Antonio Solanas

Comparing N = 1 effect size indices in presence of autocorrelation.

Generalization from single-case designs can be achieved by replicating individual studies across different experimental units and settings. When replications are available, their findings can be summarized using effect size measurements and integrated through meta-analyses. Several procedures are available for quantifying the magnitude of treatment effect in N = 1 designs, and some of them are studied in this article. Monte Carlo simulations were used to generate different data patterns (trend, level change, and slope change). The experimental conditions simulated were defined by the degrees of serial dependence and phase length. Out of all the effect size indices studied, the percentage of nonoverlapping data and standardized mean difference proved to be less affected by autocorrelation and to perform better for shorter data series. The regression-based procedures proposed specifically for single-case designs did not differentiate between data patterns as well as did simpler indices.

Estimating slope and level change in N=1 designs

The current study proposes a new procedure for separately estimating slope change and level change between two adjacent phases in single-case designs. The procedure eliminates baseline trend from the whole data series before assessing treatment effectiveness. The steps necessary to obtain the estimates are presented in detail, explained, and illustrated. A simulation study is carried out to explore the bias and precision of the estimators and compare them to an analytical procedure matching the data simulation model. The experimental conditions include 2 data generation models, several degrees of serial dependence, trend, and level and/or slope change. The results suggest that the level and slope change estimates provided by the procedure are unbiased for all levels of serial dependence tested and trend is effectively controlled for. The efficiency of the slope change estimator is acceptable, whereas the variance of the level change estimator may be problematic for highly negatively autocorrelated data series.

A comparison of mean phase difference and generalized least squares for analyzing single-case data

The present study focuses on single-case data analysis specifically on two procedures for quantifying differences between baseline and treatment measurements. The first technique tested is based on generalized least square regression analysis and is compared to a proposed non-regression technique, which allows obtaining similar information. The comparison is carried out in the context of generated data representing a variety of patterns including both independent and serially related measurements arising from different underlying processes. Heterogeneity in autocorrelation and data variability was also included, as well as different types of trend, and slope and level changes. The results suggest that the two techniques perform adequately for a wide range of conditions and that researchers can use both of them with certain guarantees. The regression-based procedure offers more efficient estimates, whereas the proposed non-regression procedure is more sensitive to intervention effects. Considering current and previous findings, some tentative recommendations are offered to applied researchers in order to help choosing among the plurality of single-case data analysis techniques.

Changes in dreaming induced by CPAP in severe obstructive sleep apnea syndrome patients

To study dream content in patients with severe obstructive sleep apnea syndrome (OSAS) and its modification with Continuous Positive Airway Pressure (CPAP) therapy. We assessed twenty consecutive patients with severe OSAS and 17 healthy controls. Polysomnograms were recorded at baseline in patients and controls and during the CPAP titration night, 3 months after effective treatment and 2 years later in patients. Subjects were awakened 5–10 min after the beginning of the first and last rapid eye movement (REM) sleep periods and we measured percentage of dream recall, emotional content of the dream, word count, thematic units, sleep architecture and REM density. Dream recall in REM sleep was similar in patients at baseline and controls (51.5% versus 44.4% respectively; P = .421), decreased to 20% and 24.3% the first and third month CPAP nights, and increased to 39% 2 years later (P = 0.004). Violent/highly anxious dreams were only seen in patients at baseline. Word count was higher in patients than in controls. REM density was highest the first CPAP night. Severe OSAS patients recall dreams in REM sleep as often as controls, but their dreams have an increased emotional tone and are longer. Despite an increase in REM density, dream recall decreased the first months of CPAP and recovered 2 years later. Violent/highly anxious dreams disappeared with treatment. A dream recall decrease with CPAP is associated with normalization of sleep in OSAS patients.

Percentage of nonoverlapping corrected data

In the present study, we proposed a modification in one of the most frequently applied effect-size procedures in single-case data analysis: the percentage of nonoverlapping data. In contrast with other techniques, the calculus and interpretation of this procedure are straightforward and can be easily complemented by visual inspection of the graphed data. Although the percentage of nonoverlapping data has been found to perform reasonably well in N = 1 data, the magnitude of effect estimates that it yields can be distorted by trend and autocorrelation. Therefore, the data-correction procedure focuses on removing the baseline trend from data prior to estimating the change produced in the behavior as a result of intervention. A simulation study was carried out in order to compare the original and the modified procedures in several experimental conditions. The results suggest that the new proposal is unaffected by trend and autocorrelation and that it can be used in case of unstable baselines and sequentially related measurements.

