dat.crede2010.RdResults from 68 studies on the relationship between class attendence and class performance and/or grade point average in college students.
dat.crede2010The data frame contains the following columns:
| studyid | numeric | study number |
| year | numeric | publication year |
| source | character | study source (journal, dissertation, other) |
| sampleid | numeric | sample within study number |
| criterion | character | criterion variable (grade, gpa) |
| class | character | class type (science, nonscience) |
| ni | numeric | sample size |
| ri | numeric | observed correlation |
The 68 studies included in this dataset provide information about the relationship between class attendance of college students and their performance (i.e., grade) in the class and/or their overall grade point average. Some studies included multiple samples and hence the dataset actually contains 97 correlation coefficients.
The dataset was obtained via personal communication. Note that this dataset differs just slightly from the one used by Credé et al. (2010).
Personal communication.
Credé, M., Roch, S. G., & Kieszczynka, U. M. (2010). Class attendance in college: A meta-analytic review of the relationship of class attendance with grades and student characteristics. Review of Educational Research, 80(2), 272–295. https://doi.org/10.3102/0034654310362998
education, correlation coefficients, multilevel models
### copy data into 'dat' and examine data
dat <- dat.crede2010
head(dat, 18)
#> studyid year source sampleid criterion class ni ri
#> 1 1 2009 dissertation 1 grade nonscience 76 0.8860
#> 2 2 1975 journal 1 grade nonscience 297 0.3000
#> 3 3 2007 dissertation 1 gpa <NA> 191 0.7200
#> 4 4 1989 journal 1 grade nonscience 265 0.4750
#> 5 4 1989 journal 2 grade nonscience 154 0.3340
#> 6 5 2008 journal 1 grade nonscience 162 0.6150
#> 7 6 1999 journal 1 grade nonscience 28 0.1450
#> 8 6 1999 journal 2 grade nonscience 33 0.2300
#> 9 6 1999 journal 3 grade nonscience 47 0.2700
#> 10 6 1999 journal 4 grade nonscience 25 -0.0228
#> 11 6 1999 journal 5 grade nonscience 48 0.4290
#> 12 6 1999 journal 6 grade nonscience 39 0.3490
#> 13 6 1999 journal 7 grade nonscience 41 0.2200
#> 14 6 1999 journal 8 grade nonscience 35 0.3390
#> 15 6 1999 journal 9 grade nonscience 46 0.4470
#> 16 7 2007 dissertation 1 gpa <NA> 350 0.3320
#> 17 7 2007 dissertation 1 grade nonscience 350 0.4010
#> 18 8 2003 journal 1 grade nonscience 421 0.2200
### load metafor package
library(metafor)
### calculate r-to-z transformed correlations and corresponding sampling variances
dat <- escalc(measure="ZCOR", ri=ri, ni=ni, data=dat)
############################################################################
### meta-analysis for the relationship between attendance and grades
res <- rma(yi, vi, data=dat, subset=criterion=="grade")
res
#>
#> Random-Effects Model (k = 67; tau^2 estimator: REML)
#>
#> tau^2 (estimated amount of total heterogeneity): 0.0511 (SE = 0.0104)
#> tau (square root of estimated tau^2 value): 0.2261
#> I^2 (total heterogeneity / total variability): 93.83%
#> H^2 (total variability / sampling variability): 16.21
#>
#> Test for Heterogeneity:
#> Q(df = 66) = 1068.7213, p-val < .0001
#>
#> Model Results:
#>
#> estimate se zval pval ci.lb ci.ub
#> 0.4547 0.0300 15.1343 <.0001 0.3958 0.5136 ***
#>
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
### estimated average correlation with 95% CI/PI
predict(res, transf=transf.ztor, digits=2)
#>
#> pred ci.lb ci.ub pi.lb pi.ub
#> 0.43 0.38 0.47 0.01 0.72
#>
### examine if relationship between attendance and grades differs for nonscience/science classes
res <- rma(yi, vi, mods = ~ class, data=dat, subset=criterion=="grade")
res
#>
#> Mixed-Effects Model (k = 67; tau^2 estimator: REML)
#>
#> tau^2 (estimated amount of residual heterogeneity): 0.0515 (SE = 0.0106)
#> tau (square root of estimated tau^2 value): 0.2269
#> I^2 (residual heterogeneity / unaccounted variability): 93.45%
#> H^2 (unaccounted variability / sampling variability): 15.26
#> R^2 (amount of heterogeneity accounted for): 0.00%
#>
#> Test for Residual Heterogeneity:
#> QE(df = 65) = 1009.6949, p-val < .0001
#>
#> Test of Moderators (coefficient 2):
#> QM(df = 1) = 0.6234, p-val = 0.4298
#>
#> Model Results:
#>
#> estimate se zval pval ci.lb ci.ub
#> intrcpt 0.4441 0.0330 13.4603 <.0001 0.3794 0.5087 ***
#> classscience 0.0640 0.0810 0.7895 0.4298 -0.0948 0.2228
#>
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
