Prevention of Depressive Symptoms and Promotion of Well-being in Adolescents: A Randomized Controlled Trial of the Smile Program Un ensayo controlado aleatorizado del Programa Sonrisa / Prevención de Síntomas Depresivos y Promoción del Bienestar: Un ensayo controlado aleatorizado del Programa Sonrisa

This study addressed the development and evaluation of the Smile Program whose main objective was the prevention of depression and the promotion of well-being in adolescents. The program is based on interventions that have been shown to be efficacious (a cognitive-behavioral approach). Participants were 89 adolescents (mean age = 13.88 years; SD = 0.95) recruited from a sample of 1212 students from seven schools. Results showed a significant reduction in self-reported depressive symptoms in the intervention group (n= 51) as compared to youth in the control group (n= 38). Based on parents' report (n=56), youth in the intervention group had significantly better self-esteem at post-test as compared to youth in the control group. At four months post intervention, youth in the intervention group had higher psychological well-being than those in the control group; at the 8-month follow-up, youth in the intervention condition reported better family self-concept

Este estudio consistió en describir el desarrollo y la evaluación del Programa Sonrisa cuyo principal objetivo fue la prevención de la depresión y la promoción del bienestar en adolescentes. El programa se basa en intervenciones que han demostrado ser eficaces (enfoque cognitivo-conductual). Los participantes fueron 89 adolescentes (edad media = 13,88 años, SD = 0,95) reclutados de una muestra de 1212 estudiantes de 7 escuelas. Los resultados de los autoinformes de los adolescentes mostraron una reducción significativa en los síntomas depresivos en el grupo de intervención (n = 51) en comparación con los adolescentes del grupo control (n = 38). Respecto a los cuestionarios de los padres (n = 56), se halló que los adolescentes en el grupo de intervención tuvieron una autoestima significativamente mejor en el postest en comparación con los del grupo control. Cuatro meses después del programa, los adolescentes del grupo de intervención tenían un mayor bienestar psicológico que los del grupo de control y , en el seguimiento de 8 meses, los adolescentes de la condición de intervención informaron de un mejor autoconcepto familiar

Sample size estimation for heterogeneous growth curve models with attrition.

In this study, two approaches were employed to calculate how large the sample size needs to be in order to achieve a desired statistical power to detect a significant group-by-time interaction in longitudinal intervention studies-a power analysis method, based on derived formulas using ordinary least squares estimates, and an empirical method, based on restricted maximum likelihood estimates. The performance of both procedures was examined under four different scenarios: (a) complete data with homogeneous variances, (b) incomplete data with homogeneous variances, (c) complete data with heterogeneous variances, and (d) incomplete data with heterogeneous variances. Several interesting findings emerged from this research. First, in the presence of heterogeneity, larger sample sizes are required in order to attain a desired nominal power. The second interesting finding is that, when there is attrition, the sample size requirements can be quite large. However, when attrition is anticipated, derived formulas enable the power to be calculated on the basis of the final number of subjects that are expected to complete the study. The third major finding is that the direct mathematical formulas allow the user to rigorously determine the sample size required to achieve a specified power level. Therefore, when data can be assumed to be missing at random, the solution presented can be adopted, given that Monte Carlo studies have indicated that it is very satisfactory. We illustrate the proposed method using real data from two previously published datasets.

Power analysis to detect treatment effect in longitudinal studies with heterogeneous errors and incomplete data / Análisis de potencia para detectar el efecto del tratamiento en estudios longitudinales con errores heterogéneos y datos incompletos

BACKGROUND: S. Usami (2014) describes a method to realistically determine sample size in longitudinal research using a multilevel model. The present research extends the aforementioned work to situations where it is likely that the assumption of homogeneity of the errors across groups is not met and the error term does not follow a scaled identity covariance structure. METHOD: For this purpose, we followed a procedure based on transforming the variance components of the linear growth model and the parameter related to the treatment effect into specific and easily understandable indices. At the same time, we provide the appropriate statistical machinery for researchers to use when data loss is unavoidable, and changes in the expected value of the observed responses are not linear. RESULTS: The empirical powers based on unknown variance components were virtually the same as the theoretical powers derived from the use of statistically processed indexes. CONCLUSIONS: The main conclusion of the study is the accuracy of the proposed method to calculate sample size in the described situations with the stipulated power criteria

