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Name: Seong Kwan Cho
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Summary
According to the results of previous research, increased anxiety and attentional focus on
performance caused performance degradation under pressure and additional resource allocation
mediated between anxiety and performance. These results have been well explained by explicit
monitoring hypothesis (EMH) and processing efficiency theory (PET) in sport psychology
literature.
As an extension study of previous research, the purpose of this study was to examine the
prediction of EMH and PET of performance changes in threatening conditions with attentional
focus manipulation. In terms of the prediction of EMH, it was hypothesized that the skill-focused
situation in high-threat conditions would be most disruptive to driving performance. PET would
also predict that driving performance in both dual-task situations would be similar under the
similar level of attentional demands, and increased anxiety would be a positive effect on driving
performance as increased effort to allocate additional attentional resources. Therefore, driving
performance in high-threat conditions with greater mental effort would be similar to low-threat
conditions in the dual-task situation.
Twenty-four female participants (Mage = 19.04 years; SD = 1.62) took part in this study
with a mean of 1.91-year driving experience (SD = 0.74). The selection criteria was that the
participants had no driving game experience and had general video game usage less than once
per week or preferably no usage. The reason only female participants were recruited was based
on the results of previous research that women had both higher state and trait anxiety scores than
men had and thus the manipulation of anxiety might be more effective to them.
For the driving task, a motorsport video game was used and the apparatus included a
steering wheel with force feedback, pedals, and rally car seat. To eliminate any confounding
variable, all participants drove the same course, a 3 km circuit with 32 curves and no long
straight sections, with the same conditions.
As an alternative and shorter version of CSAI-2, the Mental Readiness Form-Likert
(MRF-L) containing three scales (i.e., cognitive and somatic anxiety, and self-confidence) was
used to test participants’ level of anxiety using an 11-point Likert scale. Additionally, the Rating
Scale for Mental Effort (RSME) was used to measure the amount of mental effort the
participants thought they invested in each condition in this study. Regarding measures of the
primary task (i.e., single task) and secondary tasks (i.e., tone recognition and hand position tasks)
in each condition, completion time was recorded and used for the primary task performance data,
while time and response accuracy was measured for the secondary tasks.
This study consisted of three tasks with two conditions: single, distraction (tone
recognition), and skill-focused (hand position) tasks with either low- or high-threat conditions. In
the low-threat condition, the participants received nonevaluative instructions (i.e., the purpose of
this study would be to gather the characteristics of their driving), whereas they received
evaluative instructions (i.e., their driving performance would be recorded and receive the
monetary reward if improving their performance) in the high-threat condition. In the distraction
task, the participants were asked to answer a reference tone while driving. In the skill-focused
task, the participants responded the position of their left hand on the steering wheel when hearing
a tone while driving. In the primary task performance, the participants were asked to drive the
course as quickly as possible.
Results of MRF-L showed that the manipulation of the anxiety conditions was effective.
That is, the participants had higher scores of anxiety in the high-threat condition than the lowthreat condition. The driving task results showed that the participants maintained their
Name: Seong Kwan Cho
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performance in the high-threat condition compared to the low-threat condition. This result
supported the prediction of PET rather than the EMH in that the performance in the high-threat
condition in both distraction and skill-focused tasks was not significantly slower than the lowthreat condition. Results of RMSE also supported the PET in that the participants’ effort in the
high-threat condition was greater than the low-threat condition.
Critique
I believe that the authors designed this study well and clearly explained how they
conducted the experimental manipulation even though there is minor confusion. This study again
has many strengths. For example, although recruiting both male and female participants for
future research is more meaningful to test the purpose of this study and to generalize results,
selecting only female participants is reasonable because the authors explained gender effects on
anxiety-performance relationship. The selection criteria was also very clear. Providing training
sessions for the participants to obtain the similar/same baseline ability was a very nice way to
maintain the validity of this study. Owing to the authors’ endeavor on the detailed explanation of
the procedures and experimental manipulations, replication research of this study would be
possible in future.
