MetaCorrect.Rmd

---
title: "How Effective are Methods of Correction for Publication Bias?"
output: html_document
---

```{r libraries, echo=FALSE,results=FALSE,warning=FALSE,error=FALSE,message=FALSE,results='hide'}
library(osfr)
library(RMySQL)
library(dplyr)
library(readxl)
library(stringr)
library(metafor)
library(ggplot2)
```

```{r parameters,echo=FALSE,warning=FALSE,error=FALSE,message=FALSE,results='hide'}
cst <- "50%"
```


```{r source,echo=FALSE,warning=FALSE,error=FALSE,message=FALSE,results='hide'}
source('source.R')
read_chunk('SKY_core_functions.R')
# databse where the original Kvarven data is stored
Kvarven.db <- dbConnect(MySQL(),dbname='Kvarven',username=username,password=password,host=host)
# SKY database
SKY.db <- dbConnect(MySQL(),dbname='SKY',username=username,password=password,host=host)
```


[Publication bias](https://chabefer.github.io/STCI/sec-meta.html#publication-bias-and-site-selection-bias) generates [adverse aggregate outcomes for science](Pvalues.html).
There are several attempts at solving the issue of publication bias, noth before (ex-ante) and after (ex-post) publication of the results.
Ex ante, one solution to fight publication bias is to commit to a pre-analysis plan before seeing the data and to commit to publish the results of every analysis whatever their results, a solution generally called pre-registration.
Ex-post, [several methods](https://chabefer.github.io/STCI/sec-meta.html#detection-of-and-correction-for-publication-bias) have been proposed to try to recover the true effect from data plagued by publication bias.
A key question is whether these methods are able to do what they were designed for, namely to correct for publication bias. 
In [an innovative and insightful paper](https://www.gwern.net/docs/statistics/bias/2019-kvarven.pdf) [published by Nature Human Behavior](https://www.nature.com/articles/s41562-019-0787-z), Kvarven, Stromland and Johannesson have proposed a deceptively simple but extremely efficient way to test for the validity of ex-post methods of correction for publication bias.
Their idea is simply to compare what is obtained when implementing correction ex-post to the estimate obtained by using ex-ante methods.
In order to implement their approach, they gather data from 11 meta-analysis of published results in psychology and compare them with the results of pre-registered replications of the same effects.
The interpretation of the results is [subject to debate](https://economistjourney.blogspot.com/2020/01/how-large-is-publication-bias-and-can.html), but there seems to be a good grounds for concluding that, of the three methods compared, two fail to decrease bias in any way (Trim-and-Fill and selection models), while one is able to reach unbiasedness and to significantly decrease prediction error (FAT-PET-PEESE).
In this article, I reproduce their results and extend them to methods of correction for publication bias that did not consider (namely the most recent version of FAT-PET-PEESE and p-curving). 

# Performance of alternative methods of correction for publication bias


# Analysis of each separate dataset

In this section, we look at each dataset separately.
We start by downloading the aggregated dataset where a lot of information is stored already.

```{r downloadAggregate, echo=TRUE, warning=FALSE,error=FALSE,message=FALSE,results='hide',cache=TRUE}
# download dataset from SQL server
Aggregate <- dbReadTable(Kvarven.db,"Aggregate")
```

## Belle dataset

```{r downloadBelle, echo=TRUE, warning=FALSE,error=FALSE,message=FALSE,results='hide',cache=TRUE}
# download dataset from SQL server
Belle <- dbReadTable(Kvarven.db,"Belle")
# get the comment associated with the study, so that we know what it is about
Belle.description <- dbGetQuery(Kvarven.db,"
    SELECT table_comment 
    FROM INFORMATION_SCHEMA.TABLES 
    WHERE table_schema='Kvarven' 
        AND table_name='Belle';")
# get the original study, the meta-analysis and the replication
Belle.papers <- Aggregate %>%
                    filter(str_detect(metaanalysis,"Belle")==TRUE) %>%
                    select(original,replication,metaanalysis)
```

The Belle dataset is a `r Belle.description[1,1] `.
The original study is by `r Belle.papers[1,1] `.
The meta-analysis is by `r Belle.papers[1,3] `.
The replication is by `r Belle.papers[1,2] `.
The fact that the identity of the replicator is unknown was already the case in the original Kvarven study.

