Category Archives: TIVA

A List of R-Index Blogs

In decreasing chronological order from November 30, 2014 to January 6, 2018

(statistics recorded on January 6)

Why the Journal of Personality and Social Psychology Should Retract Article DOI: 10.1037/a0021524 “Feeling the Future: Experimental evidence for anomalous retroactive influences on cognition and affect” by Daryl J. Bem

A day ago

‘Before you know it’ by John A. Bargh: A quantitative book review

Nov 28, 2017 12:41 PM

(Preprint) Z-Curve: A Method for Estimating Replicability Based on Test Statistics in Original Studies (Schimmack & Brunner, 2017)

Nov 16, 2017 3:46 PM

Preliminary 2017 Replicability Rankings of 104 Psychology Journals

Oct 24, 2017 2:56 PM

P-REP (2005-2009): Reexamining the experiment to replace p-values with the probability of replicating an effect

Sep 19, 2017 12:01 PM

The Power of the Pen Paradigm: A Replicability Analysis

Sep 4, 2017 8:48 PM

What would Cohen say? A comment on p < .005

Aug 2, 2017 11:46 PM

How Replicable are Focal Hypothesis Tests in the Journal Psychological Science?

May 15, 2017 9:24 PM

How replicable are statistically significant results in social psychology? A replication and extension of Motyl et al. (in press). 

May 4, 2017 8:41 PM

Hidden Figures: Replication Failures in the Stereotype Threat Literature

Apr 7, 2017 10:18 AM

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Personalized Adjustment of p-values for publication bias

Mar 13, 2017 2:31 PM

Meta-Psychology: A new discipline and a new journal (draft)

Mar 5, 2017 2:35 PM

2016 Replicability Rankings of 103 Psychology Journals

Mar 1, 2017 12:01 AM

An Attempt at Explaining Null-Hypothesis Testing and Statistical Power with 1 Figure and 1,500 Words

Feb 26, 2017 10:35 AM

Random measurement error and the replication crisis: A statistical analysis

Feb 23, 2017 7:38 AM

How Selection for Significance Influences Observed Power

Feb 21, 2017 10:38 AM

Reconstruction of a Train Wreck: How Priming Research Went off the Rails

Feb 2, 2017 11:33 AM

Are Most Published Results in Psychology False? An Empirical Study

Jan 15, 2017 1:42 PM

Reexamining Cunningham, Preacher, and Banaji’s Multi-Method Model of Racism Measures

Jan 8, 2017 7:50 PM

Validity of the Implicit Association Test as a Measure of Implicit Attitudes

Jan 5, 2017 5:20 PM

Replicability Review of 2016

Dec 31, 2016 5:25 PM

Z-Curve: Estimating Replicability of Published Results in Psychology (Revision)

Dec 12, 2016 5:35 PM

How did Diedrik Stapel Create Fake Results? A forensic analysis of “From Seeing to Being: Subliminal Social Comparisons Affect Implicit and Explicit Self-Evaluations”

Dec 6, 2016 12:27 PM

A sarcastic comment on “Promise, peril, and perspective: Addressing concerns about reproducibility in social–personality psychology” by Harry Reis

Dec 3, 2016 9:31 PM

A replicability analysis of”I like myself but I don’t know why: Enhancing implicit self-esteem by subliminal evaluative conditioning”

Dec 3, 2016 3:15 PM

Bayesian Meta-Analysis: The Wrong Way and The Right Way

Nov 28, 2016 3:25 PM

Peer-Reviews from Psychological Methods

Nov 18, 2016 6:33 PM

How replicable is psychology? A comparison of four methods of estimating replicability on the basis of test statistics in original studies

Sep 17, 2016 5:44 PM

A Critical Review of Schwarz and Strack’s (1999) “Reports of Subjective Well-Being: Judgmental Processes and Their Methodological Implications”

Sep 16, 2016 11:20 AM

Dr. R responds to Finkel, Eastwick, & Reis (FER)’s article “Replicability and Other Features of a High-Quality Science: Toward a Balanced and Empirical Approach”

Sep 13, 2016 10:10 PM

The decline effect in social psychology: Evidence and possible explanations

Sep 4, 2016 9:26 AM

Fritz Strack’s self-serving biases in his personal account of the failure to replicate his most famous study.