I think that this article contains one issue that may arise from two potential factors. The
first factor is the authors’ misinterpretation of MRF-L. Even though the results of MRF-L
showed the experimental manipulation was successful, I do not fully agree with the authors’
interpretation. The mean of the cognitive anxiety scores in the high-threat condition was below
the half point of the Likert scale (i.e., an 11-point Likert scale was used for MRF-L and the mean
was 5.08). It means that the participants in the high-threat condition might not actually perceive
their anxiety level as a highly anxious state. Even though the anxiety scores in the high-threat
condition were higher than the low-threat condition, the participants were not anxious enough to
be choked or to degrade their driving performance.
Second, using MRF-L to test the level of cognitive state anxiety itself was problematic.
MRF-L contains three factors (i.e., cognitive, somatic, and confidence) as well as CSAI-2, and
including the factor of self-confidence into CSAI-2 was inappropriate as we discussed in class.
Additionally, in MRF-L each factor includes only one item. Even though the authors cited
Krane’s work for validation of MRF-L, it may not reflect the correct concept of cognitive state
anxiety, especially in this study. For example, the participants in the high-threat condition might
have the low levels of both cognitive and somatic anxiety (i.e., lower scores means lower anxiety
level) However, they might have low self-confidence improving 20% of their performance to get
the monetary reward (i.e., higher scores means lower confidence level). In that case, overall
MRF-L scores would be interpreted as a high level of anxiety. If my interpretation of both
factors (or at least one) is correct, then the authors may not conclude that the results of this study
were supported by only PET, or the interpretation of the results would be incorrect.
KINE 3316 – Analytical Rubric for Article Summary-Critique
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competentdiscussion of
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Psychology of Sport and Exercise 23 (2016) 13e20
Contents lists available at ScienceDirect
Psychology of Sport and Exercise
journal homepage: www.elsevier.com/locate/psychsport
Predicting physical activity intention and behaviour using
achievement goal theory: A person-centred analysis
John C.K. Wang a, c, *, Alexandre J.S. Morin b, W.C. Liu a, L.K. Chian a
a
National Institute of Education, Nanyang Technological University, Singapore
Australian Catholic University, Australia
c
Tianjin University of Sport, China
b
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 4 June 2015
Received in revised form
14 October 2015
Accepted 15 October 2015
Available online 20 October 2015
The purpose of the current study was to identify the 2 2 achievement goals profiles at the intraindividual level using a latent profile analyses (LPA) approach while controlling for the nesting of students within classroom. Additional analyses involving the direct inclusion of predictors and outcomes to
the final latent profile solution were also used to examine the relationships between the latent profiles
and perceived motivational climate, intention to be physically active and physical activity participation. A
sample of 1810 school children aged 14e19 years drawn from 79 classes in 13 Singaporean schools took
part in the study. Using the latent profile analysis, four distinct motivational profiles could be identified.
The results from multinomial logistic regressions showed that profile membership was significantly
predicted by perceptions of mastery and performance climate. Finally, the results showed that the four
profiles differed significantly in terms of intention to be physically active and physical activity
participation.
© 2015 Elsevier Ltd. All rights reserved.
Keywords:
2 2 achievement goals
Physical activity
Perceived motivational climate
Latent profile analysis
Multinomial logistic regression
Outcomes
In the past decades, researchers have focused on a social
cognitive approach to understand motivation and human behaviours in achievement contexts. Within the social cognitive
approach, achievement goal theory (Ames, 1992; Dweck & Leggett,
1988; Elliot, 1997; Nicholls, 1984, 1989) is one of the most popular
frameworks in studying achievement motivation, and it has
generated much research in sport and exercise psychology. In this
approach, researchers typically examine the effects of dispositional
goal orientation and perceived motivational climate on various
outcomes. Thus, Biddle, Wang, Kavussanu, and Spray (2003)
reviewed the correlates of achievement goal orientations in physical activity classes and found 98 studies, published between 1990
and 2000, including a total of 110 independent samples (total
N ¼ 21,076). In addition, Ntoumanis and Biddle (1999) reviewed 14
studies (total N ¼ 4484) on the motivational impact of perceived
classroom climates within physical education classes. This clearly
illustrates the importance that achievement goal theory has had in
research on physical education and physical activity within the last
decade.
