Are internal replications the solution to the replication crisis in Psychology? No.

Most Psychology findings are not replicable. What can be done? Stanford psychologist Michael Frank has an idea : Cumulative study sets with internal replication. ‘If I had to advocate for a single change to practice, this would be it.’ I took a look whether this makes any difference.

A recent paper in the journal Science has tried to replicate 97 statistically significant effects (Open Science Collaboration, 2015). In only 35 cases this was successful. Most findings were suddenly a lot weaker upon replication. This has led to a lot of soul searching among psychologists. Fortunately, the authors of the Science paper have made their data freely available. So, soul searching can be accompanied by trying out different ideas for improvements.

What can be done to solve Psychology’s replication crisis?

One idea to improve the situation is to demand study authors to replicate their own experiments in the same paper. Stanford psychologist Michael Frank writes:

If I had to advocate for a single change to practice, this would be it. In my lab we never do just one study on a topic, unless there are major constraints of cost or scale that prohibit that second study. Because one study is never decisive.* Build your argument cumulatively, using the same paradigm, and include replications of the key effect along with negative controls. […] If you show me a one-off study and I fail to replicate it in my lab, I will tend to suspect that you got lucky or p-hacked your way to a result. But if you show me a package of studies with four internal replications of an effect, I will believe that you know how to get that effect – and if I don’t get it, I’ll think that I’m doing something wrong.

If this argument were true, then the 41 studies which were successfully, conceptually replicated in their own paper should show higher rates of replication than the 56 studies which were not. Of the 41 internally replicated studies, 19 were replicated once, 10 twice, 8 thrice, 4 more than three times. I will treat all of these as equally internally replicated.

Are internal replications the solution? No.

So, does the data by the reprocucibility project show a difference? I made so-called violin plots, thicker parts represent more data points. In the left plot you see the reduction in effect sizes from a bigger original effect to a smaller replicated effect. The reduction associated with internally replicated effects (left) and effects which were only reported once in a paper (right) is more or less the same. In the right plot you can see the p-value of the replication attempt. The dotted line represents the arbitrary 0.05 threshold used to determine statistical significance. Again, replicators appear to have had as hard a task with effects that were found more than once in a paper as with effects which were only found once.

If you do not know how to read these plots, don’t worry. Just focus on this key comparison. 29% of internally replicated effects could also be replicated by an independent team (1 effect was below p = .055 and is not counted here). The equivalent number of not internally replicated effects is 41%. A contingency table Bayes factor test (Gunel & Dickey, 1974) shows that the null hypothesis of no difference is 1.97 times more likely than the alternative. In other words, the 12 %-point replication advantage for non-replicated effects does not provide convincing evidence for an unexpected reversed replication advantage. The 12%-point difference is not due to statistical power. Power was 92% on average in the case of internally replicated and not internally replicated studies. So, the picture doesn’t support internal replications at all. They are hardly the solution to Psychology’s replication problem according to this data set.

The problem with internal replications

I believe that internal replications do not prevent many questionable research practices which lead to low replication rates, e.g., sampling until significant and selective effect reporting. To give you just one infamous example which was not part of this data set: in 2011 Daryl Bem showed his precognition effect 8 times. Even with 7 internal replications I still find it unlikely that people can truly feel future events. Instead I suspect that questionable research practices and pure chance are responsible for the results. Needless to say, independent research teams were unsuccessful in replication attempts of Bem’s psi effect (Ritchie et al., 2012; Galak et al., 2012). There are also formal statistical reasons which make papers with many internal replications even less believable than papers without internal replications (Schimmack, 2012).

What can be done?

In my previous post I have shown evidence for questionable research practices in this data set. These lead to less replicable results. Pre-registering studies makes questionable research practices a lot harder and science more reproducible. It would be interesting to see data on whether this hunch is true.

[update 7/9/2015: Adjusted claims in paragraph starting ‘If you do not know how to read these plots…’ to take into account the different denominators for replicated and unreplicated effects. Lee Jussim pointed me to this.]

[update 24/10/2015: Adjusted claims in paragraph starting ‘If you do not know how to read these plots…’ to provide correct numbers, Bayesian analysis and power comparison.]

— — —
Bem DJ (2011). Feeling the future: experimental evidence for anomalous retroactive influences on cognition and affect. Journal of personality and social psychology, 100 (3), 407-25 PMID: 21280961

Galak, J., LeBoeuf, R., Nelson, L., & Simmons, J. (2012). Correcting the past: Failures to replicate psi. Journal of Personality and Social Psychology, 103 (6), 933-948 DOI: 10.1037/a0029709

Gunel, E., & Dickey, J. (1974). Bayes Factors for Independence in Contingency Tables. Biometrika, 61(3), 545–557. http://doi.org/10.2307/2334738

Open Science Collaboration (2015). PSYCHOLOGY. Estimating the reproducibility of psychological science. Science (New York, N.Y.), 349 (6251) PMID: 26315443

Ritchie SJ, Wiseman R, & French CC (2012). Failing the future: three unsuccessful attempts to replicate Bem’s ‘retroactive facilitation of recall’ effect. PloS one, 7 (3) PMID: 22432019

