dat.bangertdrowns2004.RdResults from 48 studies on the effectiveness of school-based writing-to-learn interventions on academic achievement.
dat.bangertdrowns2004The data frame contains the following columns:
| id | numeric | study number |
| author | character | study author(s) |
| year | numeric | publication year |
| grade | numeric | grade level (1 = elementary; 2 = middle; 3 = high-school; 4 = college) |
| length | numeric | treatment length (in weeks) |
| minutes | numeric | minutes per assignment |
| wic | numeric | writing tasks were completed in class (0 = no; 1 = yes) |
| feedback | numeric | feedback on writing was provided (0 = no; 1 = yes) |
| info | numeric | writing contained informational components (0 = no; 1 = yes) |
| pers | numeric | writing contained personal components (0 = no; 1 = yes) |
| imag | numeric | writing contained imaginative components (0 = no; 1 = yes) |
| meta | numeric | prompts for metacognitive reflection (0 = no; 1 = yes) |
| subject | character | subject matter |
| ni | numeric | total sample size of the study |
| yi | numeric | standardized mean difference |
| vi | numeric | corresponding sampling variance |
In each of the studies included in this meta-analysis, an experimental group (i.e., a group of students that received instruction with increased emphasis on writing tasks) was compared against a control group (i.e., a group of students that received conventional instruction) with respect to some content-related measure of academic achievement (e.g., final grade, an exam/quiz/test score). The outcome measure for this meta-analysis was the standardized mean difference (with positive values indicating a higher mean level of academic achievement in the intervention group).
The standardized mean differences given here are bias-corrected and therefore differ slightly from the values reported in the article. Also, since only the total sample size is given in the article, the sampling variances were computed under the assumption that \(n_{i1} = n_{i2} = n_i / 2\).
Bangert-Drowns, R. L., Hurley, M. M., & Wilkinson, B. (2004). The effects of school-based writing-to-learn interventions on academic achievement: A meta-analysis. Review of Educational Research, 74(1), 29–58. https://doi.org/10.3102/00346543074001029
education, standardized mean differences, meta-regression
### copy data into 'dat' and examine data
dat <- dat.bangertdrowns2004
dat[1:10,-13]
#>
#> id author year grade length minutes wic feedback info pers imag meta ni yi vi
#> 1 1 Ashworth 1992 4 15 NA 1 1 1 1 0 1 60 0.650 0.070
#> 2 2 Ayers 1993 2 10 NA 1 NA 1 1 1 0 34 -0.750 0.126
#> 3 3 Baisch 1990 2 2 NA 1 0 1 1 0 1 95 -0.210 0.042
#> 4 4 Baker 1994 4 9 10 1 1 1 0 0 0 209 -0.040 0.019
#> 5 5 Bauman 1992 1 14 10 1 1 1 1 0 1 182 0.230 0.022
#> 6 6 Becker 1996 4 1 20 1 0 0 1 0 0 462 0.030 0.009
#> 7 7 Bell & Bell 1985 3 4 NA 1 1 1 1 0 1 38 0.260 0.106
#> 8 8 Brodney 1994 1 15 NA 1 1 1 1 0 1 542 0.060 0.007
#> 9 9 Burton 1986 4 4 NA 0 1 1 0 0 0 99 0.060 0.040
#> 10 10 Davis, BH 1990 1 9 10 1 0 1 1 0 0 77 0.120 0.052
#>
### load metafor package
library(metafor)
### fit random-effects model
res <- rma(yi, vi, data=dat)
res
#>
#> Random-Effects Model (k = 48; tau^2 estimator: REML)
#>
#> tau^2 (estimated amount of total heterogeneity): 0.0499 (SE = 0.0197)