* Corresponding author. Physical Education and Sports Science, National Institute
of Education, Blk 5 #03-28, 1 Nanyang Walk, Singapore 637616, Singapore.
E-mail address: john.wang@nie.edu.sg (J.C.K. Wang).
http://dx.doi.org/10.1016/j.psychsport.2015.10.004
1469-0292/© 2015 Elsevier Ltd. All rights reserved.
1. Achievement goal theory
The dichotomous achievement goal theory proposed by Nicholls
(1989) and Dweck (1999) focuses on two contrasting and complementary goals, conceptualised as dispositional. The first focuses on
self-referenced mastery or learning how to do the task, and is
usually labelled “mastery” goal. The second emphasises normative
comparison of ability or performance relative to others and is
labelled “performance” goal (Pintrich, 2000). Furthermore, variations in these two goal orientations, or tendencies, are thought to
be linked to different cognitive, affective, and behavioural
outcomes.
In the revised achievement goal framework, Elliot (2005) proposes to separate achievement goals from dispositions. He views
achievement goals as “aims” toward which individuals strive, a
conceptualisation that is consistent with the “prototypical use of
the term in the broader motivational literature, and it affords
conceptual precision without, ultimately, sacrificing conceptual
breadth” (p. 65). In addition, Elliot et al. (Elliot, 2005; Elliot &
Harackiewicz, 1996; Elliot & McGregor, 2001) propose to incorporate an approach-avoidance dimension to the masteryperformance distinction of the dichotomous achievement-goal
theory, leading to a 2 2 conceptualisation of achievement goals.
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J.C.K. Wang et al. / Psychology of Sport and Exercise 23 (2016) 13e20
Mastery-approach goals focus on achieving task-based intrapersonal competence, with objectives related to skill development,
mastery of task, and self-improvement. Mastery-avoidance goals
focus on avoiding task-based intrapersonal incompetence, aiming
to avoid not learning or not completing the task. Performanceapproach goals focus on normative competence, with the objective to outperform others, win, or show others that you are better.
Performance-avoidance goals focus on avoiding normative incompetence, aiming to avoid losing or performing badly compared to
others. Interestingly, the 2 2 achievement goal framework does
not assume that these goals are mutually exclusive, and recognises
that individuals will vary along each of these 2 2 dimensions.
Research has showed these four goals predicted different cognitions, affects, and outcomes. Generally, mastery-approach and
performance-approach goals contribute to positive affects and
consequences, while mastery-avoidance and performanceavoidance goals predict less adaptive outcomes (Elliot &
McGregor, 2001; Lochbaum, Podlog, Litchfield, Surles, & Hilliard,
2013; Lochbaum & Gottardy, 2015; McGregor & Elliot, 2002;
Rawsthorne & Elliot, 1999; Wang, Biddle, & Elliot, 2007). These
achievement goals reflect the personal perspective of motivation
(Lau & Nie, 2008).
It is noted that researchers who examined the relationships
between 2 2 achievement goals and related outcomes adopted
variable-centred (multiple regressions, structural equation
modelling, etc.) approaches (e.g., Cury, Elliot, Fonseca, & Moller,
2006; Elliot & McGregor, 2001), which describe the average relations among variables observed within the complete sample.
However, such variable-centred approaches provide information
about the underlying continuous structure of psychological constructs, their stability over time, and their relations with other
meaningful variables as they apply to the average person in the
sample, but ignore potentially critical differences occurring between various subgroups present in the sample (Morin & Wang, in
press).
