Extrapolating baseline trend in single-case data: Problems and tentative solutions.

Single-case data often contain trends. Accordingly, to account for baseline trend, several data-analytical techniques extrapolate it into the subsequent intervention phase. Such extrapolation led to forecasts that were smaller than the minimal possible value in 40% of the studies published in 2015 that we reviewed. To avoid impossible predicted values, we propose extrapolating a damping trend, when necessary. Furthermore, we propose a criterion for determining whether extrapolation is warranted and, if so, how far out it is justified to extrapolate a baseline trend. This criterion is based on the baseline phase length and the goodness of fit of the trend line to the data. These proposals were implemented in a modified version of an analytical technique called Mean phase difference. We used both real and generated data to illustrate how unjustified extrapolations may lead to inappropriate quantifications of effect, whereas our proposals help avoid these issues. The new techniques are implemented in a user-friendly website via the Shiny application, offering both graphical and numerical information. Finally, we point to an alternative not requiring either trend line fitting or extrapolation.

Quantifying differences between conditions in single-case designs: Possible analysis and meta-analysis.

The current paper is a call for and illustration of a way of closing the gap between basic research and professional practice in the field of neurorehabilitation. Methodologically, single-case experimental designs and the guidelines created regarding their conduct are highlighted. Statistically, we review two data analytical options, namely (a) indices quantifying the difference between pairs of conditions in the same metric as the target behavior and (b) a formal statistical procedure offering a standardized overall quantification. The paper provides guidance in the analysis and suggests free software in order to illustrate, in the context of data from behavioral interventions with children with developmental disorders, that informative analyses are feasible. We also show how the results of individual studies can be made eligible for meta-analyses, which are useful for establishing the evidence basis of interventions. Nevertheless, we also point at decisions that need to be made during the process of data analysis.

Flow dimensions on daily activities with the Spanish Version of the Flow Scale (DFS)

A sample of 250 students of psychology with an average age of 20.37 years, answered the Flow Q questionnaire indicating their favorite flow activity, and the Spanish version of the Dispositional Flow Scale (DFS). A confirmatory factor analysis assessed the DFS construct validity of the flow model on daily activities. Both a hierarchical model of eight first order factors reflecting a second order global flow factor, and a model with eight formative first order flow dimensions, showed good fit and discriminant power. Most optimal activities were found to be individual and structured, such as studying, reading and certain forms of individual sports. Leisure activities turned out to be more rewarding than studying. Sports displayed more flow, clear goals, merging of action and awareness, and autotelic experience. Reading also showed more flow, balance of challenge and skills, feedback, merging of action and awareness, and loss of self-consciousness. On the other hand, studying displayed less flow, merging of action and awareness, and autotelic experience (AU)

No disponible

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.

Flow dimensions on daily activities with the Spanish version of the Flow Scale (DFS).

A sample of 250 students of psychology with an average age of 20.37 years, answered the Flow Q questionnaire indicating their favorite flow activity, and the Spanish version of the Dispositional Flow Scale (DFS). A confirmatory factor analysis assessed the DFS construct validity of the flow model on daily activities. Both a hierarchical model of eight first order factors reflecting a second order global flow factor, and a model with eight formative first order flow dimensions, showed good fit and discriminant power. Most optimal activities were found to be individual and structured, such as studying, reading and certain forms of individual sports. Leisure activities turned out to be more rewarding than studying. Sports displayed more flow, clear goals, merging of action and awareness, and autotelic experience. Reading also showed more flow, balance of challenge and skills, feedback, merging of action and awareness, and loss of self-consciousness. On the other hand, studying displayed less flow, merging of action and awareness, and autotelic experience.

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.

Assigning and combining probabilities in single-case studies: a second study.

The present study builds on a previous proposal for assigning probabilities to the outcomes computed using different primary indicators in single-case studies. These probabilities are obtained by comparing the outcome to previously tabulated reference values, and they reflect the likelihood of the results in the case that no intervention effect is present. In the present study, we explored how well different metrics are translated into p values in the context of simulation data. Furthermore, two published multiple-baseline data sets were used to illustrate how well the probabilities might reflect the intervention effectiveness, as assessed by the original authors. Finally, the importance of which primary indicator would be used in each data set to be integrated was explored; two ways of combining probabilities were used: a weighted average and a binomial test. The results indicated that the translation into p values worked well for the two nonoverlap procedures, with the results for the regression-based procedure diverging due to some undesirable features of its performance. These p values, when either taken individually or combined, were well aligned with effectiveness for the real-life data. These results suggest that assigning probabilities can be useful for translating the primary measure into the same metric, using these probabilities as additional evidence of the importance of behavioral change, complementing visual analysis and professionals' judgments.