Aug 29, 2016 12:10 PM

How Can We Interpret Inferences with Bayesian Hypothesis Tests?

Aug 9, 2016 4:16 PM

Bayes Ratios: A Principled Approach to Bayesian Hypothesis Testing

Jul 25, 2016 12:51 PM

How Does Uncertainty about Population Effect Sizes Influence the Probability that the Null-Hypothesis is True?

Jul 16, 2016 11:53 AM

Subjective Bayesian T-Test Code

Jul 5, 2016 6:58 PM

Wagenmakers’ Default Prior is Inconsistent with the Observed Results in Psychologial Research

Jun 30, 2016 10:15 AM

A comparison of The Test of Excessive Significance and the Incredibility Index

Jun 18, 2016 11:52 AM

R-Code for (Simplified) Powergraphs with StatCheck Dataset

Jun 17, 2016 6:32 PM

Replicability Report No.2: Do Mating Primes have a replicable effects on behavior?

May 21, 2016 9:37 AM

Subjective Priors: Putting Bayes into Bayes-Factors

May 18, 2016 12:22 PM

Who is Your Daddy? Priming women with a disengaged father increases their willingness to have sex without a condom

May 11, 2016 4:15 PM

Bayes-Factors Do Not Solve the Credibility Problem in Psychology

May 9, 2016 6:03 PM

Die Verdrängung des selektiven Publizierens: 7 Fallstudien von prominenten Sozialpsychologen

Apr 20, 2016 10:05 PM

Replicability Report No. 1: Is Ego-Depletion a Replicable Effect?

Apr 18, 2016 7:28 PM

Open Ego-Depletion Replication Initiative

Mar 26, 2016 10:10 AM

Estimating Replicability of Psychological Science: 35% or 50%

Mar 12, 2016 11:56 AM


Mar 4, 2016 10:11 AM

Replicability Ranking of Psychology Departments

Mar 2, 2016 5:01 PM

Reported Success Rates, Actual Success Rates, and Publication Bias In Psychology: Honoring Sterling et al. (1995)

Feb 26, 2016 5:50 PM

Are You Planning a 10-Study Article? You May Want to Read This First

Feb 10, 2016 5:24 PM

Dr. R Expresses Concerns about Results in Latest Psycholgical Science Article by Yaacov Trope and colleagues

Feb 9, 2016 11:41 AM

Dr. R’s Blog about Replicability

Feb 5, 2016 5:32 PMSticky

A Scathing Review of “Best Research Practices in Psychology: Illustrating Epistemological and Pragmatic Considerations With the Case of Relationship Science”

Feb 3, 2016 10:32 AM

Keep your Distance from Questionable Results

Jan 31, 2016 5:05 PM

Too good to be true: A reanalysis of Damisch, Stoberock, and Mussweiler (2010). Keep Your Fingers Crossed! How Superstition Improves Performance. Psychological Science, (21)7, p.1014-1020

Jan 31, 2016 5:01 PM

A Revised Introduction to the R-Index

Jan 31, 2016 3:50 PM

2015 Replicability Ranking of 100+ Psychology Journals

Jan 26, 2016 12:17 PM

Is the N-pact Factor (NF) a Reasonable Proxy for Statistical Power and Should the NF be used to Rank Journals’ Reputation and Replicability? A Critical Review of Fraley and Vazir (2014)

Jan 16, 2016 7:56 PM

On the Definition of Statistical Power

Jan 14, 2016 3:36 PM

The Abuse of Hoenig and Heisey: A Justification of Power Calculations with Observed Effect Sizes

Jan 14, 2016 2:06 PM

Do Deceptive Reporting Practices in Social Psychology Harm Social Psychology?

