dat.craft2003.RdResults from 10 studies on the relationship between the Competitive State Anxiety Inventory-2 (CSAI-2) and sport performance.
dat.craft2003The data frame contains the following columns:
| study | numeric | study number |
| ni | numeric | sample size |
| sport | character | type of sport (T = team sport, I = individual sport) |
| ri | numeric | correlation coefficient |
| var1 | character | variable 1 of the correlation coefficient (see ‘Details’) |
| var2 | character | variable 2 of the correlation coefficient (see ‘Details’) |
The 10 studies included in this dataset are a subset of the studies included in the meta-analysis by Craft et al. (2003) on the relationship between the Competitive State Anxiety Inventory-2 (CSAI-2) and sport performance.
The CSAI-2 has three subscales: cognitive anxiety (acog), somatic anxiety (asom), and self-confidence (conf). The studies included in this dataset administered the CSAI-2 prior to some sport competition and then measured sport performance based on the competition. Most studies provided all 6 correlations (3 for the correlations among the 3 subscales and 3 for the correlations between the subscales and sport performance), but 2 studies (with study numbers 6 and 17) only provided a subset.
Becker, B. J., & Aloe, A. M. (2019). Model-based meta-analysis and related approaches. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta-analysis (3nd ed., pp. 339–363). New York: Russell Sage Foundation.
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 and Exercise Psychology, 25(1), 44–65. https://doi.org/10.1123/jsep.25.1.44
psychology, correlation coefficients, multivariate models
### copy data into 'dat' and examine data
dat <- dat.craft2003
head(dat, 18)
#> study ni sport ri var1 var2
#> 1 1 142 I -0.55 acog perf
#> 2 1 142 I -0.48 asom perf
#> 3 1 142 I 0.66 conf perf
#> 4 1 142 I 0.47 acog asom
#> 5 1 142 I -0.38 acog conf
#> 6 1 142 I -0.46 asom conf
#> 7 3 37 I 0.53 acog perf
#> 8 3 37 I -0.12 asom perf
#> 9 3 37 I 0.03 conf perf
#> 10 3 37 I 0.52 acog asom
#> 11 3 37 I -0.48 acog conf
#> 12 3 37 I -0.40 asom conf
#> 13 6 16 T 0.44 acog perf
#> 14 6 16 T 0.46 asom perf
#> 15 6 16 T NA conf perf
#> 16 6 16 T 0.67 acog asom
#> 17 6 16 T NA acog conf
#> 18 6 16 T NA asom conf
### load metafor package
library(metafor)
### construct dataset and var-cov matrix of the correlations
tmp <- rcalc(ri ~ var1 + var2 | study, ni=ni, data=dat)
V <- tmp$V
dat <- tmp$dat
### examine data for study 1
dat[dat$study == 1,]
#> study var1 var2 var1.var2 yi ni
#> 1 1 acog perf acog.perf -0.55 142
#> 2 1 asom perf asom.perf -0.48 142
#> 3 1 conf perf conf.perf 0.66 142
#> 4 1 acog asom acog.asom 0.47 142
#> 5 1 acog conf acog.conf -0.38 142
#> 6 1 asom conf asom.conf -0.46 142
V[dat$study == 1, dat$study == 1]
#> acog.perf asom.perf conf.perf acog.asom acog.conf asom.conf
#> acog.perf 0.0034503989 0.0013265149 -0.0005545798 -0.0013967848 0.002501895 0.0009322372
#> asom.perf 0.0013265149 0.0042005969 -0.0009521407 -0.0019433591 0.001264856 0.0025160783
#> conf.perf -0.0005545798 -0.0009521407 0.0022592011 0.0005791091 -0.001533798 -0.0010692460
#> acog.asom -0.0013967848 -0.0019433591 0.0005791091 0.0043049419 -0.001802689 -0.0012050560