### FAT-PET-PEESE

In this section, we are looking at how the Belle dataset behaves with the [FAT-PET-PEESE method of Stanley and Docouliagos](https://chabefer.github.io/STCI/sec-meta.html#detection-of-and-correction-for-publication-bias).
There are three ways that we can FAT-PET-PEESE: using a Fixed Effects (FE) meta-analysis, a Random Effects (RE) meta-analysis and Weighted Least Squares (WLS).
Recently, [Stanley and Docouliago](https://doi.org/10.1002/jrsm.1211) have argued that the WLS approach was the best one. 
WLS obtains the same estimated effect size as FE, but it computes its estimate of the standard error by taking into account inter-study variability, as RE does.

```{r BellePEESE,echo=TRUE,error=FALSE,message=FALSE,warning=FALSE,results='hide',fig.cap="FAT-PET-PEESE estimation for the Belle dataset",fig.align='center',out.width="20%",fig.pos='htbp',fig.height=8,fig.width=12}
# weights for WLS estimator
Belle <- Belle %>% 
          mutate(weightsWLS=(1/v)/(sum(1/v)))
# WLS Meta estimator
Belle.WLS.Meta <- lm(d~1,weights = weightsWLS,data=Belle)
# WLS FAT PET estimator
Belle.WLS.FAT.PET <- lm(d~sed,weights = weightsWLS,data=Belle)
# WLS PEESE estimator
Belle.WLS.PEESE <- lm(d~v,weights = weightsWLS,data=Belle)
# FE Meta Estimator
Belle.FE.Meta <- rma(yi=d,vi=v,data=Belle,method="FE")
# FE FAT PET estimator
Belle.FE.FAT.PET <- rma(d~sed,vi=v,data=Belle,method="FE")
# FE PEESE estimator
Belle.FE.PEESE <- rma(d~v,vi=v,data=Belle,method="FE")
# RE Meta Estimator
Belle.RE.Meta <- rma(yi=d,vi=v,data=Belle,method="REML")
# RE FAT PET estimator
Belle.RE.FAT.PET <- rma(d~sed,vi=v,data=Belle,method="REML")
# RE PEESE estimator
Belle.RE.PEESE <- rma(d~v,vi=v,data=Belle,method="REML")

# plot of results
colors <- c("MetaAnalysisOriginal"="red","Replication"="blue","MetaAnalysisWLS"="green","MetaAnalysisRE"="purple")
lines <- c("FATPETWLS"="solid","PEESEWLS"="dashed","FATPETRE"="dotted","PEESERE"="dotdash")

ggplot(Belle,aes(x=sed,y=d))+
  geom_point()+
  xlim(0,0.5)+
  ylim(-0.1,1)+
  theme_bw()+
  xlab("Standard error")+
  ylab("Effect size")+
  geom_hline(aes(yintercept=Aggregate %>%
                    filter(str_detect(metaanalysis,"Belle")==TRUE) %>%
                    select(meta_s) %>% 
                    as.numeric(),colour="MetaAnalysisOriginal"))+
  geom_hline(aes(yintercept=Aggregate %>%
                    filter(str_detect(metaanalysis,"Belle")==TRUE) %>%
                    select(replication_s) %>% 
                    as.numeric(),colour="Replication")) +
  geom_hline(aes(yintercept=coef(Belle.WLS.Meta)[[1]],colour="MetaAnalysisWLS"))+
  geom_hline(aes(yintercept=coef(Belle.RE.Meta)[[1]],colour="MetaAnalysisRE"))+
  stat_function(fun=function(x){coef(Belle.WLS.FAT.PET)[1] + coef(Belle.WLS.FAT.PET)[2]*x},aes(linetype="FATPETWLS"),color="black")+
  stat_function(fun=function(x){coef(Belle.WLS.PEESE)[1] + coef(Belle.WLS.PEESE)[2]*x^2},aes(linetype="PEESEWLS"),color="black")+
  stat_function(fun=function(x){coef(Belle.RE.FAT.PET)[1] + coef(Belle.RE.FAT.PET)[2]*x},aes(linetype="FATPETRE"),color="black")+
  stat_function(fun=function(x){coef(Belle.RE.PEESE)[1] + coef(Belle.RE.PEESE)[2]*x^2},aes(linetype="PEESERE"),color="black")+
  scale_colour_manual("Estimate",values = colors)+
  scale_linetype_manual("Method",values = lines)

```

Figure \@ref(fig:BellePEESE) shows the result of the FAT-PET-PEESE analysis applied to the Belle dataset.
This data set is characterized by severe publication bias, since the estimated meta-analytical effect is of `r Aggregate %>%  filter(str_detect(metaanalysis,"Belle")==TRUE) %>% select(meta_s) %>% as.numeric() %>% round(digits=2)` while the effect estimated after the pre-registered replications is of `r Aggregate %>%  filter(str_detect(metaanalysis,"Belle")==TRUE) %>% select(replication_s) %>% as.numeric() %>% round(digits=2)`.

How does FAT-PET-PEESE perform?
Let's focus on the WLS results.
The FAT test detects funnel asymmetry: we see that the slope of the FATPETWLS curve is downward sloping, indicating that less precise results have larger effect sizes.
The slope of the FAT-PET curve is equal to `r Belle.WLS.FAT.PET %>% coef(.) %>% t(.) %>% as.data.frame(.) %>% select(sed) %>% as.numeric(.) %>% round(digits=2)` $\pm$ `r round(Belle.WLS.FAT.PET %>% vcov(.) %>% diag(.) %>% sqrt(.) %>% t(.) %>% as.data.frame(.) %>% select(sed) %>% as.numeric(.)*qnorm((0.95+1)/2),digits=2)`
The p-value of the one-sided test that this value is zero against the alternative assumption that it is positive is equal to  `r round(1-pnorm(coef(Belle.WLS.FAT.PET)[[2]]/sqrt(diag(vcov(Belle.WLS.FAT.PET)))[[2]]),digits=2)` when using the normal approximation to the distribution of the parameter.
So we reject the absence of publication bias.

Now, what is the FAT-PET-PEESE estimate corrected for publication bias?
It depends on whether the PET estimate is different from zero or not.
If it is not, then the PET estimate is the publication bias corrected estimate.
If the PET estimate is different from zero, we look at the PEESE estimate.
The PET estimate is of `r round(coef(Belle.WLS.FAT.PET)[[1]],digits=2)` $\pm$ `r round(sqrt(diag(vcov(Belle.WLS.FAT.PET)))[[1]]*qnorm((0.95+1)/2),digits=2)`.
This obviously is not significantly different from zero, and thus becomes our preferred estimate of the treatment effect.
Despite is large imprecision, this estimate is in reality extremely close to the truth of `r Aggregate %>%  filter(str_detect(metaanalysis,"Belle")==TRUE) %>% select(replication_s) %>% as.numeric() %>% round(digits=2)`.

