Similar but different: Profiling secondary school students based on their perceived motivational climate and psychological need-based experiences in physical education

dancing, gymnastics, etc.)’. The response options were (1) ‘Less than 1 time a week on average’; (2) 1 or 2 times a week on average; (3) ‘3 or more times a week on average’. Data analysis An exploratory cluster analysis was used to group students into homogeneous clusters repre- senting similar perceptions of the motivational PE learning climate. Cluster analysis is a conve- nient method for identifying groups of individual students that are similar to each other but different from individuals in other groups [59]. The clustering variables in this study were autonomy satisfaction, autonomy frustration, competence satisfaction, competence frustra- tion, relatedness satisfaction, and relatedness frustration based on the theoretical framework of the self-determination theory, together with the variables mastery climate and performance climate based on the achievement goal theory. The two-step cluster analysis procedure using the log-likelihood measure was conducted. This procedure automatically clusters similar groups of respondents within data sets [60]. The first step of the two-step procedure is assigning the original cases to pre-clusters based on dis- tance measure in order to reduce the size of the matrix that contains distances between all pos- sible pairs of cases. In the second step, the standard hierarchical clustering algorithm was used on the pre-clusters resulting from the first step, to define the optimal number of clusters. The Schwarz Bayesian information criterion (BIC) was used to determine the optimal number of

clusters. The BIC is considered as an objective and useful selection criterion [61,62,63]. After the first cluster solution was formed measures of validity were applied. First, following recommendations of Norusis [60] and Dietrich, Rundle-Thiele & Kubacki [64], the silhouette measure of cohesion and separation was conducted to measure the validity of the within and between cluster distances. Second, a multivariate analysis of variance (MANOVA) was per- formed to assess latent differences among clusters. Followed-up by analysis of variances (ANOVA) on each cluster variable to assess significant differences among cluster solutions. Subsequently, the input (predictor) importance was measured to determine the importance of variables in a cluster. Third, the data-set was randomly split into two (using ‘select cases’ option in SPSS) and another two-step cluster analysis was performed to provide the last valida- tion measure. To present the characteristics of the final clusters descriptive statistics were carried out. Each profile was then labelled based on the motivational variable scores and with which the students in that profile were characterized. Chi-squared tests (p<0.05 was considered signifi- cant) with post hoc testing (through z-scores and adjusted p-values; Bonferroni-method), and one-way ANOVA were used to examine the possible link between profile membership and demographic characteristics (i.e., gender, age), motivational characteristics (i.e., achievement goal orientation, motivational regulation), and PE-related characteristics (i.e., leisure time

sport participation and valuation of PE). Results In total 2,562 students were included, whilst data from 268 students was deleted because of invalid, partially completed questionnaires. The two-step cluster analysis identified three meaningful clusters based on Schwarz’s BIC and the highest Log-likelihood distance measures. In clusters 1, 2, and 3, there were 834 (32.5%), 1,080 (42.2%), and 648 (25.3%) students, respec- tively. In Fig 1, the three clusters and their results in the clustering variables are presented. This three-cluster solution was deemed acceptable based on the silhouette measure value of 0.3. The variable importance rating was 0.58 or higher for all variables (i.e., autonomy satisfac- tion = 1.00; competence frustration = 0.91; relatedness frustration = 0.83; competence Similar but different PLOS ONE | https://doi.org/10.1371/journal.pone.0228859 February 10, 2020 7 / 17