Jan 13, 2016 12:24 PM

“Do Studies of Statistical Power Have an Effect on the Power of Studies?” by Peter Sedlmeier and Gerg Giegerenzer

Jan 12, 2016 1:51 PM

Distinguishing Questionable Research Practices from Publication Bias

Dec 8, 2015 6:00 PM

2015 Replicability Ranking of 54 Psychology Journals

Oct 27, 2015 7:05 PM

Dr. R’s comment on the Official Statement by the Board of the German Psychological Association (DGPs) about the Results of the OSF-Reproducibility Project published in Science.

Oct 10, 2015 12:01 PM

Replicability Ranking of 27 Psychology Journals (2015)

Sep 28, 2015 7:42 AM


Sep 28, 2015 7:02 AM

Replicability Report for PERSONAL RELATIONSHIPS

Sep 27, 2015 5:40 PM

Replicability Report for DEVELOPMENTAL SCIENCE

Sep 27, 2015 3:16 PM


Sep 26, 2015 8:08 PM

Replicability-Report for CHILD DEVELOPMENT

Sep 26, 2015 10:37 AM

Replicability-Report for PSYCHOLOGY & AGING

Sep 25, 2015 5:47 PM


Sep 25, 2015 12:33 PM


Sep 22, 2015 7:11 AM


Sep 18, 2015 6:40 PM

Replicability-Ranking of 100 Social Psychology Departments

Sep 15, 2015 12:49 PM

Replicability Report for the journal SOCIAL PSYCHOLOGY

Sep 13, 2015 4:54 PM

Replicability-Report for the journal JUDGMENT AND DECISION MAKING

Sep 13, 2015 1:08 PM


Sep 12, 2015 12:32 PM

Replicability-Report for SOCIAL COGNITION

Sep 11, 2015 6:43 PM

Examining the Replicability of 66,212 Published Results in Social Psychology: A Post-Hoc-Power Analysis Informed by the Actual Success Rate in the OSF-Reproducibilty Project

Sep 7, 2015 9:20 AM

The Replicability of Cognitive Psychology in the OSF-Reproducibility-Project

Sep 5, 2015 2:47 PM

The Replicability of Social Psychology in the OSF-Reproducibility Project

Sep 3, 2015 8:18 PM

Which Social Psychology Results Were Successfully Replicated in the OSF-Reproducibility Project? Recommeding a 4-Sigma Rule

Aug 30, 2015 11:04 AM

Predictions about Replication Success in OSF-Reproducibility Project

Aug 26, 2015 9:54 PM


Aug 22, 2015 8:00 PM


Aug 22, 2015 5:30 PM


Aug 22, 2015 3:22 PM


Aug 21, 2015 5:52 PM


Aug 21, 2015 4:36 PM


Aug 19, 2015 10:21 AM

Replicability-Report for COGNITIVE PSYCHOLOGY

Aug 18, 2015 10:03 AM

Replicability-Report for COGNITION & EMOTION

Aug 18, 2015 8:37 AM


Aug 18, 2015 7:35 AM

Replicability-Report for EMOTION

Aug 17, 2015 7:53 PM


Aug 17, 2015 9:59 AM


Aug 16, 2015 9:51 AM


Aug 16, 2015 6:12 AM

Replicability-Report for JPSP: Personality Processes and Individual Differences

Aug 15, 2015 8:30 PM

Replicability Report for PSYCHOLOGICAL SCIENCE

Aug 15, 2015 5:51 PM


Aug 13, 2015 4:16 PM

Using the R-index to detect questionable research practices in SSRI studies

Aug 5, 2015 2:34 PM

R-Index predicts lower replicability of “subliminal” studies than “attribution” studies in JESP