#> tau (square root of estimated tau^2 value): 0.2235
#> I^2 (total heterogeneity / total variability): 58.37%
#> H^2 (total variability / sampling variability): 2.40
#>
#> Test for Heterogeneity:
#> Q(df = 47) = 107.1061, p-val < .0001
#>
#> Model Results:
#>
#> estimate se zval pval ci.lb ci.ub
#> 0.2219 0.0460 4.8209 <.0001 0.1317 0.3122 ***
#>
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
### some examples of mixed-effects meta-regression models
res <- rma(yi, vi, mods = ~ factor(grade), data=dat)
res
#>
#> Mixed-Effects Model (k = 48; tau^2 estimator: REML)
#>
#> tau^2 (estimated amount of residual heterogeneity): 0.0539 (SE = 0.0216)
#> tau (square root of estimated tau^2 value): 0.2322
#> I^2 (residual heterogeneity / unaccounted variability): 59.15%
#> H^2 (unaccounted variability / sampling variability): 2.45
#> R^2 (amount of heterogeneity accounted for): 0.00%
#>
#> Test for Residual Heterogeneity:
#> QE(df = 44) = 102.0036, p-val < .0001
#>
#> Test of Moderators (coefficients 2:4):
#> QM(df = 3) = 5.9748, p-val = 0.1128
#>
#> Model Results:
#>
#> estimate se zval pval ci.lb ci.ub
#> intrcpt 0.2639 0.0898 2.9393 0.0033 0.0879 0.4399 **
#> factor(grade)2 -0.3727 0.1705 -2.1856 0.0288 -0.7069 -0.0385 *
#> factor(grade)3 0.0248 0.1364 0.1821 0.8555 -0.2425 0.2922
#> factor(grade)4 -0.0155 0.1160 -0.1338 0.8935 -0.2429 0.2118
#>
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
res <- rma(yi, vi, mods = ~ length, data=dat)
#> Warning: 2 studies with NAs omitted from model fitting.
res
#>
#> Mixed-Effects Model (k = 46; tau^2 estimator: REML)
#>
#> tau^2 (estimated amount of residual heterogeneity): 0.0441 (SE = 0.0188)
#> tau (square root of estimated tau^2 value): 0.2100
#> I^2 (residual heterogeneity / unaccounted variability): 55.26%
#> H^2 (unaccounted variability / sampling variability): 2.24
#> R^2 (amount of heterogeneity accounted for): 5.08%
#>
#> Test for Residual Heterogeneity:
#> QE(df = 44) = 96.2810, p-val < .0001
#>
#> Test of Moderators (coefficient 2):
#> QM(df = 1) = 4.2266, p-val = 0.0398
#>
#> Model Results:
#>
#> estimate se zval pval ci.lb ci.ub
#> intrcpt 0.0692 0.0825 0.8384 0.4018 -0.0925 0.2309
#> length 0.0149 0.0073 2.0559 0.0398 0.0007 0.0292 *
#>
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
res <- rma(yi, vi, mods = ~ info + pers + imag + meta, data=dat)
#> Warning: 2 studies with NAs omitted from model fitting.
res
#>
#> Mixed-Effects Model (k = 46; tau^2 estimator: REML)
#>
#> tau^2 (estimated amount of residual heterogeneity): 0.0412 (SE = 0.0192)
#> tau (square root of estimated tau^2 value): 0.2030
#> I^2 (residual heterogeneity / unaccounted variability): 51.71%
#> H^2 (unaccounted variability / sampling variability): 2.07
#> R^2 (amount of heterogeneity accounted for): 18.34%
#>
#> Test for Residual Heterogeneity:
#> QE(df = 41) = 82.7977, p-val = 0.0001
#>
#> Test of Moderators (coefficients 2:5):
#> QM(df = 4) = 10.0061, p-val = 0.0403
#>
#> Model Results:
#>
#> estimate se zval pval ci.lb ci.ub
#> intrcpt 0.3440 0.2179 1.5784 0.1145 -0.0831 0.7711
#> info -0.1988 0.2106 -0.9438 0.3453 -0.6115 0.2140
#> pers -0.3223 0.1782 -1.8094 0.0704 -0.6715 0.0268 .
#> imag 0.2540 0.2023 1.2557 0.2092 -0.1424 0.6504
#> meta 0.4817 0.1678 2.8708 0.0041 0.1528 0.8106 **
#>
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>