A measure of group dissimilarity for psychological attributes

El funcionamiento y el rendimiento de los grupos en contextos diferentes están relacionados con el grado en que las características de los miembros son complementarias o suplementarias. El presente artículo describe un procedimiento para cuantificar el grado de disimilitud a nivel de grupo. A diferencia de la mayoría de técnicas existentes, el procedimiento que aquí se describe está normalizado y es invariante a los cambios de localización y escala. Por lo tanto, es posible comparar la disimilitud en escalas con diferente métrica y en grupos de distinto tamaño. La disimilitud está medida en términos relativos, independientemente de la posición que ocupan los individuos en la dimensión que mide la escala. Cuando no existe una justificación teórica para combinar las diversas propiedades medidas, se puede cuantificar la disimilitud para cada escala por separado. También es posible obtener las contribuciones diádicas e individuales respecto a la diversidad global y la asignada a cada escala. Las medidas descriptivas pueden ser complementadas con la significación estadística para, así, comparar los resultados obtenidos con distribuciones discretas de referencia, ya sean simétricas o asimétricas. Se ha elaborado un paquete en R que permite obtener los índices descriptivos y los valores p, además de contener las expresiones desarrolladas para simular una amplia variedad de distribuciones discretas de probabilidad(AU)

Group functioning and performance in different contexts is related to the extent to which group members are complementary or supplementary in terms of psychological attributes. This paper describes a procedure for quantifying the degree of dissimilarity at group level. Unlike most existing techniques the one described here is normalized and is both location and scale invariant, thereby making it suitable for comparing dissimilarity on interval and ratio scales with different ranges and in groups of different sizes. Dissimilarity is measured in relative terms regardless of the exact place on the scale at which individuals are located. When a combination of several scales is not theoretically justified, the dissimilarity for each scale can be quantified. Additionally, dyadic and individual contributions to either the global or scale index can be obtained. The descriptive measures are complemented by statistical significance values in order to compare the results obtained with several discrete distributions of reference, both symmetrical and skewed, which can be specified using the expressions developed. The information that can be provided by the indices and the p values - both obtainable through an R package - is illustrated using data from an empirical study (AU)

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 article 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, R2, 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 2 potentially useful methods-one based on a weighted average and the other on the binomial test.

Percepción interpersonal, personalidad y rendimiento académico: un enfoque diádico para el estudio del rendimiento de los estudiantes universitarios / Interpersonal perception, personality, and academic achievement: a dyadic approach for the study of undergraduate performance

El presente trabajo trata sobre la cuantificación de características grupales mediante índices diádicos. Concretamente, el objetivo del presente estudio fue explorar la posible relación entre indicadores diádicos e individuales de percepción interpersonal y personalidad y el rendimiento académico en grupos de trabajo en un contexto académico real. 88 estudiantes universitarios formaron 22 grupos de cuatro personas para llevar a cabo un trabajo de curso. Tras trabajar juntos durante el semestre, los participantes contestaron a un Cuestionario de Percepción Interpersonal y al cuestionario de personalidad NEO-FFI y el trabajo de curso fue evaluado. Los resultados muestran que algunos índices diádicos de percepción interpersonal están asociados a las puntuaciones obtenidas en el trabajo de curso. Además, se propone un modelo de regresión exponencial que explica el 50.3% de la variabilidad en las notas de los grupos. Los resultados para predecir el rendimiento en grupos encontrados en la literatura científica, siguiendo una perspectiva individual, no son mayores de 18%. Los resultados del presente estudio concuerdan con resultados previos obtenidos en un contexto de laboratorio y dan apoyo a la perspectiva diádica para el estudio de grupos (AU)

The present work deals with the quantification of group characteristics by means of dyadic indices. Specifically, the aim of the present study was to explore whether dyadic and individual measures of interpersonal perceptions and personality could be related to academic achievement when dealing with project groups in a real academic setting. 88 undergraduate students formed 22 groups of four people to carry out a course report. After working together throughout the semester, participants filled in an Interpersonal Perception Questionnaire and NEO-FFI and the course report was assessed. Results showed that some dyadic measurements of interpersonal perceptions are associated to the marks obtained in the course report. Furthermore, an exponential regression function is proposed accounting for 50.3% of group marks variance. The predictive results found in the scientific literature revised, that follows an individualistic approach, are no larger than 18%. The results of the present study concur with previous results obtained in a laboratory context supporting the usefulness of the dyadic approach for the study of groups (AU)

Some common indices of group diversity: upper boundaries.