On the other hand, person-centred approaches aim to identify
meaningful subgroups of participants (also called profiles) characterised by different patterns of relationships among the variables
under study (e.g., Chen, 2012; Smith, Deemer, Thoman, &
Zazworsky, 2014; Zuber, Zibung, & Conzelmann, 2015). In relation
to achievement goal theory, a variable-centred approach may
investigate the relations between achievement goals (masteryperformance; approach-avoidance) alone, in combination, or in
interaction, and a variety of relevant predictors, correlates and
outcomes. However, these relations are assumed to apply to all
individuals forming the sample. In contrast, a person-centred
approach aims to identify subgroups of participants presenting
distinct achievement goals profiles, and then relate these profiles to
meaningful covariates (predictors or outcomes). Importantly, we
are not arguing that person-centred approaches are inherently
“better” than variable-centred approaches. Rather, we argue that
person-centred approaches contribute to enrich our understanding
of important research questions by providing a complementary,
and perhaps more heuristic, perspective focused on interindividual differences and similarities on a configuration of key
constructs of interest, rather than focussing on relations among
constructs (e.g., Delbridge & Fiss, 2013; Morin & Wang, in press).
Conceptually, some researchers (e.g., Ntoumanis & Biddle, 1999;
Wang, Liu, Chatzisarantis, & Lim, 2010) have argued that since all
the goals may vary within the same person, the variable-centred
approach imposes an artificial structure on the observed data,
and this may not fit the ‘reality’. Therefore, the use of the personcentred approach may further our understanding of the intraindividual differences in goal profiles and relationships with other
variables.
Another limitation of most previous studies is the failure to
consider the nesting of students within classroom, even though
many of the processes under investigation are assumed to occur
within classrooms (e.g., physical education classes) under the influence of a specific teacher shared by all students forming the
classroom. The purpose of this study is to address these limitations
through the identification of achievement goals profiles using a
latent profile analysis (LPA) while controlling for the nesting of
students within classrooms. In addition, predictors and outcomes
were incorporated to this model to further investigate the relationships between the profiles and perceived motivational
climate (predictor), intention to be physically active (outcome) and
physical activity (outcome).
2. Students perceptions of classroom goal structures
At the classroom level, the learning context is expected to have a
direct impact on the adoption of specific goals (Ames, 1992;
Nicholls, 1989). The study of perceived goal structures in the
classroom thus becomes very important as it directly relates to the
adoption of specific achievement goals by students (Papaioannou,
Marsh, & Theodorakis, 2004). There are two main types of classroom goal structures derived from achievement goal theory: ‘performance’ (ego-involving) and ‘mastery’ (task-involving)
motivational climates (Ames, 1992; Ntoumanis & Biddle, 1999). In
performance-oriented classrooms, instructional practices and
evaluation procedures are structured to emphasise interpersonal
competition, discourage mistakes, and reward normative ability. In
mastery-oriented classrooms, instructional practices and evaluation procedures would rather emphasise learning and improvement, effort is rewarded, mistakes are seen as part of learning, and
choice is provided for task engagement.
Findings from variable-centred correlational studies (e.g.,
Ntoumanis & Biddle, 1999; Papaioannou, 1995; Wang et al., 2008)
have consistently shown that perceptions of a mastery structure are
related to adaptive outcomes, and performance goal structures are
linked to maladaptive consequences. A study by Wang et al. (2010)
adopted a person-centred approach. Their results showed that
subgroups (or profiles) of students presenting different perceptions
of the physical education classroom motivational climate, also
tended to favour different types of achievement goals. Specifically,
they found that differences in perceptions of mastery climates
seemed influential in determining mastery goals adoption, and
enjoyment. However, it should be noted that this study failed to
take into consideration students’ nesting within classes. Similarly,
since achievement goals are personal constructs operating at the
individual level, it would make more sense to create the subgroups
(or profiles) of students to present more distinctive achievement
goal profiles, rather than to classify these same individuals based on
their perceptions of their classroom motivational climate. This way,
the association of perceived motivational climate (predictor) on the
adoption of distinct achievement goals profiles can be studied in
combination with the impact of achievement goal profiles on intentions to be physically active and involvement in physical activity
(outcomes). Recently, Morin and Wang (in press) suggested a
method allowing for the integration of predictors and outcomes to
a LPA solution that we use in the current study.
