The research design used for this study was mixed methods as described by Creswell  and Creswell and Plano Clark . The theory that underpins mixed methods research presumes that the collection and analysis of data consists of the combination of both qualitative and quantitative methods . The design of this study was ‘sequential exploratory’, which is a two-stage design that involves using the results of the first method, the qualitative study, to build into or form the basis for the second method, the quantitative study .
The measures of child participation used in this study were based on previous work on children’s perspectives on school participation. An initial qualitative participative study facilitated a three-phase participative design, which actively engaged children in describing and defining what participation in school means from their own perspectives. Three schools were randomly selected from the Irish Department of Education National Primary Schools list. Workshops were organised with children aged 9–13 years in nine class groups in the three primary schools (n = 248) to gather conceptualisations and descriptions of participation in school from children’s perspective. The conceptualisations of school participation from children’s perspectives  formed the basis of the measurement of children’s participation in this study and were used for the development of the survey instrument. Participation in decision-making processes did not arise from the children’s conceptualisations but was added in order to more adequately represent conceptualisations of participation extant in the literature [7, 13]. This paper presents quantitative data collected by questionnaires.
The working definition of participation in school employed in this study comprised the general participation of pupils in everyday school life (including school activities and school events); decision-making by pupils; interpersonal relationships in the school environment; having a sense of belonging and ensuring equal participation of all pupils within the school.
Participants comprised of 231 pupils aged 9–13 years in 4th, 5th and 6th classes who were recruited from nine primary schools. Three of the nine schools were designated as Health Promoting Schools (HPS) (one with only male pupils, one with only female pupils and one co-educational). The HPS were identified by the Health Promotion Department of the Health Services Executive (West) as schools that were currently actively engaging with the HPS principles, with the support of professional health promotion staff. Each HPS was matched by gender and location (i.e., urban/rural) against two NHPS in the county, which were randomly selected from the Department of Education primary school list.
Ethical approval for the study was granted by the National University of Ireland, Galway Research Ethics Committee. Following agreement from the principals of the schools to participate, introduction letters and information sheets were sent to schools, parents and pupils. Active consent was sought from parents and pupils. Parents were requested to return consent forms for their child to the class teacher. Only pupils whose parents gave consent, and who themselves also assented to participate by signing a consent form, completed the questionnaire.
Confidentiality of the data provided was assured and all questionnaires were anonymous. All questions were piloted before questionnaires were distributed to pupils during the school day.
Three key steps were taken to pilot the survey instrument. Initially, the questionnaire was reviewed by colleagues who are working in children’s research. Their suggestions and comments on clarity and question format informed revisions to the questionnaire. The questionnaires were then piloted in a primary school with pupils from 4th, 5th and 6th class (ages 10–12 years) - a similar population to the participants in the main study. An information sheet about the study was provided to the school, teacher and pupils. Pupils were also informed that all the information from the questionnaire would be kept confidential, that taking part in the pilot was totally voluntary and that they did not have to answer any question they did not want to, or, indeed, to take part at all. The pilot questionnaires were self-administered and pupils were informed that filling in each pilot questionnaire could take about 20 minutes long, but this was one of the things that we wanted to test. A total of 27 primary school pupils participated in the pilot study.
After completing the questionnaire pupils were asked how well they understood the questionnaire, if there were any difficult words and how long it took them to complete the questionnaire (the time that each pupil returned their completed questionnaire was also recorded on their sheets). Based on feedback from the pupils, ambiguous questions were either reframed or removed and difficult words were re-worded. Third, the pilot questionnaire was again given to colleagues to validate the questions after revision. Further comments and suggestions were used to revise the questionnaire before data collection (see Additional file 1).