Let's send the results to the SQL dataset.
I'm going to send the results in the SKY database using as a benchmark the summary table of results in the original Kvarven dataset.

```{r SendBelleResultsSQL,echo=TRUE,error=FALSE,message=FALSE,warning=FALSE,results='hide'}
# send the table with the main initial data
dbWriteTable(SKY.db,"MetaCorrect",Aggregate %>% select(id,original,replication,metaanalysis,replication_s,meta_s,ser,sem),row.names=FALSE,overwrite=TRUE)
# explain name of variable
dbSendQuery(SKY.db,"
            ALTER TABLE `SKY`.`MetaCorrect` 
            CHANGE COLUMN `original` `original` TEXT NULL DEFAULT NULL COMMENT 'Name of the original paper.' ,
            CHANGE COLUMN `replication` `replication` TEXT NULL DEFAULT NULL COMMENT 'Name of the replication paper.' ,
            CHANGE COLUMN `metaanalysis` `metaanalysis` TEXT NULL DEFAULT NULL COMMENT 'Name of the meta-analysis paper.' ,
            CHANGE COLUMN `replication_s` `replication_s` DOUBLE NULL DEFAULT NULL COMMENT 'Effect size (Cohen d) estimated in the replication.' ,
            CHANGE COLUMN `meta_s` `meta_s` DOUBLE NULL DEFAULT NULL COMMENT 'Effect size (Cohen d) estimated in the meta-analysis.' ,
            CHANGE COLUMN `ser` `ser` DOUBLE NULL DEFAULT NULL COMMENT 'Standard error of the effect size (Cohen d) estimated in the replication.' ,
            CHANGE COLUMN `sem` `sem` DOUBLE NULL DEFAULT NULL COMMENT 'Standard error of the effect size (Cohen d) estimated in the meta-analysis.' ,
            COMMENT = 'Results of the methods correcting for publication bias.' ;")
# create a new column in the SQL table for the results of FATPETPEESE
dbSendQuery(SKY.db,"
            ALTER TABLE `SKY`.`MetaCorrect` 
            ADD COLUMN `fatpetpeese_s` DOUBLE NULL DEFAULT NULL AFTER `meta_s`,
            ADD COLUMN `sef` DOUBLE NULL DEFAULT NULL AFTER `sem`
            ;")
# comment on the names of the new column
dbSendQuery(SKY.db,"
            ALTER TABLE `SKY`.`MetaCorrect` 
            CHANGE COLUMN `fatpetpeese_s` `fatpetpeese_s` DOUBLE NULL DEFAULT NULL COMMENT 'Effect size (Cohen d) estimated with FATPETPEESE',
            CHANGE COLUMN `sef` `sef` DOUBLE NULL DEFAULT NULL COMMENT 'Standard error of the effect size (Cohen d) estimated with FATPETPEESE'
            ;")
# sending the Belle results to the new SQL table in SKY
dbSendQuery(SKY.db,paste("
            UPDATE `SKY`.`MetaCorrect` 
            SET 
              `fatpetpeese_s` = ",coef(Belle.WLS.FAT.PET)[[1]],",
              `sef` = ",sqrt(diag(vcov(Belle.WLS.FAT.PET)))[[1]],"
            WHERE 
              SUBSTRING_INDEX(metaanalysis,' ',1)='Belle'
            ;",sep=""))
```


**It would be great to recover the original individual replication estimates to enrich Figure \@ref(fig:BellePEESE).**

### P-curving

[P-curving](https://chabefer.github.io/STCI/sec-meta.html#detection-of-and-correction-for-publication-bias) uses the distribution of the statistically significant p-values to test for the existence of a real effect and to correct for it.
The first step in a p-curving analysis is to generate p-values (in generate for the two-sided t-test of absence of effect) and to derive the distribution of the significant p-values.
In the absence of any impact, the significant p-values should be distributed uniformly.
In the presence of a real effect, the distribution of the significant p-values should exhibit a peak at lower p-values.
In case there are Questionable Research Practices, the distribution of significant p-values exhibits a peak close to 0.05.
Let's see what happens.

```{r BellePcurve,echo=TRUE,error=FALSE,warning=FALSE,message=FALSE,results='hide',fig.cap="Simple p-curve for the Belle dataset",fig.align='center',out.width="75%",fig.pos='htbp',fig.height=8,fig.width=12}
# create the p-values for the two-sided t-test that the effect size is zero
Belle <- Belle %>%
          mutate(
            tstat = d/sed,
            pvalue= 2*(1-pnorm(tstat)))
# function that generates the proportion of significant pvalues in two half intervals
p_value_prop <- function(pvalues){
    pvaluessig <- pvalues[pvalues<=0.05]
    p.upper <- ifelse(pvaluessig>0.025,1,0)
    p.lower <- ifelse(pvaluessig<=0.025,1,0)
    p.upper.prop <- sum(p.upper)/length(pvaluessig)
    p.lower.prop <- sum(p.lower)/length(pvaluessig)
    return(c(p.lower.prop, p.upper.prop))
}

prop_pval <- p_value_prop(Belle$pvalue)

intervals <- c("[0,0.025]","[0.025,0.05]")

ggplot(, aes(x = intervals, prop_pval)) +
  geom_bar(stat="identity", fill="steelblue") +
  theme_minimal() +
  scale_x_discrete() +
  geom_text(aes(label=round(prop_pval, 2)), vjust=1.6, color="white", size=3.5) +
  labs(x = "Intervals", y = "Proportion")
```