Workgroup diversity can be conceptualized as variety, separation, or disparity. Thus, the proper operationalization of diversity depends on how a diversity dimension has been defined. Analytically, the minimal diversity must be obtained when there are no differences on an attribute among the members of a group, however maximal diversity has a different shape for each conceptualization of diversity. Previous work on diversity indexes indicated maximum values for variety (e.g., Blau's index and Teachman's index), separation (e.g., standard deviation and mean Euclidean distance), and disparity (e.g., coefficient of variation and the Gini coefficient of concentration), although these maximum values are not valid for all group characteristics (i.e., group size and group size parity) and attribute scales (i.e., number of categories). We demonstrate analytically appropriate upper boundaries for conditional diversity determined by some specific group characteristics, avoiding the bias related to absolute diversity. This will allow applied researchers to make better interpretations regarding the relationship between group diversity and group outcomes.

Predicting team output using indices at group level.

The present study explores the usefulness of dyadic quantification of group characteristics to predict team work performance. After reviewing the literature regarding team member characteristics predicting group performance, percentages of explained variance between 3% and 18% were found. These studies have followed an individualistic approach to measure group characteristics (e. g., mean and variance), based on aggregation. The aim of the present work was testing whether by means of dyadic measures group output prediction percentage could be increased. The basis of dyadic measures is data obtained from an interdependent pairs of individuals. Specifically, the present research was intended to develop a new dyadic index to measure personality dissimilarity in groups and to explore whether dyadic measurements allow improving groups' outcome predictions compared to individualistic methods. By means of linear regression, 49.5 % of group performance variance was explained using the skew-symmetry and the proposed dissimilarity index in personality as predictors. These results support the usefulness of the dyadic approach for predicting group outcomes.

Predicting team output using indices at group level

The present study explores the usefulness of dyadic quantification of group characteristics to predict team work performance. After reviewing the literature regarding team member characteristics predicting group performance, percentages of explained variance between 3% and 18% were found. These studies have followed an individualistic approach to measure group characteristics (e. g., mean and variance), based on aggregation. The aim of the present work was testing whether by means of dyadic measures group output prediction percentage could be increased. The basis of dyadic measures is data obtained from an interdependent pairs of individuals. Specifically, the present research was intended to develop a new dyadic index to measure personality dissimilarity in groups and to explore whether dyadic measurements allow improving groups’ outcome predictions compared to individualistic methods. By means of linear regression, 49.5 % of group performance variance was explained using the skewsymmetry and the proposed dissimilarity index in personality as predictors. These results support the usefulness of the dyadic approach for predicting group outcomes (AU)

El presente estudio explora la utilidad de la cuantificación diádica de las características grupales para predecir el rendimiento en equipos de trabajo. Tras revisar la literatura relacionada con el estudio de las características de los miembros de un grupo para predecir el rendimiento grupal, se encontraron porcentajes de varianza explicada de entre el 3% y el 18%. Estos estudios han seguido el denominado enfoque individual, fundamentado en la agregación, para resumir las características de los grupos (e. g., media y varianza). El objetivo del presente estudio es poner a prueba si, mediante medidas diádicas se puede incrementar el porcentaje de predicción del rendimiento grupal. La base de las medidas diádicas son datos obtenidos a partir de pares de individuos interdependientes. Concretamente, en la presente investigación se pretende desarrollar un nuevo índice diádico para medir disimilitud en personalidad en grupos y verificar si las medidas diádicas mejoran la predicción del rendimiento grupal en comparación con las predicciones obtenidas mediante índices basados en la perspectiva individual. Mediante regresión lineal fue explicado el 49.5% de la variabilidad en el rendimiento grupal utilizando como predictoras las medidas tomadas mediante los índices diádicos de antisimetría y disimilitud en personalidad. Estos resultados apoyan la utilidad de la perspectiva diádica para predecir el rendimiento grupal (AU)

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.

