This problem is based on data collated by: Craft, L. L., Magyar, T. M., Becker, B. J., & Feltz, D. L. (2003). The relationship between the competitive state anxiety inventory-2 and sport performance: A meta-analysis. Journal of Sport & Exercise Psychology, 25(1), 44–65.
The Competitive State Anxiety Index (CSAI) measures three factors: cognitive anxiety, somatic anxiety and self-confidence. The goal is to study the relation these factors and sports performance. Precisely, cognitive and somatic anxiety are hypothesized to predict self-confidence, and all three factors measured by the CSAI predict performance. Hence, self-confidence potentially mediates the relation cognitive and somatic forms of anxiety have with sports performance.
We used path analysis to test the CSAI predict performance path model based on data from 142 students for individual sport performance and 128 students for team sport performance. We used lavaan version 0.6.14 (Rosseel, 2012), with maximum likelihood estimation.
library(lavaan)## Warning: package 'lavaan' was built under R version 4.2.3## This is lavaan 0.6-15
## lavaan is FREE software! Please report any bugs.library(lavaanPlot) # for plotting later## Warning: package 'lavaanPlot' was built under R version 4.2.2Individual sport performance , n=142
We used path analysis to test the CSAI predict performance path model based on data from 142 students for individual sport performance. We used lavaan version 0.6.14 (Rosseel, 2012), with maximum likelihood estimation.
Model (1) for individual sports
Coefficients from cognitive anxiety and somatic anxiety → self-confidence are named a_co and a_so respectively.
Coefficient from self-confidence → sports performance is named b.
ind_co (product of a_co and b) is indirect effect of cognitive anxiety on sports performance via self-confidence.
c_ab (product of a_so and b) is indirect effect of somatic anxiety on sports performance via self-confidence.
Mi <- as.matrix(read.csv("matrix i.csv", row.names = 1))
Mi## Self_Confidence_i Performance_i Cognitive_i Somatic_i
## Self_Confidence_i 1.00 0.66 -0.38 -0.46
## Performance_i 0.66 1.00 -0.55 -0.48
## Cognitive_i -0.38 -0.55 1.00 NA
## Somatic_i -0.46 -0.48 0.47 1.00# Model(1) :
###### Indirect effect ,we use labeled syntax
Performance_i_pa<-'
Self_Confidence_i ~ a_co * Cognitive_i + a_so * Somatic_i
Performance_i ~ b * Self_Confidence_i+ Cognitive_i + Somatic_i
ind_co := a_co * b
ind_so := a_so * b'
Performance_i_pa <- sem(model= Performance_i_pa, sample.cov = Mi,sample.nobs = 142)
Performance_i_pa## lavaan 0.6.15 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 7
##
## Number of observations 142
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0summary(Performance_i_pa, header = FALSE, standardize = TRUE, ci = TRUE)##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## Self_Confidence_i ~
## Cogntv_ (a_co) -0.210 0.083 -2.547 0.011 -0.372 -0.048
## Somatc_ (a_so) -0.361 0.083 -4.375 0.000 -0.523 -0.199
## Performance_i ~
## Slf_Cn_ (b) 0.492 0.065 7.573 0.000 0.365 0.619
## Cogntv_ -0.313 0.065 -4.788 0.000 -0.441 -0.185
## Somatc_ -0.107 0.068 -1.565 0.118 -0.240 0.027
## Std.lv Std.all
##
## -0.210 -0.210
## -0.361 -0.361
##
## 0.492 0.492
## -0.313 -0.313
## -0.107 -0.107
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .Self_Confidnc_ 0.749 0.089 8.426 0.000 0.575 0.923
## .Performance_i 0.449 0.053 8.426 0.000 0.344 0.553
## Std.lv Std.all
## 0.749 0.754
## 0.449 0.452
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ind_co -0.103 0.043 -2.414 0.016 -0.187 -0.019
## ind_so -0.178 0.047 -3.788 0.000 -0.270 -0.086
## Std.lv Std.all
## -0.103 -0.103
## -0.178 -0.178lavaanPlot(model = Performance_i_pa, coefs = TRUE, covs = TRUE, stars = "regress")Students with higher cognitive anxiety (b = -0.21, se = 0.083, p = .011) and higher somatic anxiety (b = -0.36, se = 0.083, p < 0.001) tended to have lower self-confidence. And students with higher self-confidence had higher sport performance when they play individually (b = 0.49, se = 0.065, p < .001).
The indirect effects from cognitive anxiety (b = -0.1, se = 0.043, p = 0.016) and somatic anxiety (b = - 0.18, se = 0.047, p < .001) to sport performance via self-confidence were statistically significant. This suggests that in the case of individual sports, self-confidence mediated the relation between both cognitive and somatic forms of anxiety and sport performance.
