficients used to make statistical decisions regarding intervention effectiveness in single-case designs. Ordinary least squares estimation is compared to two correction techniques dealing with general trend and one eliminating autocorrelation whenever it is present. Type I error rates and statistical power are studied for experimental conditions defined by the presence or absence of treatment effect (change in level or in slope), general trend, and serial dependence. The results show that empirical Type I error rates do not approximate the nominal ones in presence of autocorrelation or general trend when ordinary and generalized least squares are applied. The techniques controlling trend show lower false alarm rates, but prove to be insufficiently sensitive to existing treatment effects. Consequently, the use of the statistical significance of the regression coefficients for detecting treatment effects is not recommended for short data series.

Randomization tests for ABAB designs: Comparing-data-division-specific and common distributions

Monte Carlo simulations were used to generate data for ABAB designs of different lengths. The points of change in phase are randomly determined before gathering behaviour measurements, which allows the use of a randomization test as an analytic technique. Data simulation and analysis can be based either on data-division-specific or on common distributions. Following one method or another affects the results obtained after the randomization test has been applied. Therefore, the goal of the study was to examine these effects in more detail. The discrepancies in these approaches are obvious when data with zero treatment effect are considered and such approaches have implications for statistical power studies. Data-division-specific distributions provide more detailed information about the performance of the statistical technique.

Effect of flushing frequency on emitter clogging in microirrigation with effluents

Flushing is an important maintenance task that removes accumulated particles in microirrigation laterals that can help to reduce clogging problems. The effect of three dripline flushing frequency treatments (no flushing, one flushing at the end of each irrigation period, and a monthly flushing during the irrigation period) was studied in surface and subsurface drip irrigation systems that operated using a wastewater treatment plant effluent for three irrigation periods of 540 h each. The irrigation systems had two different emitters, one pressure compensating and the other not, both molded and welded onto the interior dripline wall, placed in laterals 87 meters long. Dripline flow of the pressure compensating emitter increased 8% over time, while in the nonpressure compensating emitter, dripline flow increased 25% in the surface driplines and decreased 3% in the subsurface driplines by the emitter clogging. Emitter clogging was affected primarily by the interactions between emitter location, emitter type, and flushing frequency treatment. The number of completely clogged emitters was affected by the interaction between irrigation system and emitter type. There was an average of 3.7% less totally clogged emitters in flushed surface driplines with the pressurecompensating emitter as compared to flushed subsurface laterals with the nonpressure compensating emitter