ANTECEDENTES: S. Usami (2014) describe un método que permite determinar de forma realista el tamaño de muestra en la investigación longitudinal utilizando un modelo multinivel. En la presente investigación se extiende el trabajo aludido a situaciones donde es probable que se incumpla el supuesto de homogeneidad de los errores a través de los grupos y la estructura del término de error no sea de identidad escalada. MÉTODO: para ello, se ha seguido procedimiento basado en transformar los componentes de varianza del modelo de crecimiento lineal y el parámetro relacionado con el efecto del tratamiento en índices de fácil comprensión y especificación. También se proporciona la maquinaria estadística adecuada para que los investigadores puedan usarlo cuando la pérdida de información resulte inevitable y los cambios en el valor esperado de las respuestas observadas no sean lineales. RESULTADOS: las potencias empíricas basadas en componentes de varianza desconocidos fueron virtualmente idénticas a las potencias teóricas derivadas a partir del uso de índices estadísticos transformados. CONCLUSIONES: la principal conclusión del trabajo es la exactitud del enfoque propuesto para calcular el tamaño de muestra bajo las situaciones reseñadas con el criterio de potencia estipulado

Power analysis to detect treatment effect in longitudinal studies with heterogeneous errors and incomplete data.

BACKGROUND:  S. Usami (2014) describes a method to realistically determine sample size in longitudinal research using a multilevel model. The present research extends the aforementioned work to situations where it is likely that the assumption of homogeneity of the errors across groups is not met and the error term does not follow a scaled identity covariance structure.  METHOD:  For this purpose, we followed a procedure based on transforming the variance components of the linear growth model and the parameter related to the treatment effect into specific and easily understandable indices. At the same time, we provide the appropriate statistical machinery for researchers to use when data loss is unavoidable, and changes in the expected value of the observed responses are not linear.  RESULTS:  The empirical powers based on unknown variance components were virtually the same as the theoretical powers derived from the use of statistically processed indexes.  CONCLUSIONS:  The main conclusion of the study is the accuracy of the proposed method to calculate sample size in the described situations with the stipulated power criteria.

Un sistema de clasificación de los diseños de investigación en psicología / A classification system for research designs in psychology

En este trabajo se elabora un marco conceptual y se desarrollan unos principios básicos para fundamentar un sistema de clasificación de los diseños de investigación más usuales en psicología basado en tres estrategias (manipulativa, asociativa y descriptiva) de donde emanan varios tipos de estudios, tres para la estrategia manipulativa (experimentales, cuasiexperimentales y de caso único), tres para la asociativa (comparativos, predictivos y explicativos) y dos para la descriptiva (observacionales y selectivos) (AU)

In this work we devise a conceptual framework and develop some basic principles to promove a classification system for the most usual research designs in psychology based on three strategies (manipulative, associative and descriptive) from which emerge different types of studies, three for manipulative strategy (experimental, quasi-experimental and single-case), three for associative strategy (comparative, predictive and explanatory) and two for descriptive strategy (observational and selective) (AU)

Robust tests for multivariate factorial designs under heteroscedasticity.

The question of how to analyze several multivariate normal mean vectors when normality and covariance homogeneity assumptions are violated is considered in this article. For the two-way MANOVA layout, we address this problem adapting results presented by Brunner, Dette, and Munk (BDM; 1997) and Vallejo and Ato (modified Brown-Forsythe [MBF]; 2006) in the context of univariate factorial and split-plot designs and a multivariate version of the linear model (MLM) to accommodate heterogeneous data. Furthermore, we compare these procedures with the Welch-James (WJ) approximate degrees of freedom multivariate statistics based on ordinary least squares via Monte Carlo simulation. Our numerical studies show that of the methods evaluated, only the modified versions of the BDM and MBF procedures were robust to violations of underlying assumptions. The MLM approach was only occasionally liberal, and then by only a small amount, whereas the WJ procedure was often liberal if the interactive effects were involved in the design, particularly when the number of dependent variables increased and total sample size was small. On the other hand, it was also found that the MLM procedure was uniformly more powerful than its most direct competitors. The overall success rate was 22.4% for the BDM, 36.3% for the MBF, and 45.0% for the MLM.