Figure \@ref(fig:BellePcurve) shows that, from a p-curve perspective, there does seem to be genuine evidence of an effect in this meta-analysis.
Let's look at the full distribution of the p-values and compare it to a flat p-curve and a p-curve with a true effect.

```{r BellePcurveFull,echo=TRUE,error=FALSE,warning=FALSE,message=FALSE,results='hide',fig.cap="Full p-curve for the Belle dataset",fig.align='center',out.width="75%",fig.pos='htbp',fig.height=8,fig.width=12}
MDE.var <- function(alpha=0.05,kappa=0.33,varE=1){
  return((qnorm(kappa)+qnorm(1-alpha/2))*sqrt(varE))
}

ppCurvePower <- function(p1,p2,alpha=0.05,kappa=0.33,varE=1){
  return((pnorm(MDE.var(alpha=alpha,kappa=kappa)-qnorm(1-p2/2))
    -pnorm(MDE.var(alpha=alpha,kappa=kappa)-qnorm(1-p1/2)))/kappa)
}

pCurve.hist <- function(pvalues,power=.33){
  pvaluessig <- pvalues[pvalues<=0.05]  
  dens1 <- sum(ifelse(abs(pvaluessig-0.005)<0.005,1,0)/length(pvaluessig))
  dens2 <- sum(ifelse(abs(pvaluessig-0.015)<0.005,1,0)/length(pvaluessig))
  dens3 <- sum(ifelse(abs(pvaluessig-0.025)<0.005,1,0)/length(pvaluessig))
  dens4 <- sum(ifelse(abs(pvaluessig-0.035)<0.005,1,0)/length(pvaluessig))
  dens5 <- sum(ifelse(abs(pvaluessig-0.045)<0.005,1,0)/length(pvaluessig))
  dens <- c(dens1,dens2,dens3,dens4,dens5)
  p.hist.1 <- cbind(c(0.01,0.02,0.03,0.04,0.05),dens)
  p.hist.1 <- as.data.frame(p.hist.1)
  colnames(p.hist.1) <- c('p','density')
  p.hist.1$Data <- c("Observed")
  p.hist.2 <- cbind(c(0.01,0.02,0.03,0.04,0.05),0.2)
  p.hist.2 <- as.data.frame(p.hist.2)
  colnames(p.hist.2) <- c('p','density')
  p.hist.2$Data <- c("Uniform")
  dens331 <- ppCurvePower(0,0.01)
  dens332 <- ppCurvePower(0.01,0.02)
  dens333 <- ppCurvePower(0.02,0.03)
  dens334 <- ppCurvePower(0.03,0.04)
  dens335 <- ppCurvePower(0.04,0.05)
  dens33 <- c(dens331,dens332,dens333,dens334,dens335)
  p.hist.3 <- cbind(c(0.01,0.02,0.03,0.04,0.05),dens33)
  p.hist.3 <- as.data.frame(p.hist.3)
  colnames(p.hist.3) <- c('p','density')
  p.hist.3$Data <- c("Power33")
  p.hist <- rbind(p.hist.1,p.hist.2,p.hist.3)
  return(p.hist)
}

p.hist <- pCurve.hist(Belle$pvalue)
p.hist$Data <- factor(p.hist$Data,levels=c("Observed","Uniform","Power33"))

ggplot(data=p.hist, aes(x=p, y=density, color=Data)) +
geom_point() +
geom_line() +
theme_bw()
```

Figure \@ref(fig:BellePcurveFull) suggests confirms that, for the p-curve approach, there is evidence in favor of a genuine true effect, close to the effect that would give 33\% power.
Let's see whether a formal test confirms that.

```{r BellePcurveFullTest,echo=TRUE,error=FALSE,warning=FALSE,message=FALSE,results='hide'}
pp.test <- function(pvalues,alter='True'){
  pvaluessig <- pvalues[pvalues<=0.05]
  pp <- pvaluessig/0.05
  if (alter=='QRP'){
    pp <- 1 - pp
  }
  Fpp <- -2*sum(log(pp)) # Chi-square statistic
  dfChis <- 2*length(pvaluessig)
  pChisquare.Fpp <- pchisq(Fpp,dfChis,lower.tail=F) # Corresponding p-value
  qChisquare.5 <- qchisq(0.05,dfChis,lower.tail=F) 
  return(c(pChisquare.Fpp,Fpp,dfChis,qChisquare.5))
}
# Only including p-values in [0,0.05] interval.

 #I checked that I did in fact got rid of them all by contrasting with excel file since sample is small.
pp.ex.sig.True <- pp.test(Belle$pvalue) # p-value close to 0, Chi statistic of 275.1
pp.ex.sig.QRP <- pp.test(Belle$pvalue, alter = 'QRP') # p-value of 0.993 and Chi statistic of 12.75
```

The p-value for the null hypothesis that there is no effect is of `r round(pp.ex.sig.True,2)` while the p-value for the null that there are QRPs is of `r round(pp.ex.sig.QRP,2)`.
Clearly, p-curves seems to detect a true effect here.

Finally, let's implement the p-curve correction for publication bias.

```{r BellePcurveEstimate,echo=TRUE,error=FALSE,warning=FALSE,message=FALSE,results='hide'}
ppCurveEst <- function(thetac,thetak,sigmak,alpha=0.05){
  return((pnorm((thetac-thetak)/sigmak)/pnorm(thetac/sigmak-qnorm(1-alpha/2))))
}
#KS statistic
KS.stat.unif <- function(vector){
  return(ks.test(x=vector,y=punif)$statistic)
}
ppCurve.Loss.KS <- function(thetac,thetak,sigmak,alpha=0.05){
  ppvalues <- ppCurveEst(thetac=thetac,thetak=thetak,sigmak=sigmak,alpha=alpha)
  return(KS.stat.unif(ppvalues))
}

#Estimating thetac that minimizes the KS distance by brute grid search first
# will program the optimize function after
ppCurveEstES <- function(thetak,sigmak,thetacl,thetach,alpha=0.05,ngrid=100){
  # keep significant coefficients and standard errors
  thetaksig <- thetak[2*(1-pnorm(thetak/sigmak))<=0.05]
  sigmaksig <- sigmak[2*(1-pnorm(thetak/sigmak))<=0.05]
  # break thetac values in a grid
  thetac.grid <- seq(from=thetacl,to=thetach,length.out=ngrid)
  # computes the ppcurve for each point of the grid: outputs a matrix where columns are the ppcurves at each values of thetac
  ppCurve.grid <- sapply(thetac.grid,ppCurveEst,thetak=thetaksig,sigmak=sigmaksig,alpha=alpha)
  # compute KS stat for each value of thetac (over columns)
  KS.grid <- apply(ppCurve.grid,2,KS.stat.unif)
  # computes the value of thetac for which the KS stat is minimum (match identifies the rank of the min in the KSgrid)
  min.theta.c <- thetac.grid[match(min(KS.grid),KS.grid)]
  # optimizes over KS stat to find value of thetac that minimizes the KS stat
  thetahat <- optimize(ppCurve.Loss.KS,c(min.theta.c-0.1,min.theta.c+0.1),thetak=thetaksig,sigmak=sigmaksig,alpha=alpha)
  # returns the optimal thetac, the grid of thetac, the KS stats on the grid, for potential plot, and the ecdf of ppvalues at the optimum theta for graph against the uniform
  return(list(thetahat$minimum,thetac.grid,KS.grid,ecdf(ppCurve.grid[,match(min(KS.grid),KS.grid)])))
}

test <- ppCurveEstES(thetak=Belle$d,sigmak = Belle$sed ,thetacl=0,thetach=10,alpha=0.05,ngrid=50)
```

The p-curve bias-corrected estimate is of `r round(test[[1]],2)`.
Lower than the meta-analytic estimate but still pretty far off.

