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

satisfaction = 0.80; autonomy satisfaction = 0.77; relatedness satisfaction = 0.67; mastery cli- mate = 0.66; performance climate = 0.58). In the halved sample validation, a two-step cluster analysis also produced a final cluster solution with three similar/identical profiles (silhouette measure value = 0.3) and characteristics. Based on MANOVA, clustering variables were significantly different between clusters (Pil- lai’s Trace = .82, F (16, 5106) = 222.93, p < .001). Follow-up ANOVA’s with Games-Howell post-hoc tests revealed significant differences between all three profiles on each of the eight clustering variables (see Table 3), supporting the three-cluster solution. Based on the scores on the clustering variables, the first profile 1 was labelled negative per- ceivers, the second profile was labelled moderate perceivers, and the third profile was labelled positive perceivers. The labels are based on the relative differences between the clusters rather Fig 1. Graphic display of profiles based on eight motivational factors. AUTs = Autonomy satisfaction; COMs = Competence satisfaction; RELs = Relatedness satisfaction; MASc = Mastery Climate; AUTf = Autonomy frustration; COMf = Competence frustration; RELf = Relatedness frustration; PERc = Performance Climate. https://doi.org/10.1371/journal.pone.0228859.g001 Table 3. Descriptive statistics for the three profiles emerged from two-step cluster analysis. Overall Profile 1 negative perceivers (n = 834) Profile 2 moderate perceivers (n = 1080) Profile 3 positive perceivers (n = 648) M SD M SD M SD M SD p F ω

Autonomy satisfaction 3.17 .77 2.61a .77 3.19b .56 3.86c .61 p < .001a-b, a-c, b-c 678.22 .59 Autonomy frustration 2.49 .83 3.27a .83 2.42b .58 1.61c .52 p < .001a-b, a-c, b-c 1172.56 .69 Competence satisfaction 3.44 .80 2.81a .80 3.55b .55 4.07c .59 p < .001a-b, a-c, b-c 712.73 .60 Competence frustration 2.24 .96 2.99a .96 2.12b .59 1.48c .52 p < .001a-b, a-c, b-c 833.45 .63 Relatedness satisfaction 3.78 .84 3.19a .84 3.90b .52 4.31c .57 p < .001a-b, a-c, b-c 572.85 .56 Relatedness frustration 1.90 .78 2.48a .78 1.81b .46 1.33c .41 p < .001a-b, a-c, b-c 744.28 .61 Mastery climate 3.84 .73 3.38a .73 3.85b .53 4.41c .45 p < .001a-b, a-c, b-c 561.89 .55 Performance climate 2.13 .74 2.59a .74 2.08b .51 1.63c .49 p < .001a-b, a-c, b-c 484.02 .52 Note. Means and SD’s were on a 5-point Likert scale. a-b, a-c, b-c indicate significant differences between profiles based on Games-Howell post-hoc tests. https://doi.org/10.1371/journal.pone.0228859.t003 Similar but different PLOS ONE | https://doi.org/10.1371/journal.pone.0228859 February 10, 2020 8 / 17