3. The present study
The purpose of the current study was to identify subgroups of
students with distinct achievement goal profiles, while controlling
for their nesting within classrooms. In addition, a multinomial logistic regression was conducted to examine the relation of classroom climate on profile membership. Finally, outcomes were added
J.C.K. Wang et al. / Psychology of Sport and Exercise 23 (2016) 13e20
to the final latent profile solution to examine the differences in
intention to be physically active and physical activity participation
among the different profiles. Based on findings from Wang et al.
(2007, 2010), the following hypotheses were formulated:
H1: There will be at least four distinct profiles based on the 2 2
achievement goals. Three profiles will show high, moderate, and
low levels of achievement goals, and one profile will show high
mastery goals and low performance goals (Wang et al., 2007).
H2: Different levels of achievement goals will be related to
different levels of motivational climate, physical activity intention and participation. Specifically, participants with high
achievement approach goals will report high mastery climate,
high intention, and physical activity participation, compared to
those from the lower achievement goals profiles.
4. Methods
4.1. Participants
A sample of 1810 school students aged 14e19 years from 13
schools took part in the study. The students were drawn from 79
intact classes with different Physical Education (PE) teachers (79
different teachers); each class size averaged 20.3 students. This
sample included 1407 secondary school students and 403 junior
college students; 665 boys and 1145 girls. The students were
attending Secondary One level (equivalent to Year 7 in the UK or US
system) to Junior College Year Two (equivalent to Year 12 in the UK
or US system) in the Singapore school system.
4.2. Procedure
Ethical approval was obtained from the university Ethical Review Board. Permission to collect data from the students was obtained from the Ministry of Education and schools’ principals. The
heads of departments for PE were then contacted to arrange for the
administration of the questionnaire. The participants took 15 min
to complete the questionnaire which was administered by research
assistants in quiet classroom settings without the PE teachers being
present. Before responding to the questionnaires, students provided informed consent after having been informed of the nature of
the research project, that participating in the study was voluntary,
that they could withdraw at any time, and that their confidentiality
would be maintained.
4.3. Measures
4.3.1. The achievement goal in physical education questionnaire
(AGPEQ)
Students’ achievement goal orientation was obtained using the
AGPEQ (Wang et al., 2007), which includes four 3-item subscales:
mastery-approach (e.g., “I want to learn as much as possible from
this PE class”), mastery-avoidance (e.g., “I am often concerned that I
may not learn all that there is to learn in this PE class”),
performance-approach (e.g., “It is important for me to do better
than other students in this PE class”), and performance-avoidance
(e.g., “My fear of performing poorly in this PE class is often what
motivates me”). A 7-point Likert scale was used (1 ¼ strongly
disagree; 7 ¼ strongly agree). Evidence for the reliability and validity of the AGPEQ has been provided by Conroy, Elliot, and Hofer
(2003) and Wang et al. (2007).
4.3.2. Perceived classroom climate
Students rated the motivational climate of their PE classes using
15
the short version of the Learning and Performance Orientations in
Physical Education Classes Questionnaire (LAPOPECQ; Marsh,
Papaioannou, Martin, & Theodorakis, 2006; Papaioannou, 1994).
There were seven items measuring mastery climate (e.g., “In my PE
class, my PE teacher pays special attention to whether my skills are
improving”), and 6-items measuring performance climate (e.g., “In
my PE class, my PE teacher praises the students only when they are
better than their schoolmates”). Items are rated on a 7-point scale
(1 ¼ strongly disagree; 7 ¼ strongly agree). The psychometric
properties of the LAPOPECQ have been shown to be satisfactory
with Singaporean sample (Sproule, Wang, Morgan, McNeill, &
McMorris, 2007).