Los efectos de terceras variables en la investigación psicológica / The effects of third variables in psychological research

Dada una aparente relación causa-efecto entre una variable independiente (X) y una variable de respuesta (Y), muchos investigadores se interesan en determinar el papel que juegan otras variables intervinientes (terceras variables o variables Z) en tal relación, y particularmente el papel de variables mediadoras y moderadoras. En repetidas ocasiones se ha denunciado que existe cierta confusión en lo relativo al significado y uso apropiado de los efectos de terceras variables como hipótesis causales en la investigación psicológica. En este trabajo se pretende reforzar la comprensión y utilización de algunos de los efectos debidos a terceras variables, en concreto los efectos de covariación, espuriedad o confundido, supresión, y particularmente los de mediación y moderación, concediendo especial atención a la correcta aplicación de pruebas estadísticas y a los errores que con mayor frecuencia suelen cometerse cuando se aborda un análisis causal con tales efectos. Se utiliza con esta finalidad un lenguaje sencillo mediante diagramas path que asumimos asequible al investigador aplicado y se pro-pone finalmente un diagrama de flujo con el objeto de ayudar a distinguir los efectos de las terceras variables y a facilitar la aplicación de los procedimientos estadísticos apropiados (AU)

Given a causal relationship between an independent variable (X) and a response variable (Y), the interest of some applied researchers is sometimes focused on knowing the role playing for alternative intervening variables (third variables or Z-variables), and particularly the role of mediating and moderating variables. Some influential works have repeatedly denounced that in applied psychology some confusion exists with respect to the meaning and appropriate use of third variables effects as causal hypotheses. This work is intended to reinforce the comprehension and using of five of more known effects of third variables and concretely the effects of covariation, spuriousness or confounding, suppression, and particularly of mediation and moderation, with special attention towards the application of statistical tests and the report of most common mistakes that usually appear when we tackle a causal analysis. An accessible language for applied researcher with path diagrams is used. A flow diagram is finally proposed in order to help applied researchers to distinguish between third variable effects and to make easier the application of the appropriate statistical procedures (AU)

A simulation study of rater agreement measures with 2x2 contingency tables

Mediante un estudio de simulación se aborda una comparación entre seis medidas obtenidas usando tres enfoques diferentes para la evaluación del acuerdo. Los coeficientes de acuerdo elegidos fueron Sigma de Bennet (1954), Pi de Scott (1955), Kappa de Cohen (1960) y Gamma de Gwet (2001; 2008) para representar el enfoque clásico descriptivo, el coeficiente Alfa de Aickin (1990), para representar el enfoque de los modelos loglineal y mixtura (“mixture models”) y la medida Delta de Martín and Femia (2004) para representar el enfoque de los test de elección multiple. Los resultados obtenidos confirman que los coeficientes Pi y Kappa presentan diferencias notables en relación a los restantes coeficientes particularmente en presencia de valores extremos de prevalencia y sesgo entre observadores. El mejor comportamento fue observado con los coeficientes Sigma de Bennet y Delta de Martín and Femia para todos los valores de prevalencia y sesgo entre observadores(AU)

A comparison between six rater agreement measures obtained using three different approaches was achieved by means of a simulation study. Rater coefficients suggested by Bennet’s Sigma (1954), Scott’s Pi (1955), Cohen’s Kappa (1960) and Gwet’s Gamma (2008) were selected to represent the classical, descriptive approach, Alpha agreement parameter from Aickin (1990) to represent loglinear and mixture model approaches and Delta measure from Martín and Femia (2004) to represent multiple-choice test. Main results confirm that Pi and Kappa descriptive measures present high levels of mean bias in presence of extreme values of prevalence and rater bias but small to null levels with moderate values. The best behavior was observed with Bennet and Martín and Femia agreement measures for all levels of prevalence(AU)

Estatus social, género, clima del aula y bullying entre estu-diantes adolescentes / Social status, gender, classroom climate and bullying among adolescents pupils