Team Sport Performance ,n= 128 We used path analysis to test the CSAI predict performance path model based on data from 128 students for team sport performance. We used lavaan version 0.6.14 (Rosseel, 2012), with maximum likelihood estimation.
Model (2) for team’s sports
Coefficients from cognitive anxiety and somatic anxiety → self-confidence are named a_co and a_so respectively.
Coefficient from self-confidence → sports performance is named b.
ind_co (product of a_co and b) is indirect effect of cognitive anxiety on sports performance via self-confidence.
c_ab (product of a_so and b) is indirect effect of somatic anxiety on sports performance via self-confidence.
Mt <- as.matrix(read.csv("matrix t.csv", row.names = 1))
Mt## Self_Confidence_t Performance_t Cognitive_t Somatic_t
## Self_Confidence_t 1.00 0.13 -0.53 -0.27
## Performance_t 0.13 1.00 0.14 0.02
## Cognitive_t -0.53 0.14 1.00 0.56
## Somatic_t -0.27 0.02 0.56 1.00###### Indirect effect ,we use labeled syntax
Performance_t_pa<-'
Self_Confidence_t ~ a_cot * Cognitive_t + a_sot * Somatic_t
Performance_t ~ bt * Self_Confidence_t+ Cognitive_t + Somatic_t
ind_cot := a_cot * bt
ind_sot := a_sot * bt'
Performance_t_pa <- sem(model= Performance_t_pa, sample.cov = Mt,sample.nobs = 128)
Performance_t_pa## lavaan 0.6.15 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 7
##
## Number of observations 128
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0summary(Performance_t_pa, header = FALSE, standardize = TRUE, ci = TRUE)##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## Self_Confidence_t ~
## Cgntv_t (a_ct) -0.552 0.090 -6.104 0.000 -0.729 -0.375
## Somtc_t (a_st) 0.039 0.090 0.432 0.666 -0.138 0.216
## Performance_t ~
## Slf_Cn_ (bt) 0.288 0.100 2.880 0.004 0.092 0.483
## Cgntv_t 0.346 0.116 2.985 0.003 0.119 0.574
## Somtc_t -0.096 0.102 -0.943 0.346 -0.297 0.104
## Std.lv Std.all
##
## -0.552 -0.552
## 0.039 0.039
##
## 0.288 0.288
## 0.346 0.346
## -0.096 -0.096
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .Self_Confdnc_t 0.712 0.089 8.000 0.000 0.538 0.887
## .Performance_t 0.909 0.114 8.000 0.000 0.686 1.132
## Std.lv Std.all
## 0.712 0.718
## 0.909 0.916
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ind_cot -0.159 0.061 -2.605 0.009 -0.278 -0.039
## ind_sot 0.011 0.026 0.427 0.669 -0.040 0.063
## Std.lv Std.all
## -0.159 -0.159
## 0.011 0.011lavaanPlot(model = Performance_t_pa, coefs = TRUE, covs = TRUE, stars = "regress")On the other hand, when student play in teams we can conclude the following: Students with higher cognitive anxiety (b = -0.55, se = 0.09, p < 0.001) tended to have lower self-confidence.
While somatic anxiety (b = 0.39, se = 0.09, p = 0.666) has no significant effect on self-confidence. Students with higher self-confidence had higher sport performance when they play individually (b = -0.29, se = 0.1, p =0.004).
The indirect effects from cognitive anxiety (b = -0.16, se = 0.061, p = 0.009) to sport performance via self-confidence were statistically significant.
While The indirect effects from somatic anxiety (b = 0.01, se = 0.026, p = .669) to sport performance via self-confidence was not statistically significant.
This suggests that in the case of team sports, self-confidence mediated the relation between cognitive anxiety and sport performance while the mediation was not significant in the case of team sports with somatic forms of anxiety.
At the significant level of 0.05 , The results suggests that in the case of individual sports, self-confidence mediated the relation between both cognitive and somatic forms of anxiety and sport performance .
While in the case of team sports, self-confidence mediated the relation between cognitive anxiety and sport performance while the mediation was not significant in the case of team sports with somatic forms of anxiety.
Although R-square is equal to zero , it suggests that the indirect effect is not significantly different from 0, indicating that there is no evidence that the mediator variable explains or accounts for the relationship between the predictors and the outcome variable. However, it’s important to note that a non-significant result does not necessarily mean that there is no mediation effect. It could be that the effect size is small or that there are other factors or variables that are influencing the relationship.