\title{studies on the relationship between course instructor ratings and student achievement}
\description{results from 20 studies on the correlation between course instructor ratings and student achievement.}
\bold{study}     \tab \code{character} \tab study author(s) and year \cr
\bold{sample}    \tab \code{character} \tab course type \cr
\bold{control}   \tab \code{character} \tab ability control \cr
\bold{ni}        \tab \code{numeric}   \tab sample size of the study (number of sections) \cr
\bold{ri}        \tab \code{numeric}   \tab 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.), \emph{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. \emph{review of educational research}, \bold{51}(3), 281--309. \verb{https://doi.org/10.3102/00346543051003281}
### calculate r-to-z transformed correlations and corresponding sampling variances
dat <- escalc(measure="zcor", ri=ri, ni=ni, data=dat[c(1,4,5)])
### meta-analysis of the transformed correlations using a random-effects model
### predicted average correlation with 95\% ci

\title{studies on the treatment of upper gastrointestinal bleeding by a histamine h2 antagonist}
\description{results from studies examining the effectiveness of histamine h2 antagonists (cimetidine or ranitidine) in treating patients with acute upper gastrointestinal hemorrhage.}
\bold{id}    \tab \code{numeric}   \tab study number \cr
\bold{trial} \tab \code{character} \tab first author of trial \cr
\bold{year}  \tab \code{numeric}   \tab year of publication \cr
\bold{ref}   \tab \code{numeric}   \tab reference number \cr
\bold{trt}   \tab \code{character} \tab c = cimetidine, r = ranitidine \cr
\bold{ctrl}  \tab \code{character} \tab p = placebo, aa = antacids, ut = usual treatment \cr
\bold{nti}   \tab \code{numeric}   \tab number of patients in treatment group \cr
\bold{b.xti} \tab \code{numeric}   \tab number of patients in treatment group with persistent or recurrent bleedings \cr
\bold{o.xti} \tab \code{numeric}   \tab number of patients in treatment group in need of operation \cr
\bold{d.xti} \tab \code{numeric}   \tab number of patients in treatment group that died \cr
\bold{nci}   \tab \code{numeric}   \tab number of patients in control group \cr
\bold{b.xci} \tab \code{numeric}   \tab number of patients in control group with persistent or recurrent bleedings \cr
\bold{o.xci} \tab \code{numeric}   \tab number of patients in control group in need of operation \cr
\bold{d.xci} \tab \code{numeric}   \tab number of patients in control group that died
the data were obtained from tables 1 and 2 in collins and langman (1985). the authors used peto's (one-step) method for meta-analyzing the 27 trials. this approach is implemented in the \code{\link[metafor]{rma.peto}} function. using the same dataset, van houwelingen, zwinderman, and stijnen (1993) describe some alternative approaches for analyzing these data, including fixed- and random-effects conditional logistic models. those are implemented in the \code{\link[metafor]{rma.glmm}} function.
collins, r., & langman, m. (1985). treatment with histamine h2 antagonists in acute upper gastrointestinal hemorrhage. \emph{new england journal of medicine}, \bold{313}(11), 660--666. \verb{https://doi.org/10.1056/nejm198509123131104}
van houwelingen, h. c., zwinderman, k. h., & stijnen, t. (1993). a bivariate approach to meta-analysis. \emph{statistics in medicine}, \bold{12}(24), 2273--2284. \verb{https://doi.org/10.1002/sim.4780122405}
### meta-analysis of log ors using peto's method (outcome: persistent or recurrent bleedings)
res <- rma.peto(ai=b.xti, n1i=nti, ci=b.xci, n2i=nci, data=dat)
### meta-analysis of log ors using a conditional logistic regression model (fe model)
res <- rma.glmm(measure="or", ai=b.xti, n1i=nti, ci=b.xci, n2i=nci, data=dat,
### plot the likelihoods of the odds ratios
llplot(measure="or", ai=b.xti, n1i=nti, ci=b.xci, n2i=nci, data=dat,
### meta-analysis of log odds ratios using a conditional logistic regression model (re model)
### meta-analysis of log ors using peto's method (outcome: need for surgery)
res <- rma.peto(ai=o.xti, n1i=nti, ci=o.xci, n2i=nci, data=dat)
### meta-analysis of log ors using peto's method (outcome: death)
res <- rma.peto(ai=d.xti, n1i=nti, ci=d.xci, n2i=nci, data=dat)
medicine, odds ratios, peto's method, generalized linear models