dat.cohen1981.RdResults from 20 studies on the correlation between course instructor ratings and student achievement.
dat.cohen1981The data frame contains the following columns:
| study | character | study author(s) and year |
| sample | character | course type |
| control | character | ability control |
| ni | numeric | sample size of the study (number of sections) |
| ri | numeric | observed correlation |
The studies included in this dataset examined to what extent students' ratings of a course instructor correlated with their achievement in the course. Instead of correlating individual ratings and achievement scores, the studies were carried out in multisection courses, in which the sections had different instructors but all sections used a common achievement measure (e.g., a final exam). The correlation coefficients reflect the correlation between the mean instructor rating and the mean achievement score of each section. Hence, the unit of analysis are the sections, not the individuals.
Note that this dataset (extracted from Table A.3 in Cooper & Hedges, 1994) only contains studies with at least 10 sections.
Cooper, H., & Hedges, L. V. (1994). Appendix A: Data Sets. In H. Cooper & L. V. Hedges (Eds.), The handbook of research synthesis (pp. 543–547). New York: Russell Sage Foundation.
Cohen, P. A. (1981). Student ratings of instruction and student achievement: A meta-analysis of multisection validity studies. Review of Educational Research, 51(3), 281–309. https://doi.org/10.3102/00346543051003281
education, correlation coefficients
### copy data into 'dat' and examine data
dat <- dat.cohen1981
dat[c(1,4,5)]
#> study ni ri
#> 1 Bolton et al. 1979 10 0.68
#> 2 Bryson 1974 20 0.56
#> 3 Centra 1977 13 0.23
#> 4 Centra 1977 22 0.64
#> 5 Crooks & Smock 1974 28 0.49
#> 6 Doyle & Crichton 1978 12 -0.04
#> 7 Doyle & Whitely 1974 12 0.49
#> 8 Elliott 1950 36 0.33
#> 9 Ellis & Rickard 1977 19 0.58
#> 10 Frey et al. 1975 12 0.18
#> 11 Greenwood et al. 1976 36 -0.11
#> 12 Hoffman 1978 75 0.27
#> 13 McKeachie et al. 1971 33 0.26
#> 14 Morsh et al. 1956 121 0.40
#> 15 Remmers et al. 1949 37 0.49
#> 16 Sullivan & Skanes 1974 14 0.51
#> 17 Sullivan & Skanes 1974 40 0.40
#> 18 Sullivan & Skanes 1974 16 0.34
#> 19 Sullivan & Skanes 1974 14 0.42
#> 20 Wherry 1952 20 0.16
### 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[c(1,4,5)])
dat
#>
#> study ni ri yi vi
#> 1 Bolton et al. 1979 10 0.68 0.8291 0.1429
#> 2 Bryson 1974 20 0.56 0.6328 0.0588
#> 3 Centra 1977 13 0.23 0.2342 0.1000
#> 4 Centra 1977 22 0.64 0.7582 0.0526
#> 5 Crooks & Smock 1974 28 0.49 0.5361 0.0400
#> 6 Doyle & Crichton 1978 12 -0.04 -0.0400 0.1111
#> 7 Doyle & Whitely 1974 12 0.49 0.5361 0.1111
#> 8 Elliott 1950 36 0.33 0.3428 0.0303
#> 9 Ellis & Rickard 1977 19 0.58 0.6625 0.0625
#> 10 Frey et al. 1975 12 0.18 0.1820 0.1111
#> 11 Greenwood et al. 1976 36 -0.11 -0.1104 0.0303
#> 12 Hoffman 1978 75 0.27 0.2769 0.0139
#> 13 McKeachie et al. 1971 33 0.26 0.2661 0.0333
#> 14 Morsh et al. 1956 121 0.40 0.4236 0.0085
#> 15 Remmers et al. 1949 37 0.49 0.5361 0.0294
#> 16 Sullivan & Skanes 1974 14 0.51 0.5627 0.0909
#> 17 Sullivan & Skanes 1974 40 0.40 0.4236 0.0270
#> 18 Sullivan & Skanes 1974 16 0.34 0.3541 0.0769
#> 19 Sullivan & Skanes 1974 14 0.42 0.4477 0.0909
#> 20 Wherry 1952 20 0.16 0.1614 0.0588
#>
### meta-analysis of the transformed correlations using a random-effects model
res <- rma(yi, vi, data=dat, digits=2)
res
#>
#> Random-Effects Model (k = 20; tau^2 estimator: REML)
#>
#> tau^2 (estimated amount of total heterogeneity): 0.01 (SE = 0.01)
#> tau (square root of estimated tau^2 value): 0.07
#> I^2 (total heterogeneity / total variability): 11.64%
#> H^2 (total variability / sampling variability): 1.13
#>
#> Test for Heterogeneity:
#> Q(df = 19) = 20.97, p-val = 0.34
#>
#> Model Results:
#>
#> estimate se zval pval ci.lb ci.ub
#> 0.38 0.05 7.88 <.01 0.29 0.48 ***
#>
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
### predicted average correlation with 95% CI
predict(res, transf=transf.ztor)
#>
#> pred ci.lb ci.ub pi.lb pi.ub
#> 0.36 0.28 0.44 0.21 0.50
#>