El presente estudio ex post facto analiza la estructura de las relaciones sociales (en términos sociométricos y afectivos) y las características del clima socio-afectivo del aula y su relación con el bullying. La muestra estuvo compuesta por 421 adolescentes de edades comprendidas entre los 14 y 17 años, de 17 grupos aula de centros españoles de educación secundaria (241 varones y 180 mujeres). El nivel de prevalencia del bullying (17.6%) se distribuye de manera similar entre agresores y víctimas. Se encontraron importantes diferencias en género: tres de cada cuatro agresores y más de la mitad de las víctimas eran chicos. Los análisis multinivel confirmaron que todos los grupos aula presentan características similares en conductas bullying. Los resultados indican que, por lo general, aquellos que están implicados en la dinámica bullying son chicos, con bajo estatus social y con una percepción del clima del aula mas negativa que los no implicados, especialmente los sujetos víctimas que muestran serias dificultades en sus relaciones intrerpersonales. Así mismo, se encontró que las chicas suelen estar mejor adaptadas al ambiente escolar. Estos datos sugieren que un conjunto de variables sociales contribuyen a mantener el bullying e incluso podrían ser la clave para explicar por qué los niveles de bullying no disminuyen sensiblemente y por qué la incidencia es mayor en los chicos que en las chicas (AU)

This ex post facto study examines how the structure of the social relations (in sociometric and affective terms) and the social-affective class-room characteristics environment are related to bullying in 421 adolescents, aged 14 to 17, from 17 group classes of Spanish Secondary school (241 males and 180 females). Level of incidence (17.6%) was similar for bullies and victims. There were important differences by gender: three in four bullies and more than a half of the victims are boys. Multilevel analyses confirmed that all the classes displayed very similar characteristics of bullying behaviour. Findings indicated that those who are involved in bully/victim problems were usually males of lower social status, with a classroom climate perception more negative than neutral or not involved pupils, and, especially victim pupils showed serious difficulties in relation-ships. It was also found that girls are better adapted and more involved in the social climate of the classroom than boys. All that results suggest that social aspects contribute to maintain bullying among peers, and it may be a clue to explain why levels of bullying do not decrease and why the incidence is higher among boys than among girls (AU)

Análisis de la relación entre el estado de ánimo y las conductas de adherencia en deportistas lesionados / Analysis of the relationship between mood states and adherence behavior in injured athletes

El objetivo del presente estudio es analizar la relación entre diferentes estados de ánimo (tensión, depresión, cólera, vigor y fatiga) y el nivel de adherencia al programa de rehabilitación de los deportistas lesionados. La muestra está formada por 5 deportistas federados en distintas disciplinas, de edades comprendidas entre los 17 y los 21 años, con lesiones moderadas o graves. Tanto los estados de ánimo como la adherencia a la rehabilitación se han evaluado de forma continuada durante 15 días. Los resultados indican que tensión, depresión y cólera muestran una evolución inversa respecto al nivel de adherencia en todos los momentos del proceso de recuperación; por el contrario, tanto vigor, como fatiga muestran una evolución paralela, de manera que cuanto mayor es el nivel de adherencia, mayores son las puntuaciones en vigor y fatiga. Se discute sobre la influencia de los estados de ánimo, asociados a la lesión, en las conductas de adherencia del deportista; parece que pueden frenar su proceso de recuperación, por lo que puede ser beneficioso intervenir sobre estos aspectos psicológicos durante el proceso de rehabilitación(AU)

The purpose of the present study was to analyze the relation-ship between different mood states (tension, depression, anger, vigor, and fatigue) in injured athletes and the athletes' level of adherence to a rehabilitation program. The sample consisted of five federated athletes of different sports between the ages of 17 and 21 years who suffered from moderate or serious injuries. Both the mood states and the rehabilitation adherence were evaluated continuously for 15 days. The results indicate that tension, depression, and anger progress inversely with regard to the level of adherence throughout the process of recuperation. On the other hand, vigor and fatigue demonstrate a parallel progression, such that when the level of adherence is greater, the vigor and fatigue cited by the athletes is also greater. The influence of mood states, associated with the injury, in the adherence behaviors of the athlete is discussed. It seems that they can slow the athletes' process of recuperation; therefore, it may be beneficial for intervention regarding these psychological aspects during the rehabilitation process (AU)

A robust approach for analyzing unbalanced factorial designs with fixed levels.