4.3.3. Intention to exercise during leisure time
Three items were used to measure intention to exercise during
leisure time in the next two weeks (Hagger et al., 2007; Wang et al.,
2008). The items were developed using guidelines from the theory
of planned behaviour (Ajzen, 2003). The students were asked
whether they planned and intended to play sport or exercise three
times a week for the next two weeks. These items were rated on a
7-point Likert scale (1 ¼ very unlikely; 7 ¼ very likely).
4.3.4. Physical activity
Two weeks after the initial survey, the students were asked to
rate their physical activity participation in the last two weeks. Two
items were used. The first item asked the student “Over the last
two weeks how often have you exercised for at least 30 min per
day during your leisure time?” This item was developed through
an adaptation of Godin and Shephard’s (1985) Leisure Time Exercise Questionnaire. The second question was “During the last
two weeks, how hard did you try to exercise, for at least 30 min,
three days per week during your leisure time?” This item assessed
the intensity of the physical activity. Response to the first item was
given on a 7-point scale (1 ¼ Not at all; 7 ¼ Most of the days).
Response to the second item was also given on a 7-point scales
(1 ¼ didn’t try at all; 7 ¼ tried extremely hard). The mean of the
two items was taken as an indication of physical activity participation. The validity and reliability of this measure of physical activity have been supported in previous research (see Hagger et al.,
2007).
4.4. Data analysis
Preliminary confirmatory factor analyses (CFA) were conducted
to examine the structure of the AGPEQ and LAPOPECQ using EQS for
Windows 6.1 (Bentler, 2006). The scale score reliability coefficients
(Rhos) of the scales were also computed (Fornell & Larcker, 1981).
Descriptive statistics and the latent variable correlations of the
main variables were tabulated. To assess the fit of these models to
the data, we used BentlereBonett normed fit index (NFI), BentlereBonett non-normed fit index (NNFI); the comparative fit index
(CFI); and the mean square error of approximation (RMSEA) and its
90% confidence intervals to evaluate the adequacy of the CFA
models. Values greater than .90 and .95 for the NFI, NNFI, and CFI
are considered to indicate adequate and excellent fit to the data,
respectively, while values smaller than .08 or .06 for the RMSEA
reflects acceptable and excellent model fit (Hu & Bentler, 1999;
Marsh, Hau, & Wen, 2004; Marsh, Hau, & Grayson, 2005).
For the main analyses, LPA were first conducted using the 2 2
achievement goal ratings as profile indicators using Mplus 7.2
& Muthen,
2014) robust maximum likelihood (MLR)
(Muthen
estimator, and Mplus design-based correction for students’ nesting
within classrooms (Asparouhov, 2005). Solutions including one to
eight profiles were estimated. The number of initial stage random
starts was set at 10,000 with the 500 best solutions retained for
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J.C.K. Wang et al. / Psychology of Sport and Exercise 23 (2016) 13e20
final stage optimisations. The number of iterations was set at 1000.1
To guide the selection of the optimal number of profiles in the data,
we relied on the Akaike’s Information Criterion (AIC), the Constant
AIC (CAIC), the Bayesian Information Criterion (BIC), the samplesize adjusted BIC (SSA-BIC), and the LoeMendelleRubin likelihood ratio test (LMR) (e.g., Marsh, LÈ•dtke, Trautwein, & Morin,
2009; Morin & Wang, in press). For the first four indicators, a
lower value suggests better fit. The LMR compares the estimated
model (k) with a model that has one class less than the estimated
model (k 1). Non-significant p values support the k 1 profile
model. However these tests remain variations of tests of statistical
significance and can still be heavily influenced by sample size so
that given a large enough sample, they will tend to support the
more complex model (i.e., the one with the most profiles; e.g.,
Marsh et al., 2009). In these situations, information criteria (AIC,
CAIC, BIC, and SSA-BIC) should be graphically presented through
“elbow plots” illustrating the gains associated with additional
profiles (Morin & Wang, in press; Petras & Masyn, 2010) where the
point after which the slope flattens out indicates the optimal
number of profiles. Finally, the entropy summarises the classification accuracy, ranging from 0 to 1 with higher value indicating
greater accuracy.