Let's send the results to the SQL dataset.

```{r SendBelleResultsSQLPcurve,echo=TRUE,error=FALSE,message=FALSE,warning=FALSE,results='hide'}
# create a new column in the SQL table for the results of Pcurve
dbSendQuery(SKY.db,"
            ALTER TABLE `SKY`.`MetaCorrect` 
            ADD COLUMN `pcurve_s` DOUBLE NULL DEFAULT NULL AFTER `fatpetpeese_s`
            ;")
# comment on the names of the new column
dbSendQuery(SKY.db,"
            ALTER TABLE `SKY`.`MetaCorrect` 
            CHANGE COLUMN `pcurve_s` `pcurve_s` DOUBLE NULL DEFAULT NULL COMMENT 'Effect size (Cohen d) estimated with Pcurve'
            ;")
# sending the Belle results to the new SQL table in SKY
dbSendQuery(SKY.db,paste("
            UPDATE `SKY`.`MetaCorrect` 
            SET 
              `pcurve_s` = ",test[[1]],"
            WHERE 
              SUBSTRING_INDEX(metaanalysis,' ',1)='Belle'
            ;",sep=""))
```

# Data 

The data comes from the [OSF webpage of the Kvarven et al paper](https://osf.io/8qvgp/).
In this section, I download the original data and send it to SKY's SQL server.
In order to so, I've had to [fork the original project](https://osf.io/vsnu5/), because the `osfr` package would not connect me to the original project.
This is not optimal since I will miss future potential updates of the project. 

```{r KvarvenDownloadData,echo=TRUE}
# Authentication on OSF (provide your own OSF authentication key here)
#osf_auth(OSFauth)
# path of forked project on OSF
#OSFid <- "vsnu5"
# finding the project on OSF
#kvarven.project <- osf_retrieve_node(paste("https://osf.io",OSFid,sep="/"))
# dowloading data in working directory
#osf_download(osf_ls_files(kvarven.project)[1,])
# extracting data
#unzip(osf_ls_files(kvarven.project)[[1,1]])
# this returns an error message since the name of one of the files to unzip contains a character in central European DOS Latin 2 encoding ("ü")
# I've had to extract manually the files and then to change the name of the file to "u" so that no similar problem happens.
```

```{r KvarvenToSQL,echo=TRUE,error=FALSE,message=FALSE,warning=FALSE,results='hide',cache=TRUE}
# summary file with main results of meta-analysis and replications
# path to access the file
path <- "./Corrected data May 2020/"
# uploading the file
data.tot <- read_excel(paste(path,"Dataset.xls",sep=""))
# correcting one character that messes up in SQL
data.tot$metaanalysis[[2]] <- "Kuhberger (1998)"
# taking out unnecessary lines and columns
data.tot <- as.data.frame(data.tot[1:15,1:21])
# sending to SQL
dbWriteTable(Kvarven.db,"Aggregate",data.tot,overwrite=TRUE,row.names=TRUE)
dbSendQuery(Kvarven.db,"
            ALTER TABLE `Kvarven`.`Aggregate` 
            CHANGE COLUMN `row_names` `id` SMALLINT(2) NULL DEFAULT NULL COMMENT 'Id of the study' ,
            CHANGE COLUMN `original` `original` TEXT NULL DEFAULT NULL COMMENT 'Name of the original paper.' ,
            CHANGE COLUMN `replication` `replication` TEXT NULL DEFAULT NULL COMMENT 'Name of the replication paper.' ,
            CHANGE COLUMN `metaanalysis` `metaanalysis` TEXT NULL DEFAULT NULL COMMENT 'Name of the meta-analysis paper.' ,
            CHANGE COLUMN `effecto` `effecto` DOUBLE NULL DEFAULT NULL COMMENT 'Effect estimated in the original meta-analysis (in original units). (I guess)' ,
            CHANGE COLUMN `originalinc` `originalinc` TINYINT(1) NULL DEFAULT NULL COMMENT 'Is the original study included in the meta-analysis? (1= yes, 0= No)' ,
            CHANGE COLUMN `replication_inc` `replication_inc` TINYINT(1) NULL DEFAULT NULL COMMENT 'Is the replication included in the meta-analysis? (1= yes, 0= No)' ,
            CHANGE COLUMN `noconvert` `noconvert` TINYINT(1) NULL DEFAULT NULL COMMENT 'I do not know what this means.' ,
            CHANGE COLUMN `publi` `publi` TINYINT(1) NULL DEFAULT NULL COMMENT 'Has the replication been published? (1= yes, 0= no) (I guess)' ,
            CHANGE COLUMN `tausqrm` `tausqrm` TINYINT(1) NULL DEFAULT NULL COMMENT 'Inter-study variability in the original meta-analysis (I guess).' ,
            CHANGE COLUMN `originalu` `originalu` TINYINT(1) NULL DEFAULT NULL COMMENT 'I do not know what this means.' ,
            CHANGE COLUMN `replication_s` `replication_s` DOUBLE NULL DEFAULT NULL COMMENT 'Effect size (Cohen d) estimated in the replication.' ,
            CHANGE COLUMN `meta_s` `meta_s` DOUBLE NULL DEFAULT NULL COMMENT 'Effect size (Cohen d) estimated in the meta-analysis.' ,
            CHANGE COLUMN `ser` `ser` DOUBLE NULL DEFAULT NULL COMMENT 'Standard error of the effect size (Cohen d) estimated in the replication.' ,
            CHANGE COLUMN `sem` `sem` DOUBLE NULL DEFAULT NULL COMMENT 'Standard error of the effect size (Cohen d) estimated in the meta-analysis.' ,