The goal of this study was to investigate the performance of Hall's transformation of the Brunner-Dette-Munk (BDM) and Welch-James (WJ) test statistics and Box-Cox's data transformation in factorial designs when normality and variance homogeneity assumptions were violated separately and jointly. On the basis of unweighted marginal means, we performed a simulation study to explore the operating characteristics of the methods proposed for a variety of distributions with small sample sizes. Monte Carlo simulation results showed that when data were sampled from symmetric distributions, the error rates of the original BDM and WJ tests were scarcely affected by the lack of normality and homogeneity of variance. In contrast, when data were sampled from skewed distributions, the original BDM and WJ rates were not well controlled. Under such circumstances, the results clearly revealed that Hall's transformation of the BDM and WJ tests provided generally better control of Type I error rates than did the same tests based on Box-Cox's data transformation. Among all the methods considered in this study, we also found that Hall's transformation of the BDM test yielded the best control of Type I errors, although it was often less powerful than either of the WJ tests when both approaches reasonably controlled the error rates.

Some factors in sanctions for unsportsmanlike behavior of players and coaches in youth soccer.

Reasons and motives for sanctions imposed on players and coaches in youth soccer were examined to evaluate frequency and type of infraction by competition category (Under 12, 13-14, 15-16, and 17-18 years). Analysis of the first 30% of competitions yielded 1,202 sanctions of 340 teams with 6,120 players and 340 coaches. For older groups, the number of sanctions for aggressive conduct by the players was significantly higher; frequency of sanctions imposed on the coaches for disrespect also was significantly higher, and those for aggression were higher although not significantly so; the number of sanctions for disrespect by players was not different. Transgressions of the game rules recorded by officials are a valid representation of a pedagogical factor important for coaches and players. Implementing informative programs for knowledge and conduct of rules is suggested.

A practical method for analyzing factorial designs with heteroscedastic data.

The Type I error rates and powers of three recent tests for analyzing nonorthogonal factorial designs under departures from the assumptions of homogeneity and normality were evaluated using Monte Carlo simulation. Specifically, this work compared the performance of the modified Brown-Forsythe procedure, the generalization of Box's method proposed by Brunner, Dette, and Munk, and the mixed-model procedure adjusted by the Kenward-Roger solution available in the SAS statistical package. With regard to robustness, the three approaches adequately controlled Type I error when the data were generated from symmetric distributions; however, this study's results indicate that, when the data were extracted from asymmetric distributions, the modified Brown-Forsythe approach controlled the Type I error slightly better than the other procedures. With regard to sensitivity, the higher power rates were obtained when the analyses were done with the MIXED procedure of the SAS program. Furthermore, results also identified that, when the data were generated from symmetric distributions, little power was sacrificed by using the generalization of Box's method in place of the modified Brown-Forsythe procedure.

Análisis comparativo de tres enfoques para evaluar el acuerdo entre observadores / Comparative analysis of three approaches for rater agreement

En este trabajo se realiza un análisis comparativo de tres enfoques generales para evaluar el acuerdo entre observadores que originan tres tipos diferentes de medidas: descriptivas (coeficientes sigma, pi y kapa), basadas en modelos loglineales y basadas en modelos con mezcla (mixture) de distribuciones. Aunque los enfoques loglineal y mixture asumen un concepto de corrección del azar diferente, la flexibilidad de ambos enfoques permite utilizar sus parámetros para realizar un análisis en profundidad de las pautas de acuerdo y desacuerdo. Se demuestra que las medidas descriptivas pueden obtenerse introduciendo restricciones al modelo loglineal de cuasi-independencia. Y que aunque los enfoques loglineal y mixture tienen una interpretación similar cuando todos los parámetros diagonales son positivos, su interpretación difiere en caso contrario debido a la diferente escala de medida utilizada

This work is a comparative analysis of three general approaches for rater agreement measurement which produce three different statistical coefficients: descriptive (sigma,pi y kappa coefficients), based on log-linear models and on mixture models. Although loglinear and mixture approaches assume a different concept of chance correction, their flexibility allow using its parameters to analyze agreement and disagreement patterns. We show that all descriptive measures can also be obtained by introducing constraints to a basic loglinear (or mixture) quasi-independence model. Due to the different measurement scale used, both loglinear and mixture approaches have a similar interpretation when diagonal parameters are positive but a different interpretation otherwise

Procedimientos para detectar y medir el sesgo entre observadores / Methods for detecting and assessing the interrater bias

En este trabajo se realiza un análisis de los distintos métodos para detectar y medir el sesgo entre observadores desde dos perspectivas básicas: el enfoque clásico, fundamentado en índices descriptivos y el enfoque del modelado, fundamentado en modelos loglineales. Se demuestra que estas medidas no son satisfactorias para detectar y medir el sesgo de forma unívoca porque presentan resultados contradictorios y se proponen nuevas alternativas a desarrollar que permitan descomponer correctamente error de medida y sesgo