Randomization Tests for Systematic Single Case Designs Are Not Always Appropriate

The authors used a Monte Carlo simulation to examine how the violation of the exchangeability assumption affects empirical Type I error rates of the LMH randomization test (J. R. Levin, L. A. Marascuilo, & L. J. Hubert, 1978). Simulation results showed that the LMH test is not always an appropriate technique for analyzing systematic designs when data are autocorrelated. The use of both conditional and unconditional randomization distributions is proposed as a way of synthesizing the literature.

Quantifying social asymmetric structures.

Many social phenomena involve a set of dyadic relations among agents whose actions may be dependent. Although individualistic approaches have frequently been applied to analyze social processes, these are not generally concerned with dyadic relations, nor do they deal with dependency. This article describes a mathematical procedure for analyzing dyadic interactions in a social system. The proposed method consists mainly of decomposing asymmetric data into their symmetric and skew-symmetric parts. A quantification of skew symmetry for a social system can be obtained by dividing the norm of the skew-symmetric matrix by the norm of the asymmetric matrix. This calculation makes available to researchers a quantity related to the amount of dyadic reciprocity. With regard to agents, the procedure enables researchers to identify those whose behavior is asymmetric with respect to all agents. It is also possible to derive symmetric measurements among agents and to use multivariate statistical techniques.

Data-Division-Specific Robustness and Power of Randomization Tests for ABAB Designs.

This study deals with the statistical properties of a randomization test applied to an ABAB design in cases where the desirable random assignment of the points of change in phase is not possible. To obtain information about each possible data division, the authors carried out a conditional Monte Carlo simulation with 100,000 samples for each systematically chosen triplet. The authors studied robustness and power under several experimental conditions—different autocorrelation levels and different effect sizes as well as different phase lengths determined by the points of change. Type I error rates were distorted by the presence of autocorrelation for the majority of data divisions. The authors obtained satisfactory Type II error rates only for large treatment effects. The relation between the lengths of the four phases appeared to be an important factor for the robustness and power of the randomization test.

Testing reciprocity in social interactions: a comparison between the directional consistency and skew-symmetry statistics.

In the present article, we focus on two indices that quantify directionality and skew-symmetrical patterns in social interactions as measures of social reciprocity: the directional consistency (DC) and skew-symmetry indices. Although both indices enable researchers to describe social groups, most studies require statistical inferential tests. The main aims of the present study are first, to propose an overall statistical technique for testing null hypotheses regarding social reciprocity in behavioral studies, using the DC and skew-symmetry statistics (Φ) at group level; and second, to compare both statistics in order to allow researchers to choose the optimal measure depending on the conditions. In order to allow researchers to make statistical decisions, statistical significance for both statistics has been estimated by means of a Monte Carlo simulation. Furthermore, this study will enable researchers to choose the optimal observational conditions for carrying out their research, since the power of the statistical tests has been estimated.

Assessing Functional Relations in Single-Case Designs Quantitative Proposals in the Context of the Evidence-Based Movement

In the context of the evidence-based practices movement, the emphasis on computing effect sizes and combining them via meta-analysis does not preclude the demonstration of functional relations. For the latter aim, we propose to augment the visual analysis to add consistency to the decisions made on the existence of a functional relation without losing sight of the need for a methodological evaluation of what stimuli and reinforcement or punishment are used to control the behavior. Four options for quantification are reviewed, illustrated, and tested with simulated data. These quantifications include comparing the projected baseline with the actual treatment measurements, on the basis of either parametric or nonparametric statistics. The simulated data used to test the quantifications include nine data patterns in terms of the presence and type of effect and comprise ABAB and multiple-baseline designs. Although none of the techniques is completely flawless in terms of detecting a functional relation only when it is present but not when it is absent, an option based on projecting split-middle trend and considering data variability as in exploratory data analysis proves to be the best performer for most data patterns. We suggest that the information on whether a functional relation has been demonstrated should be included in meta-analyses. It is also possible to use as a weight the inverse of the data variability measure used in the quantification for assessing the functional relation. We offer an easy to use code for open-source software for implementing some of the quantifications.