Importantly, LPAs present three important characteristics that
must be kept in mind when interpreting their results (Morin &
Wang, in press). First, LPAs are typological and provide a classification system to guide the categorisation of individuals into qualitatively and quantitatively distinct subpopulations. Second, this
classification system is prototypical, meaning that all participants
have a probability of membership in all profiles based on their
similarity with each latent profile. Third, because conventional
indices of absolute fit to the data (e.g., CFI, RMSEA) are not available,
LPAs are typically exploratory, meaning that the final solution is
typically selected based on a comparison of solutions including
differing numbers of latent profiles. Although it is possible to devise
confirmatory applications of LPAs in areas where theory has
advanced enough to provide clear expectations regarding the expected nature of the profiles (which is arguably not the case here),
these confirmatory models still need to be contrasted with unconstrained models to show that their degree of fit to the data remains comparatively acceptable (Finch & Bronk, 2011).
Once the final solution has been identified, predictors and outcomes were added to the model, while keeping in mind that the
addition of these covariates should not qualitatively change the
profiles (Marsh et al., 2009). Predictors were added to the final
model (mastery and performance motivational climates) using a
multinomial logistic regression, while outcomes (intention to be
physically active and physical activity participation) were included
as “distal outcomes” (including them as additional profiles indicators without allowing them to influence the solution; e.g.
& Muthen,
2014). The inclusion of these covariates in the
Muthen
model helps to limit Type 1 errors by combining analyses and have
been shown to systematically reduce biases in the estimation of the
model parameters, especially those describing the relationships
between the covariates and the profiles (which otherwise tend to
be underestimated; e.g., Bolck, Croon, & Hagenaars, 2004; Marsh
1
The variables means were freely estimated in all profiles. Models in which the
indicators’ variances were also freely estimated in all profiles (e.g., Peugh & Fan,
2013) tended to converge on improper solutions (negative variance estimates,
non-positive definite Fisher Information matrix, etc.) or not to converge at all even
after multiple attempts (e.g., increasing the random starts or iterations, decreasing
the convergence criterion). This suggests the inadequacy of these models (Bauer &
Curran, 2003; Chen, Bollen, Paxton, Curran, & Kirby, 2001), which may have been
overparameterised, and the superiority of more parsimonious models (Morin et al.,
2011).
et al., 2009; Morin & Wang, in press).
5. Results
5.1. Preliminary analyses and descriptive statistics
The a priori CFA model estimated on AGPEQ (Scaled c2 ¼ 221.48,
df ¼ 42, NFI ¼ .964, NNFI ¼ .954, CFI ¼ .971, RMSEA ¼ .049, 90% CI of
RMSEA ¼ .042 to .055) and the classroom climate measures (Scaled
c2 ¼ 467.33, df ¼ 59, NFI ¼ .920, NNFI ¼ .907, CFI ¼ .929,
RMSEA ¼ .062, 90% CI of RMSEA ¼ .056 to .067) revealed acceptable
fit indices, supporting the factor validity of these measures. The
descriptive statistics including means, standard deviations, internal
reliabilities, and correlations of all variables used in this study are
presented in Table 1. The scale score reliability of all subscales also
proved fully satisfactory, ranging from .71 to .88. The participants
were generally moderately high in mastery climate and masteryapproach goal and moderate in avoidance goals. The rest of the
variables were lower than the mid-point of the scales. The correlations show that mastery climate was positively related to
mastery-approach and mastery-avoidance goals. All achievement
goals were moderately and positively correlated with one another.
