Design and analysis of fractional factorial experiments from the viewpoint of computational algebraic statistics

We give an expository review of applications of computational algebraic statistics to design and analysis of fractional factorial experiments based on our recent works. For the purpose of design, the techniques of Gr\"obner bases and indicator functions allow us to treat fractional factorial designs without distinction between regular designs and non-regular designs. For the purpose of analysis of data from fractional factorial designs, the techniques of Markov bases allow us to handle discrete observations. Thus the approach of computational algebraic statistics greatly enlarges the scope of fractional factorial designs.Comment: 16 page

Functional Factorial K-means Analysis

A new procedure for simultaneously finding the optimal cluster structure of multivariate functional objects and finding the subspace to represent the cluster structure is presented. The method is based on the $k$-means criterion for projected functional objects on a subspace in which a cluster structure exists. An efficient alternating least-squares algorithm is described, and the proposed method is extended to a regularized method for smoothness of weight functions. To deal with the negative effect of the correlation of coefficient matrix of the basis function expansion in the proposed algorithm, a two-step approach to the proposed method is also described. Analyses of artificial and real data demonstrate that the proposed method gives correct and interpretable results compared with existing methods, the functional principal component $k$-means (FPCK) method and tandem clustering approach. It is also shown that the proposed method can be considered complementary to FPCK.Comment: 39 pages, 17 figure

Properties of Factorial Cumulant to Factorial Moment Ratio

It is shown that the ratio of factorial cumulant moments to factorial moments for a multiplicity distribution truncated in the tail reveals oscillations in sign similar to those observed in experimental data. It is suggested that this effect be taken into account in the analysis of data in order to obtain correct physical information on the multiplicity distributions.Comment: (LaTeX + epsfig, 8 pages including 3 PostScript figures, all encoded via uufiles), DFTT 46/9

Adaptation and Validation the State Mindfulness Scale (SMS) to Physical Education in a Spanish Context

The aim of this study is to validate and adapt to the Spanish context of Physical Education (PE) the State Mindfulness Scale (SMS). The study included 1428 students aged 13–19. In order to analyse the psychometric properties of the SMS, an exploratory factorial analysis was carried out to confirm the presence of two factors, a confirmatory factorial analysis that has offered support for both the structure of two factors. We also included an analysis of temporal stability, an analysis of invariance across gender, an analysis of internal consistency and an analysis of predictive validity through a t-test in which mental health (β = −0.28, p < 0.001) and physical or bodily experience (β = −0.16, p < 0.001) negatively predicted anxiety, respectively. The structure of the questionnaire was valid and reliable, gender-neutral and with adequate levels of temporal stability

The development and validation ofscale for assessing peer-mentoring processes in programs for first-year university students

Introduction. This study focuses on the development and validation of the Mentoring Processes Assessment Questionnaire –MPAQ- designed to assess mentoring processes in peermentoring programs aimed at first-year university students.Method. Participants in the study were 354 first-year students from a broad set of degrees at the University of Valencia in the 2013-14 and 2014-15 access cohorts. The factorial structure of the MPAQ was analyzed using both Exploratory and Confirmatory Factorial Analyses. A multi-group analysis was performed on the MPAQ to examine the factorial invariance and test the equivalence/non-equivalence of its structure across the participants’ sex and age. The reliability of the factorial solution was also tested. Lastly, concurrent validity was assessed by examining the MPAQ relationships with (a) students’ satisfaction with the program and the processes of mentoring and, (b) different psychosocial variables related to the permanence in the studies evaluated through the College Persistence Questionnaire.Results. The one-dimensional structure of MPAQ was confirmed, as well as its factorial invariance across sex and age. The reliability obtained was also adequate. Regarding concurrent validity, significant and positive relationships with students’ satisfaction with the program and the processes of mentoring, academic and social integration, institutional commitment and satisfaction with support services were found.Discussion or Conclusion. Results highlight the MPAQ as a valid and reliable instrument for assessing peer-mentoring processes in programs for first-year university students and its potential usefulness in predicting retention after the first year of university, given its significant relationship with the psychosocial and emotional dimensions directly related to this phenomenon.Introducción. Se presenta el proceso de desarrollo y validación del Cuestionario de Evaluación de los Procesos de Mentorización –CEPM- en los programas de mentorías entre iguales dirigidos a estudiantes de nuevo acceso a la universidad.Método. En el estudio participaron 354 estudiantes de nueva incorporación a la universidad a un amplio conjunto de titulaciones de la Universidad de Valencia de las cohortes de acceso 2013-14 y 2014-15. Se analizó su estructura factorial a través de técnicas de análisis factorial exploratorio y confirmatorio. Se aplicó un análisis multigrupo con el objetivo de analizar su invarianza factorial y comprobar su equivalencia/no-equivalencia estructural en función del sexo y edad de acceso a la universidad de los participantes, comprobando también la fiabilidad de la solución factorial obtenida. Por último, se analizó la validez concurrente del CEPM a partir de examinar sus relaciones con (a) la satisfacción de los estudiantes con los procesos de mentorizacion y (b) con distintas variables psicosociales relacionadas con la permanencia en los estudios evaluadas a través del College Persistence Questionnaire.Resultados. Se constató la estructura unidimensional del CEPM, sus adecuados niveles de fiabilidad, así como su invarianza factorial en función del sexo y de la edad de acceso a la universidad de los estudiantes. Con respecto a su validez concurrente, se obtuvieron relaciones significativas positivas de las puntuaciones en el CEPM con el nivel de satisfacción de los estudiantes con el programa de mentorización, con sus niveles de integración académica y social, así como con sus niveles de compromiso institucional y satisfacción con los servicios de apoyo al estudiante proporcionados por la universidad.Discusión y conclusiones. El CEPM constituye un instrumento válido y fiable para evaluar los procesos de mentorizacion en los programas de mentoría a través de iguales dirigidos a estudiantes de nuevo acceso a la universidad, constatándose su validez convergente con los principales constructos psicológicos relacionados con la permanencia en los estudios universitarios