Ten scales were constructed for the study and were grouped under three conceptual definitions: school participation, school socio-ecological environment (see Additional file 2) and pupil health and well-being. Negative worded items were reversed before total scores were computed for each scale and normality of scores was assessed; scale reliability was assessed to determine the scale’s internal consistency. The statistical indicator used to assess the scales’ internal consistency was the Cronbach’s alpha coefficient. Values above .6 were considered acceptable for internal consistency reliability for the scales. It has been suggested that scales with smaller number of items could have low Cronbach’s alpha coefficient values  as recorded in the parents’ participation in school scale. The multicollinearity of the variables was computed to show the correlations between the independent variables and the dependent variable. The tolerance value, showing how much of the variability of a stated independent variable (IV) is not explained by other independent variables in the template (that is 1-R2 for each variable) were higher than .10 for each scale, suggesting that the multiple correlation with other IV is low thereby signifying no possibility of multicollinearity . The VIF (Variance inflation factor) values (the opposite of the Tolerance value = 1/Tolerance), were all below 10, which indicated that IV were not highly correlated.
School participation was measured with four scales, each assessing different dimensions of school participation; ‘participation in school decisions and rules’ comprised a six-item scale (Cronbach’s Alpha (CA) = 0.646) - one of these items (Students take part in making school rules) was drawn from the 2010 Health Behaviour in School-aged Children study [15, 16]; ‘Participation in school activities’ comprised eight items (CA = 0.604) (school activities were described in terms of activities that were part of every day school life, for example, arts, physical education, music, sports, drama, school tours and after school activities); ‘Participation in school events’ comprised six items (CA = 0.623) (school events were described as special events organised by schools, for example, sports day) and ‘Positive perception of school participation’ scale contained six items (CA = 0.772) (positive perception of school participation were described in terms of pupils’ perception of feeling happy about their level of participation in school).
Socio-ecological environment of school
Socio-ecological indicators were assessed by five scales: the intrapersonal - ‘perception of school’ (CA = 0.834); the interpersonal - ‘perceptions of class relationships’ (CA = 0.806) and ‘relationship with teacher’ (CA = 0.886); the school organisation - ‘perception of school policy’ (CA = 0.605); and the community - factors ‘parents’ participation in school life’ (CA = 0.584).
Pupil health and well-being
Outcome measures comprised pupils’ perceptions of their health and well-being and were measured using four questionnaire items: ‘perceived general health’, ‘self-reported happiness’, ‘self-esteem’ and ‘life satisfaction’. These items were drawn from the 2010 Health Behaviour in School-aged Children study [15, 16]. ‘Perceived general health’ and ‘self-reported happiness’ both had four response options, ‘self-esteem’ had five response options and ‘life satisfaction’ had eleven response options. The life satisfaction scale was collapsed into five groups and relabelled to ensure that life satisfaction did not have an undue influence on the overall scores. Each item was coded or recoded from low to high and then the individual scores of the four items were collapsed into a single scale with CA = 0.723.
Pupils were asked to report their age, gender and class group.
Associations between school participation, socio-ecological indicators, outcome measures and demographic indices were assessed using chi-square and odds ratios from logistic regression binary models. Logistic regression analysis included health and well-being outcome measures and socio-ecological dimensions of school life indicators as binary dependent variables and school participation scales as independent variables.
Analysis was conducted using SPSS version 20. Each scale item was checked for reliability to determine the scale’s internal consistency; that is, the degree to which all the items that made up each scale measured the same underlying concept. Data were screened for outliers, skewness, kurtosis and multicollinearity [14, 17, 18]. Eight cases identified as extreme outliers were removed thus reducing the total sample from 231 to 223. Total scores were computed for each scale and normality of scores was assessed.
The dependent variable scale scores were dichotomised into ‘high’ and ‘low’. The median values of the dependent variable scale scores were used as cut-off values to dichotomise into ‘high’ (the median value score and above) and ‘low’ (below the median value score). All analyses were conducted separately by gender and school category (i.e., boys and girls or HPS and NHPS). Each row in the logistic regression tables below denotes a separate logistic regression model.