However, mastery-approach goals had stronger association with
mastery-avoidance goals. Mastery-approach goals also had stronger correlations with intentions to be physically active and physical
activity participation, compared to the other goals. Both masteryavoidance and performance-avoidance goals had small relationships with intention to be physically active, which was also positively associated with physical activity. In line with previous
research focussing on social or cognitive predictors of physical activities (Biddle et al., 2003; Lochbaum & Gottardy, 2015), the
observed relations between students’ physical activity and
achievement goal orientations or perceptions of classroom climate
remained much lower than the relations between intentions to be
physically active and physical activity.
5.2. Latent profile analyses
The results of the LPA are presented in Table 2. These results
show that while the LMR supports the 4-profile solution, the AIC,
CAIC, BIC, and SSA-BIC values continue to decrease with the addition of profiles to the model. However, the decrease in these values
(see Fig. 1) reaches a plateau between the 3 and 4 profile solution.
The examination of these adjacent solutions in terms of statistical
and theoretical adequacy supports the 4-profile solution. This solution is depicted in Fig. 2. Profile 1 describes only 5.19% of the
sample and is characterised by low levels of achievement motivation across the four goals, with a slight dominance for performance,
rather than mastery goals. Profile 2 is the exact opposite of profile 1,
describing 11.82% of the students with high levels on all dimensions
of achievement goals. Profile 3 is slightly more frequent (20.11%)
and presents slightly below average levels of achievement motivation across the four goals. Finally, profile 4 is the most prevalent
(62.87%), and presents average levels of achievement motivation
across the four goals. Overall, these profiles show very few discrepancies within each profile between the four achievement goals,
which seems to argue against the added value of distinguishing
between these four goals, rather than simply considering the
overall level of student’s achievement motivation for physical activity, irrespective of the specific form this motivation is taking.
5.3. Perceived classroom climate and achievement goals profiles
Students’ perceptions of their classroom’s motivation climate
were then added to this final profile solution as predictors in order
J.C.K. Wang et al. / Psychology of Sport and Exercise 23 (2016) 13e20
17
Table 1
Descriptive statistics and correlations between all variables of the overall sample.
1. Mastery climate
2. Performance climate
3. Mastery-approach
4. Mastery-avoidance
5. Performance-approach
6. Performance-avoidance
7. Intention
8. Physical activity
Rho
Mean
SD
1
2
3
4
5
6
7
.88
.71
.83
.77
.84
.71
.88
.80
4.79
3.55
4.60
4.00
3.54
3.96
3.59
3.16
1.05
.95
1.25
1.18
1.35
1.27
1.45
1.33
.05
.51**
.34**
.19**
.24**
.24**
.16**
.04
.16**
.33**
.18**
.04
.05*
.61**
.49**
.43**
.36**
.25**
.52**
.51**
.22**
.15**
.53**
.23**
.21**
.14**
.11**
.59**
Note. *p < 0.05. **p < 0.01. Table 2 Latent profile fit statistics. Model Free parameters LL Scaling AIC CAIC BIC SSA-BIC LMR Entropy 1 Profile 2 Profiles 3 Profiles 4 Profiles 5 Profiles 6 Profiles 7 Profiles 8 Profiles 8 13 18 23 28 33 38 43 11940.123 11322.703 10843.442 10739.311 10647.803 10546.706 10477.190 10416.941 2.1568 2.5741 1.8621 1.6071 1.8239 2.0689 1.9904 1.9017 23896.247 22671.406 21722.884 21524.622 21351.605 21159.411 21030.380 20919.881 23948.255 22755.920 21839.904 21674.147 21533.635 21373.947 21068.380 20962.881 23940.255 22742.920 21821.904 21651.147 21505.635 21340.947 21239.421 21156.428 23914.840 22701.620 21764.719 21578.077 21416.681 21236.108 21118.697 21019.819 e Purchase answer to see full attachment

  
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