### estimated average correlations for nonscience and science classes
predict(res, newmods=c(0,1), transf=transf.ztor, digits=2)
#>
#> pred ci.lb ci.ub pi.lb pi.ub
#> 1 0.42 0.36 0.47 -0.01 0.71
#> 2 0.47 0.35 0.57 0.04 0.75
#>
### examine if relationship between attendance and grades has changed over time
res <- rma(yi, vi, mods = ~ year, data=dat, subset=criterion=="grade")
res
#>
#> Mixed-Effects Model (k = 67; tau^2 estimator: REML)
#>
#> tau^2 (estimated amount of residual heterogeneity): 0.0504 (SE = 0.0104)
#> tau (square root of estimated tau^2 value): 0.2246
#> I^2 (residual heterogeneity / unaccounted variability): 93.70%
#> H^2 (unaccounted variability / sampling variability): 15.87
#> R^2 (amount of heterogeneity accounted for): 1.31%
#>
#> Test for Residual Heterogeneity:
#> QE(df = 65) = 1050.5282, p-val < .0001
#>
#> Test of Moderators (coefficient 2):
#> QM(df = 1) = 1.3863, p-val = 0.2390
#>
#> Model Results:
#>
#> estimate se zval pval ci.lb ci.ub
#> intrcpt -7.0137 6.3432 -1.1057 0.2689 -19.4462 5.4188
#> year 0.0037 0.0032 1.1774 0.2390 -0.0025 0.0100
#>
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
############################################################################
### meta-analysis for the relationship between attendance and GPA
res <- rma(yi, vi, data=dat, subset=criterion=="gpa")
res
#>
#> Random-Effects Model (k = 30; tau^2 estimator: REML)
#>
#> tau^2 (estimated amount of total heterogeneity): 0.0555 (SE = 0.0165)
#> tau (square root of estimated tau^2 value): 0.2356
#> I^2 (total heterogeneity / total variability): 93.76%
#> H^2 (total variability / sampling variability): 16.02
#>
#> Test for Heterogeneity:
#> Q(df = 29) = 430.9743, p-val < .0001
#>
#> Model Results:
#>
#> estimate se zval pval ci.lb ci.ub
#> 0.3724 0.0459 8.1071 <.0001 0.2824 0.4624 ***
#>
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
### estimated average correlation with 95% CI/PI
predict(res, transf=transf.ztor, digits=2)
#>
#> pred ci.lb ci.ub pi.lb pi.ub
#> 0.36 0.28 0.43 -0.10 0.69
#>
### examine if relationship between attendance and GPA has changed over time
res <- rma(yi, vi, mods = ~ year, data=dat, subset=criterion=="gpa")
res
#>
#> Mixed-Effects Model (k = 30; tau^2 estimator: REML)
#>
#> tau^2 (estimated amount of residual heterogeneity): 0.0569 (SE = 0.0173)
#> tau (square root of estimated tau^2 value): 0.2384
#> I^2 (residual heterogeneity / unaccounted variability): 93.61%
#> H^2 (unaccounted variability / sampling variability): 15.64
#> R^2 (amount of heterogeneity accounted for): 0.00%
#>
#> Test for Residual Heterogeneity:
#> QE(df = 28) = 392.0912, p-val < .0001
#>
#> Test of Moderators (coefficient 2):
#> QM(df = 1) = 0.3796, p-val = 0.5378
#>
#> Model Results:
#>
#> estimate se zval pval ci.lb ci.ub
#> intrcpt 2.5890 3.5979 0.7196 0.4718 -4.4627 9.6407
#> year -0.0011 0.0018 -0.6161 0.5378 -0.0047 0.0024
#>
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
############################################################################
### use a multilevel model to examine the relationship between attendance and grades
res <- rma.mv(yi, vi, random = ~ 1 | studyid/sampleid, data=dat, subset=criterion=="grade")
res
#>
#> Multivariate Meta-Analysis Model (k = 67; method: REML)
#>
#> Variance Components:
#>
#> estim sqrt nlvls fixed factor
#> sigma^2.1 0.0376 0.1939 54 no studyid
#> sigma^2.2 0.0159 0.1259 67 no studyid/sampleid
#>
#> Test for Heterogeneity:
#> Q(df = 66) = 1068.7213, p-val < .0001
#>
#> Model Results:
#>
#> estimate se zval pval ci.lb ci.ub
#> 0.4798 0.0331 14.5167 <.0001 0.4151 0.5446 ***
#>
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
predict(res, transf=transf.ztor, digits=2)
#>
#> pred ci.lb ci.ub pi.lb pi.ub
#> 0.45 0.39 0.50 0.02 0.73
#>
### use a multilevel model to examine the relationship between attendance and gpa
res <- rma.mv(yi, vi, random = ~ 1 | studyid/sampleid, data=dat, subset=criterion=="gpa")
res
#>
#> Multivariate Meta-Analysis Model (k = 30; method: REML)
#>
#> Variance Components:
#>
#> estim sqrt nlvls fixed factor
#> sigma^2.1 0.0572 0.2392 24 no studyid
#> sigma^2.2 0.0063 0.0796 30 no studyid/sampleid
#>
#> Test for Heterogeneity:
#> Q(df = 29) = 430.9743, p-val < .0001
#>
#> Model Results:
#>
#> estimate se zval pval ci.lb ci.ub
#> 0.3611 0.0538 6.7103 <.0001 0.2556 0.4665 ***
#>
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
predict(res, transf=transf.ztor, digits=2)
#>
#> pred ci.lb ci.ub pi.lb pi.ub
#> 0.35 0.25 0.44 -0.14 0.70
#>