            CHANGE COLUMN `sed` `sed` DOUBLE NULL DEFAULT NULL COMMENT 'Standard error of the difference in estimated effect size (Cohen d) between the meta-analysis and the replication.' ,
            CHANGE COLUMN `weight` `weight` TINYINT(1) NULL DEFAULT NULL COMMENT 'I do not know what that means.' ,
            CHANGE COLUMN `ml` `ml` TINYINT(1) NULL DEFAULT NULL COMMENT 'I do not know what that means.' ,
            CHANGE COLUMN `threepsm` `threepsm` DOUBLE NULL DEFAULT NULL COMMENT 'Effect size (Cohen d) estimated using the selection model method.' ,
            CHANGE COLUMN `threepsmse` `threepsmse` DOUBLE NULL DEFAULT NULL COMMENT 'Standard error of the effect size (Cohen d) estimated using the selection model method.' ,
            CHANGE COLUMN `diff` `diff` DOUBLE NULL DEFAULT NULL COMMENT 'Difference in estimated effect size (Cohen d) between the meta-analysis and the replication. (I guess)' ,
            CHANGE COLUMN `seo` `seo` DOUBLE NULL DEFAULT NULL COMMENT 'Standard error of the effect estimated in the original meta-analysis (in original units). (I guess)' , 
            COMMENT = 'Table with the aggregate data of the Kvarven paper.' ;")

# Files for individual studies
# path to files
path <- "./Corrected data May 2020/Meta/"
# names of the datasets
files <- c("Belle","Blanken","Coles","DeCoster","Felts","Hagger","Henriksson","Kivikangas","Kuhberger","Meissner","Miles","Rabelo","Rand","Roth","Schimmack")
# separators used in the data files
sep.data <- c(",",rep(";",8),",",rep(";",5))

# Belle dataset
Belle <- read.csv(paste(path,files[1],".csv",sep=""),sep=sep.data[1])
dbWriteTable(Kvarven.db,files[1],Belle %>% select("d","v","sed"),overwrite=TRUE,row.names=TRUE)
dbSendQuery(Kvarven.db,
            "ALTER TABLE `Kvarven`.`Belle` 
             CHANGE COLUMN `row_names` `id` SMALLINT(4) NULL DEFAULT NULL COMMENT 'Id of the result' ,
             CHANGE COLUMN `d` `d` DOUBLE NULL DEFAULT NULL COMMENT 'Effect size (Cohen d) in units of standard deviation.' ,
             CHANGE COLUMN `v` `v` DOUBLE NULL DEFAULT NULL COMMENT 'Variance of the estimated effect size.' ,
             CHANGE COLUMN `sed` `sed` DOUBLE NULL DEFAULT NULL COMMENT 'Standard error of the estimated effect size.' , 
             COMMENT = 'Dataset for the meta-analysis of self-concept maintenance originally studied by Mazar et al. (2008)' ;")

# Blanken dataset
Blanken <- read.csv(paste(path,files[2],".csv",sep=""),sep=sep.data[2])
dbWriteTable(Kvarven.db,files[2],Blanken %>% select("d","var","sed"),overwrite=TRUE,row.names=TRUE)
dbSendQuery(Kvarven.db,
            "ALTER TABLE `Kvarven`.`Blanken` 
             CHANGE COLUMN `row_names` `id` SMALLINT(4) NULL DEFAULT NULL COMMENT 'Id of the result' ,
             CHANGE COLUMN `d` `d` DOUBLE NULL DEFAULT NULL COMMENT 'Effect size (Cohen d) in units of standard deviation.' ,
             CHANGE COLUMN `var` `v` DOUBLE NULL DEFAULT NULL COMMENT 'Variance of the estimated effect size.' ,
             CHANGE COLUMN `sed` `sed` DOUBLE NULL DEFAULT NULL COMMENT 'Standard error of the estimated effect size.' , 
             COMMENT = 'Dataset for the meta-analysis of moral credentials and the expression of prejudice originally studied by Monin & Miller (2001)' ;")

# Coles dataset
Coles <- read.csv(paste(path,files[3],".csv",sep=""),sep=sep.data[3])
dbWriteTable(Kvarven.db,files[3],Coles,overwrite=TRUE,row.names=TRUE)
dbSendQuery(Kvarven.db,
            "ALTER TABLE `Kvarven`.`Coles` 
             CHANGE COLUMN `row_names` `id` SMALLINT(4) NULL DEFAULT NULL COMMENT 'Id of the result' ,
             CHANGE COLUMN `es` `d` DOUBLE NULL DEFAULT NULL COMMENT 'Effect size (Cohen d) in units of standard deviation.' ,
             CHANGE COLUMN `v` `v` DOUBLE NULL DEFAULT NULL COMMENT 'Variance of the estimated effect size.' ,
             CHANGE COLUMN `se` `sed` DOUBLE NULL DEFAULT NULL COMMENT 'Standard error of the estimated effect size.' , 
             COMMENT = 'Dataset for the meta-analysis of the facial feedback hypothesis originally studied by Strack et al. (1988)' ;")

# DeCoster dataset
DeCoster <- read.csv(paste(path,files[4],".csv",sep=""),sep=sep.data[4])
dbWriteTable(Kvarven.db,files[4],DeCoster %>% select("d","v","sed"),overwrite=TRUE,row.names=TRUE)
dbSendQuery(Kvarven.db,
            "ALTER TABLE `Kvarven`.`DeCoster` 
             CHANGE COLUMN `row_names` `id` SMALLINT(4) NULL DEFAULT NULL COMMENT 'Id of the result' ,
             CHANGE COLUMN `d` `d` DOUBLE NULL DEFAULT NULL COMMENT 'Effect size (Cohen d) in units of standard deviation.' ,
             CHANGE COLUMN `v` `v` DOUBLE NULL DEFAULT NULL COMMENT 'Variance of the estimated effect size.' ,
             CHANGE COLUMN `sed` `sed` DOUBLE NULL DEFAULT NULL COMMENT 'Standard error of the estimated effect size.' , 