Schimmack U (2012). The ironic effect of significant results on the credibility of multiple-study articles. Psychological methods, 17 (4), 551-66 PMID: 22924598
— — —

code for reproducing the figure (if you find mistakes, please tell me!):

## Estimating the association between internal replication and independent reproducibility of an effect

#Richard Kunert for Brain's Idea 5/9/2015

# a lot of code was taken from the reproducibility project code here https://osf.io/vdnrb/

# installing/loading the packages:
library(devtools)
source_url('https://raw.githubusercontent.com/FredHasselman/toolboxR/master/C-3PR.R')
in.IT(c('ggplot2','RColorBrewer','lattice','gridExtra','plyr','dplyr','httr','extrafont'))

#loading the data
RPPdata <- get.OSFfile(code='https://osf.io/fgjvw/',dfCln=T)$df
RPPdata <- dplyr::filter(RPPdata, !is.na(T.pval.USE.O),!is.na(T.pval.USE.R), complete.cases(RPPdata$T.r.O,RPPdata$T.r.R))#97 studies with significant effects

#prepare IDs for internally replicated effects and non-internally replicated effects
idIntRepl <- RPPdata$Successful.conceptual.replications.O > 0
idNotIntRepl <- RPPdata$Successful.conceptual.replications.O == 0

# Get ggplot2 themes predefined in C-3PR
mytheme <- gg.theme("clean")

#restructure data in data frame
dat <- data.frame(EffectSizeDifference = as.numeric(c(c(RPPdata$T.r.R[idIntRepl]) - c(RPPdata$T.r.O[idIntRepl]),
                                                          c(RPPdata$T.r.R[idNotIntRepl]) - c(RPPdata$T.r.O[idNotIntRepl]))),
                  ReplicationPValue = as.numeric(c(RPPdata$T.pval.USE.R[idIntRepl],
                                                   RPPdata$T.pval.USE.R[idNotIntRepl])),
                  grp=factor(c(rep("Internally Replicated Studies",times=sum(idIntRepl)),
                               rep("Internally Unreplicated Studies",times=sum(idNotIntRepl))))
  )

# Create some variables for plotting
dat$grp <- as.numeric(dat$grp)
probs   <- seq(0,1,.25)

# VQP PANEL A: reduction in effect size -------------------------------------------------

# Get effect size difference quantiles and frequencies from data
qtiles <- ldply(unique(dat$grp),
                function(gr) quantile(round(dat$EffectSizeDifference[dat$grp==gr],digits=4),probs,na.rm=T,type=3))
freqs  <- ldply(unique(dat$grp),
                function(gr) table(cut(dat$EffectSizeDifference[dat$grp==gr],breaks=qtiles[gr,],na.rm=T,include.lowest=T,right=T)))
labels <- sapply(unique(dat$grp),
                 function(gr)levels(cut(round(dat$EffectSizeDifference[dat$grp==gr],digits=4), breaks = qtiles[gr,],na.rm=T,include.lowest=T,right=T)))

# Get regular violinplot using package ggplot2
g.es <- ggplot(dat,aes(x=grp,y=EffectSizeDifference)) + geom_violin(aes(group=grp),scale="width",color="grey30",fill="grey30",trim=T,adjust=.7)
# Cut at quantiles using vioQtile() in C-3PR
g.es0 <- vioQtile(g.es,qtiles,probs)
# Garnish (what does this word mean???)
g.es1 <- g.es0 +
  ggtitle("Effect size reduction") + xlab("") + ylab("Replicated - Original Effect Size") + 
  xlim("Internally Replicated", "Not Internally Replicated") +
  mytheme + theme(axis.text.x = element_text(size=20))
# View
g.es1


# VQP PANEL B: p-value -------------------------------------------------

# Get p-value quantiles and frequencies from data
qtiles <- ldply(unique(dat$grp),
                function(gr) quantile(round(dat$ReplicationPValue[dat$grp==gr],digits=4),probs,na.rm=T,type=3))
freqs  <- ldply(unique(dat$grp),
                function(gr) table(cut(dat$ReplicationPValue[dat$grp==gr],breaks=qtiles[gr,],na.rm=T,include.lowest=T,right=T)))
labels <- sapply(unique(dat$grp),
                 function(gr)levels(cut(round(dat$ReplicationPValue[dat$grp==gr],digits=4), breaks = qtiles[gr,],na.rm=T,include.lowest=T,right=T)))

# Get regular violinplot using package ggplot2
g.pv <- ggplot(dat,aes(x=grp,y=ReplicationPValue)) + geom_violin(aes(group=grp),scale="width",color="grey30",fill="grey30",trim=T,adjust=.7)
# Cut at quantiles using vioQtile() in C-3PR
g.pv0 <- vioQtile(g.pv,qtiles,probs)
# Garnish (I still don't know what this word means!)
g.pv1 <- g.pv0 + geom_hline(aes(yintercept=.05),linetype=2) +
  ggtitle("Independent replication p-value") + xlab("") + ylab("Independent replication p-value") + 
  xlim("Internally Replicated", "Not Internally Replicated")+
  mytheme + theme(axis.text.x = element_text(size=20))
# View
g.pv1

#put two plots together
multi.PLOT(g.es1,g.pv1,cols=2)</pre>
<pre>