In this paper we present an analysis of the different methods commonly used to detect and assess interrater bias from two basic perspectives: classical approach based on descriptive-type criteria and loglinear model approach. We show that all these procedures are not satisfactory for the detection and measurement of observer bias in a univoque way due to contradictory results. We propose some new alternatives to develop which allow the correct separation of bias and measurement error

Diferencias individuales en la competencia lingüística de los sujetos referenciales y expresivos / Individual differences in the linguistic competence of referential and expressive subjects

El objetivo de este trabajo fue examinar, mediante un estudio longitudinal, las diferencias individuales de los estilos lingüísticos referencial y expresivo. Se analizó la composición del vocabulario en el período de las primeras 50 palabras, la frecuencia de gestos comunicativos, el estilo de conversación de la díada y la cantidad de vocabulario producido por los niños entre los 12 y los 24 meses de edad. El vocabulario se recogió mediante una entrevista a los padres y analizando la interacción madre-hijo en el laboratorio. Se encontraron diferencias significativas en el vocabulario de los niños referenciales y expresivos respecto a la cantidad de nombres comunes y frases hechas, y en la producción de gestos comunicativos, así como en el estilo de conversación. Los niños referenciales y sus madres utilizaron más frecuentemente el gesto de señalar que los expresivos y sus madres. Además, las madres de los niños referenciales utilizaron más el refundido

The aim of this work was to examine individual differences in referential and expressive style through a longitudinal study. The composition of the first 50 words, communicative gestures, the conversational style of dyads and the percentage of vocabulary produced from 12 to 24 month-olds were analyzed. The vocabulary was collected through interviews to parents and sessions of mother-infant interaction in the laboratory. Significant differences in the proportion of common nouns and frozen phrases between referential and expressive children in the frequency of communicative gestures and style conversation were found. Thus, referential children and their mothers used more pointing gestures than the expressive children and their mothers. Additionally, mothers of referential children used completing more frequently

[Individual differences in the linguistic competence of referential and expressive subjects]. / Diferencias individuales en la competencia lingüística de los sujetos referenciales y expresivos.

The aim of this work was to examine individual differences in referential and expressive style through a longitudinal study. The composition of the first 50 words, communicative gestures, the conversational style of dyads and the percentage of vocabulary produced from 12 to 24 month-olds were analyzed. The vocabulary was collected through interviews to parents and sessions of mother-infant interaction in the laboratory. Significant differences in the proportion of common nouns and frozen phrases between referential and expressive children in the frequency of communicative gestures and style conversation were found. Thus, referential children and their mothers used more pointing gestures than the expressive children and their mothers. Additionally, mothers of referential children used completing more frequently.

[Comparative analysis of three approaches for rater agreement]. / Análisis comparativo de tres enfoques para evaluar el acuerdo entre observadores.

This work is a comparative analysis of three general approaches for rater agreement measurement which produce three different statistical coefficients: descriptive (sigma, pi y kappa coefficients), based on log-linear models and on mixture models. Although loglinear and mixture approaches assume a different concept of chance correction, their flexibility allow using its parameters to analyze agreement and disagreement patterns. We show that all descriptive measures can also be obtained by introducing constraints to a basic loglinear (or mixture) quasi-independence model. Due to the different measurement scale used, both loglinear and mixture approaches have a similar interpretation when diagonal parameters are positive but a different interpretation otherwise.

Modified Brown-Forsythe Procedure for Testing Interaction Effects in Split-Plot Designs.

The standard univariate and multivariate methods are conventionally used to analyze continuous data from groups by trials repeated measures designs, in spite of being extremely sensitive to departures from the multisample sphericity assumption when group sizes are unequal. However, in the last 10 years several authors have offered alternative solutions to these tests that do not rest on this assumption. In an attempt to improve the precision of the Brown-Forsythe (BF) procedure, a new approximate degrees of freedom (df) approach is presented in this article. Unlike the BF test, the new method not only assures that the df will be always positive but also provides invariant solutions under linear transformations of the data. Monte Carlo methods are used to compare the new solution, in terms of control of Type I error rates, with the modified empirical generalized least squares and BF methods. Our extensive numerical studies show that the modified BF procedure outperformed the other two methods for a wide range of conditions.