             COMMENT = 'Dataset for the meta-analysis of the category accessibility hypothesis originally studied by Srull et al. (1979)' ;")

# Felts dataset
Felts <- read.csv(paste(path,files[5],".csv",sep=""),sep=sep.data[5])
dbWriteTable(Kvarven.db,files[5],Felts %>% select("d","v","sed"),overwrite=TRUE,row.names=TRUE)
dbSendQuery(Kvarven.db,
            "ALTER TABLE `Kvarven`.`Felts` 
             CHANGE COLUMN `row_names` `id` SMALLINT(4) NULL DEFAULT NULL COMMENT 'Id of the result' ,
             CHANGE COLUMN `d` `d` DOUBLE NULL DEFAULT NULL COMMENT 'Effect size (Cohen d) in units of standard deviation.' ,
             CHANGE COLUMN `v` `v` DOUBLE NULL DEFAULT NULL COMMENT 'Variance of the estimated effect size.' ,
             CHANGE COLUMN `sed` `sed` DOUBLE NULL DEFAULT NULL COMMENT 'Standard error of the estimated effect size.' , 
             COMMENT = 'Dataset for the meta-analysis of the dissociation between moral judgments and justifications originally studied by Hauser et al. (2007)' ;")

# Hagger dataset
Hagger <- read.csv(paste(path,files[6],".csv",sep=""),sep=sep.data[6])
dbWriteTable(Kvarven.db,files[6],Hagger %>% select("d","v","sed"),overwrite=TRUE,row.names=TRUE)
dbSendQuery(Kvarven.db,
            "ALTER TABLE `Kvarven`.`Hagger` 
             CHANGE COLUMN `row_names` `id` SMALLINT(4) NULL DEFAULT NULL COMMENT 'Id of the result' ,
             CHANGE COLUMN `d` `d` DOUBLE NULL DEFAULT NULL COMMENT 'Effect size (Cohen d) in units of standard deviation.' ,
             CHANGE COLUMN `v` `v` DOUBLE NULL DEFAULT NULL COMMENT 'Variance of the estimated effect size.' ,
             CHANGE COLUMN `sed` `sed` DOUBLE NULL DEFAULT NULL COMMENT 'Standard error of the estimated effect size.' , 
             COMMENT = 'Dataset for the meta-analysis of Methylphenidate and effort-induced depletion of regulatory control originally studied by Sripada et al. (2014)' ;")

# Henriksson dataset
Henriksson <- read.csv(paste(path,files[7],".csv",sep=""),sep=sep.data[7])
dbWriteTable(Kvarven.db,files[7],Henriksson,overwrite=TRUE,row.names=TRUE)
dbSendQuery(Kvarven.db,
            "ALTER TABLE `Kvarven`.`Henriksson` 
             CHANGE COLUMN `row_names` `id` SMALLINT(4) NULL DEFAULT NULL COMMENT 'Id of the result' ,
             CHANGE COLUMN `d` `d` DOUBLE NULL DEFAULT NULL COMMENT 'Effect size (Cohen d) in units of standard deviation.' ,
             CHANGE COLUMN `v` `v` DOUBLE NULL DEFAULT NULL COMMENT 'Variance of the estimated effect size.' ,
             CHANGE COLUMN `sed` `sed` DOUBLE NULL DEFAULT NULL COMMENT 'Standard error of the estimated effect size.' , 
             COMMENT = 'Dataset for the meta-analysis of incidental environmental anchors originally studied by Critcher & Gilovich (2008)' ;")


# Kivikangas dataset
Kivikangas <- read.csv(paste(path,files[8],".csv",sep=""),sep=sep.data[8])
dbWriteTable(Kvarven.db,files[8],Kivikangas,overwrite=TRUE,row.names=TRUE)
dbSendQuery(Kvarven.db,
            "ALTER TABLE `Kvarven`.`Kivikangas` 
             CHANGE COLUMN `row_names` `id` SMALLINT(4) NULL DEFAULT NULL COMMENT 'Id of the result' ,
             CHANGE COLUMN `d` `d` DOUBLE NULL DEFAULT NULL COMMENT 'Effect size (Cohen d) in units of standard deviation.' ,
             CHANGE COLUMN `v` `v` DOUBLE NULL DEFAULT NULL COMMENT 'Variance of the estimated effect size.' ,
             CHANGE COLUMN `SE` `sed` DOUBLE NULL DEFAULT NULL COMMENT 'Standard error of the estimated effect size.' , 
             COMMENT = 'Dataset for the meta-analysis of the moral foundations of liberals and conservatives originally studied by Graham et al. (2009)' ;")

# Kuhberger dataset
Kuhberger <- read.csv(paste(path,files[9],".csv",sep=""),sep=sep.data[9])
dbWriteTable(Kvarven.db,files[9],Kuhberger,overwrite=TRUE,row.names=TRUE)
dbSendQuery(Kvarven.db,
            "ALTER TABLE `Kvarven`.`Kuhberger` 
             CHANGE COLUMN `row_names` `id` SMALLINT(4) NULL DEFAULT NULL COMMENT 'Id of the result' ,
             CHANGE COLUMN `d` `d` DOUBLE NULL DEFAULT NULL COMMENT 'Effect size (Cohen d) in units of standard deviation.' ,
             CHANGE COLUMN `v` `v` DOUBLE NULL DEFAULT NULL COMMENT 'Variance of the estimated effect size.' ,
             CHANGE COLUMN `sed` `sed` DOUBLE NULL DEFAULT NULL COMMENT 'Standard error of the estimated effect size.' , 
             COMMENT = 'Dataset for the meta-analysis of the framing of decisions originally studied by Tversky & Kahneman (1981)' ;")

# Meissner dataset
Meissner <- read.csv(paste(path,files[10],".csv",sep=""),sep=sep.data[10])
dbWriteTable(Kvarven.db,files[10],Meissner %>% select("d","v","sed"),overwrite=TRUE,row.names=TRUE)
dbSendQuery(Kvarven.db,
            "ALTER TABLE `Kvarven`.`Meissner` 
             CHANGE COLUMN `row_names` `id` SMALLINT(4) NULL DEFAULT NULL COMMENT 'Id of the result' ,