#> acog.conf 0.0025018954 0.0012648562 -0.0015337979 -0.0018026891 0.005191854 0.0018844047
#> asom.conf 0.0009322372 0.0025160783 -0.0010692460 -0.0012050560 0.001884405 0.0044083302
### examine data for study 6
dat[dat$study == 6,]
#> study var1 var2 var1.var2 yi ni
#> 13 6 acog perf acog.perf 0.44 16
#> 14 6 asom perf asom.perf 0.46 16
#> 15 6 conf perf conf.perf NA 16
#> 16 6 acog asom acog.asom 0.67 16
#> 17 6 acog conf acog.conf NA 16
#> 18 6 asom conf asom.conf NA 16
V[dat$study == 6, dat$study == 6]
#> acog.perf asom.perf conf.perf acog.asom acog.conf asom.conf
#> acog.perf 0.043352064 0.025583395 NA 0.009529623 NA NA
#> asom.perf 0.025583395 0.041438304 NA 0.008459787 NA NA
#> conf.perf NA NA NA NA NA NA
#> acog.asom 0.009529623 0.008459787 NA 0.020247414 NA NA
#> acog.conf NA NA NA NA NA NA
#> asom.conf NA NA NA NA NA NA
### examine data for study 17
dat[dat$study == 17,]
#> study var1 var2 var1.var2 yi ni
#> 25 17 acog perf acog.perf 0.10 45
#> 26 17 asom perf asom.perf 0.31 45
#> 27 17 conf perf conf.perf -0.17 45
#> 28 17 acog asom acog.asom NA 45
#> 29 17 acog conf acog.conf NA 45
#> 30 17 asom conf asom.conf NA 45
V[dat$study == 17, dat$study == 17]
#> acog.perf asom.perf conf.perf acog.asom acog.conf asom.conf
#> acog.perf 0.022275 NA NA NA NA NA
#> asom.perf NA 0.01856898 NA NA NA NA
#> conf.perf NA NA 0.02143262 NA NA NA
#> acog.asom NA NA NA NA NA NA
#> acog.conf NA NA NA NA NA NA
#> asom.conf NA NA NA NA NA NA
### multivariate random-effects model
res <- rma.mv(yi, V, mods = ~ 0 + var1.var2, random = ~ var1.var2 | study, struct="UN", data=dat)
#> Warning: 9 rows with NAs omitted from model fitting.
res
#>
#> Multivariate Meta-Analysis Model (k = 51; method: REML)
#>
#> Variance Components:
#>
#> outer factor: study (nlvls = 9)
#> inner factor: var1.var2 (nlvls = 6)
#>
#> estim sqrt k.lvl fixed level
#> tau^2.1 0.0047 0.0683 9 no acog.asom
#> tau^2.2 0.0125 0.1119 8 no acog.conf
#> tau^2.3 0.1611 0.4014 9 no acog.perf
#> tau^2.4 0.0111 0.1052 8 no asom.conf
#> tau^2.5 0.0604 0.2459 9 no asom.perf
#> tau^2.6 0.0468 0.2163 8 no conf.perf
#>
#> rho.acg.s rho.acg.c rho.acg.p rho.asm.c rho.asm.p rho.cnf. acg.s acg.c acg.p
#> acog.asom 1 - 8 9
#> acog.conf -0.6961 1 no - 8
#> acog.perf 0.5491 0.0432 1 no no -
#> asom.conf -0.0891 0.4193 0.3532 1 no no no
#> asom.perf 0.4604 -0.0495 0.9497 0.2688 1 no no no
#> conf.perf -0.9345 0.7023 -0.6178 -0.1311 -0.5969 1 no no no
#> asm.c asm.p cnf.
#> acog.asom 8 9 8
#> acog.conf 8 8 8
#> acog.perf 8 9 8
#> asom.conf - 8 8
#> asom.perf no - 8
#> conf.perf no no -
#>
#> Test for Residual Heterogeneity:
#> QE(df = 45) = 334.8358, p-val < .0001
#>
#> Test of Moderators (coefficients 1:6):
#> QM(df = 6) = 596.7706, p-val < .0001
#>
#> Model Results:
#>
#> estimate se zval pval ci.lb ci.ub
#> var1.var2acog.asom 0.5671 0.0367 15.4640 <.0001 0.4953 0.6390 ***
#> var1.var2acog.conf -0.4888 0.0509 -9.6048 <.0001 -0.5886 -0.3891 ***
#> var1.var2acog.perf -0.0600 0.1408 -0.4264 0.6698 -0.3359 0.2159
#> var1.var2asom.conf -0.4750 0.0506 -9.3901 <.0001 -0.5741 -0.3758 ***
#> var1.var2asom.perf -0.1423 0.0917 -1.5527 0.1205 -0.3220 0.0373
#> var1.var2conf.perf 0.3167 0.0847 3.7393 0.0002 0.1507 0.4827 ***
#>
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>