Agreement in interpersonal perception as a predictor of group performance.

The present work deals with quantifying group characteristics. Specifically, dyadic measures of interpersonal perceptions were used to forecast group performance. Forty-six groups of students, 24 of four and 22 of five people, were studied in a real educational assignment context and marks were gathered as an indicator of group performance. Our results show that dyadic measures of interpersonal perceptions account for final marks. By means of linear regression analysis, 85% and 85.6% of group performance, respectively, was explained for group sizes equal to four and five. Results found in the scientific literature based on the individualistic approach are no larger than 18%. The results of the present study support the utility of dyadic approaches for predicting group performance in social contexts.

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 about intervention effectiveness in single-case designs. Ordinary least square estimation is compared to two correction techniques dealing with general trend and a procedure that eliminates 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 approach the nominal ones in the 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.

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.

Bias and standard error for social reciprocity measurements.

The directional consistency and skew-symmetry statistics have been proposed as global measure of social reciprocity. Although both measures can be useful for quantifying social reciprocity, researchers need to know whether these estimators are biased in order properly to assess descriptive results. That is, if estimators are biased, researchers should compare actual values with expected values under the specified null hypothesis. Furthermore, standard errors are needed to enable suitable assessment of discrepancies between actual and expected values. This paper aims to derive some exact and approximate expressions in order to obtain bias and standard error values for both estimators for round-robin designs, although the results can also be extended to other reciprocal designs.

Agreement in interpersonal perception as a predictor of group performance / Concordancia en percepción interpersonal como predictora del rendimiento grupal

The present work deals with quantifying group characteristics. Specifically, dyadic measures of interpersonal perceptions were used to forecast group performance. Forty-six groups of students, 24 of four and 22 of fi ve people, were studied in a real educational assignment context and marks were gathered as an indicator of group performance. Our results show that dyadic measures of interpersonal perceptions account for final marks. By means of linear regression analysis, 85% and 85.6% of group performance, respectively, was explained for group sizes equal to four and fi ve. Results found in the scientific literature based on the individualistic approach are no larger than 18%. The results of the present study support the utility of dyadic approaches for predicting group performance in social contexts (AU)

El presente trabajo trata sobre la cuantificación de las características grupales, concretamente, en este estudio se emplearon medidas diádicas de percepción interpersonal con el objetivo de predecir el rendimiento grupal en grupos académicos. Como indicadores del rendimiento grupal se tomaron las calificaciones del curso de 46 grupos de estudiantes, 24 de cuatro y 22 de cinco participantes. Mediante regresión lineal se obtuvo un porcentaje de varianza explicada del rendimiento grupal igual al 85% en grupos de cuatro participantes, mientras para los grupos de cinco miembros fue igual al 85,6%. Los resultados encontrados en la literatura científica basados en la perspectiva individual no son superiores al 18%. Los resultados del presente estudio apoyan la utilidad del enfoque diádico para predecir el rendimiento grupal en contextos sociales (AU)

Regression-based techniques for statistical decision making in singlecase designs / Técnicas fundamentadas en la regresión para la decisión estadística en diseños de caso único

The present study evaluates the performance of four methods for estimating regression coefficients used to make statistical decisions about intervention effectiveness in single-case designs. Ordinary least square estimation is compared to two correction techniques dealing with general trend and a procedure that eliminates 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 approach the nominal ones in the 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 (AU)

El estudio evalúa el rendimiento de cuatro métodos de estimación de los coeficientes de regresión utilizados para la toma de decisiones estadísticas sobre la efectividad de las intervenciones en diseños de caso único. La estimación por mínimos cuadrados ordinarios se compara con dos métodos que controlan la tendencia en los datos y un procedimiento que elimina la autocorrelación cuando ésta es significativa. Los resultados indican que las tasas empíricas y nominales de falsas alarmas no coinciden en presencia de dependencia serial o tendencia al aplicar mínimos cuadrados ordinarios o generalizados. Los métodos que controlan la tendencia muestran tasas más bajas de error Tipo I, pero no son suficientemente sensibles a efectos existentes (cambio de nivel o de pendiente), por lo que el uso de la significación estadística de los coeficientes de regresión para detectar efectos no se recomienda cuando se dispone de series cortas de datos (AU)