             CHANGE COLUMN `d` `d` DOUBLE NULL DEFAULT NULL COMMENT 'Effect size (Cohen d) in units of standard deviation.' ,
             CHANGE COLUMN `v` `v` DOUBLE NULL DEFAULT NULL COMMENT 'Variance of the estimated effect size.' ,
             CHANGE COLUMN `sed` `sed` DOUBLE NULL DEFAULT NULL COMMENT 'Standard error of the estimated effect size.' , 
             COMMENT = 'Dataset for the meta-analysis of the verbal overshadowing of visual memories originally studied by Schooler & Engstler-Schooler (1990)' ;")

# Miles dataset
Miles <- read.csv(paste(path,files[11],".csv",sep=""),sep=sep.data[11])
dbWriteTable(Kvarven.db,files[11],Miles %>% select("d","v","sed"),overwrite=TRUE,row.names=TRUE)
dbSendQuery(Kvarven.db,
            "ALTER TABLE `Kvarven`.`Miles` 
             CHANGE COLUMN `row_names` `id` SMALLINT(4) NULL DEFAULT NULL COMMENT 'Id of the result' ,
             CHANGE COLUMN `d` `d` DOUBLE NULL DEFAULT NULL COMMENT 'Effect size (Cohen d) in units of standard deviation.' ,
             CHANGE COLUMN `v` `v` DOUBLE NULL DEFAULT NULL COMMENT 'Variance of the estimated effect size.' ,
             CHANGE COLUMN `sed` `sed` DOUBLE NULL DEFAULT NULL COMMENT 'Standard error of the estimated effect size.' , 
             COMMENT = 'Dataset for the meta-analysis of elaboration and the imagined contact effect originally studied by Husnu & Crisp (2010)' ;")

# Rabelo dataset
Rabelo <- read.csv(paste(path,files[12],".csv",sep=""),sep=sep.data[12])
dbWriteTable(Kvarven.db,files[12],Rabelo,overwrite=TRUE,row.names=TRUE)
dbSendQuery(Kvarven.db,
            "ALTER TABLE `Kvarven`.`Rabelo` 
             CHANGE COLUMN `row_names` `id` SMALLINT(4) NULL DEFAULT NULL COMMENT 'Id of the result' ,
             CHANGE COLUMN `d` `d` DOUBLE NULL DEFAULT NULL COMMENT 'Effect size (Cohen d) in units of standard deviation.' ,
             CHANGE COLUMN `v` `v` DOUBLE NULL DEFAULT NULL COMMENT 'Variance of the estimated effect size.' ,
             CHANGE COLUMN `sed` `sed` DOUBLE NULL DEFAULT NULL COMMENT 'Standard error of the estimated effect size.' , 
             COMMENT = 'Dataset for the meta-analysis of weight as an embodiment of importance originally studied by Jostmann et al. (2009)' ;")

# Rand dataset
Rand <- read.csv(paste(path,files[13],".csv",sep=""),sep=sep.data[13])
dbWriteTable(Kvarven.db,files[13],Rand,overwrite=TRUE,row.names=TRUE)
dbSendQuery(Kvarven.db,
            "ALTER TABLE `Kvarven`.`Rand` 
             CHANGE COLUMN `row_names` `id` SMALLINT(4) NULL DEFAULT NULL COMMENT 'Id of the result' ,
             CHANGE COLUMN `d` `d` DOUBLE NULL DEFAULT NULL COMMENT 'Effect size (Cohen d) in units of standard deviation.' ,
             CHANGE COLUMN `v` `v` DOUBLE NULL DEFAULT NULL COMMENT 'Variance of the estimated effect size.' ,
             CHANGE COLUMN `sed` `sed` DOUBLE NULL DEFAULT NULL COMMENT 'Standard error of the estimated effect size.' , 
             COMMENT = 'Dataset for the meta-analysis of spontaneous giving and calculated greed originally studied by Rand et al. (2012)' ;")

# Roth dataset
Roth <- read.csv(paste(path,files[14],".csv",sep=""),sep=sep.data[14])
dbWriteTable(Kvarven.db,files[14],Roth,overwrite=TRUE,row.names=TRUE)
dbSendQuery(Kvarven.db,
            "ALTER TABLE `Kvarven`.`Roth` 
             CHANGE COLUMN `row_names` `id` SMALLINT(4) NULL DEFAULT NULL COMMENT 'Id of the result' ,
             CHANGE COLUMN `d` `d` DOUBLE NULL DEFAULT NULL COMMENT 'Effect size (Cohen d) in units of standard deviation.' ,
             CHANGE COLUMN `v` `v` DOUBLE NULL DEFAULT NULL COMMENT 'Variance of the estimated effect size.' ,
             CHANGE COLUMN `sed` `sed` DOUBLE NULL DEFAULT NULL COMMENT 'Standard error of the estimated effect size.' , 
             COMMENT = 'Dataset for the meta-analysis of instructional manipulation checks and satisficing originally studied by Oppenheimer et al. (2009)' ;")

# Schimmack dataset
Schimmack <- read.csv(paste(path,files[15],".csv",sep=""),sep=sep.data[15])
dbWriteTable(Kvarven.db,files[15],Schimmack %>% select(q,Var.q.,SE.q.),overwrite=TRUE,row.names=TRUE)
dbSendQuery(Kvarven.db,
            "ALTER TABLE `Kvarven`.`Schimmack` 
             CHANGE COLUMN `row_names` `id` SMALLINT(4) NULL DEFAULT NULL COMMENT 'Id of the result' ,
             CHANGE COLUMN `q` `d` DOUBLE NULL DEFAULT NULL COMMENT 'Effect size (Cohen d) in units of standard deviation.' ,
             CHANGE COLUMN `Var.q.` `v` DOUBLE NULL DEFAULT NULL COMMENT 'Variance of the estimated effect size.' ,
             CHANGE COLUMN `SE.q.` `sed` DOUBLE NULL DEFAULT NULL COMMENT 'Standard error of the estimated effect size.' , 
             COMMENT = 'Dataset for the meta-analysis of assimilation and contrast effects originally studied by Schwarz et al. (1991)' ;")

```