Jul 7, 2015 9:37 PM

Post-Hoc-Power Curves of Social Psychology in Psychological Science, JESP, and Social Cognition

Jul 7, 2015 7:07 PM

Post-Hoc Power Curves: Estimating the typical power of statistical tests (t, F) in Psychological Science and Journal of Experimental Social Psychology

Jun 27, 2015 10:48 PM

When Exact Replications Are Too Exact: The Lucky-Bounce-Test for Pairs of Exact Replication Studies

May 27, 2015 11:30 AM

The Association for Psychological Science Improves Success Rate from 95% to 100% by Dropping Hypothesis Testing: The Sample Mean is the Sample Mean, Type-I Error 0%

May 21, 2015 1:40 PM

R-INDEX BULLETIN (RIB): Share the Results of your R-Index Analysis with the Scientific Community

May 19, 2015 5:43 PM

A Critical Review of Cumming’s (2014) New Statistics: Reselling Old Statistics as New Statistics

May 18, 2015 6:41 PM

Power Analysis for Bayes-Factor: What is the Probability that a Study Produces an Informative Bayes-Factor?

May 16, 2015 4:41 PM

A Critical Review of Cumming’s (2014) New Statistics: Reselling Old Statistics as New Statistics

May 16, 2015 7:51 AM

The Test of Insufficient Variance (TIVA): A New Tool for the Detection of Questionable Research Practices

May 13, 2015 12:40 PM

Why Psychologists Should Not Change The Way They Analyze Their Data: The Devil is in the Default Prior

May 9, 2015 10:43 AM

Replacing p-values with Bayes-Factors: A Miracle Cure for the Replicability Crisis in Psychological Science

Apr 30, 2015 1:48 PM

Further reflections on the linearity in Dr. Förster’s Data

Apr 21, 2015 7:57 AM

The R-Index for 18 Multiple Study Articles in Science (Francis et al., 2014)

Apr 20, 2015 6:04 PM

Bayesian Statistics in Small Samples: Replacing Prejudice against the Null-Hypothesis with Prejudice in Favor of the Null-Hypothesis

Apr 9, 2015 12:26 PM

Meta-Analysis of Observed Power: Comparison of Estimation Methods

Apr 1, 2015 9:49 PM

An Introduction to Observed Power based on Yuan and Maxwell (2005)

Mar 24, 2015 7:24 PM

R-INDEX BULLETIN (RIB): Share the Results of your R-Index Analysis with the Scientific Community

Feb 6, 2015 11:20 AM

Bayesian Statistics in Small Samples: Replacing Prejudice against the Null-Hypothesis with Prejudice in Favor of the Null-Hypothesis

Feb 2, 2015 10:45 AM

Questionable Research Practices: Definition, Detect, and Recommendations for Better Practices

Jan 24, 2015 8:40 AM

Further reflections on the linearity in Dr. Förster’s Data

Jan 14, 2015 5:47 PM

Why are Stereotype-Threat Effects on Women’s Math Performance Difficult to Replicate?

Jan 6, 2015 12:01 PM

How Power Analysis Could Have Prevented the Sad Story of Dr. Förster

Jan 2, 2015 12:22 PM

A Playful Way to Learn about Power, Publication Bias, and the R-Index: Simulate questionable research methods and see what happens.

Dec 31, 2014 3:25 PM

The Test of Insufficient Variance (TIVA): A New Tool for the Detection of Questionable Research Practices

Dec 30, 2014 10:22 PM

Christmas Special: R-Index of “Women Are More Likely to Wear Red or Pink at Peak Fertility”

Dec 24, 2014 1:54 PM

The R-Index of Ego-Depletion Studies with the Handgrip Paradigm

Dec 21, 2014 2:21 PM

The R-Index of Nicotine-Replacement-Therapy Studies: An Alternative Approach to Meta-Regression

Dec 17, 2014 3:52 PM

The R-Index of Simmons et al.’s 21 Word Solution

Dec 17, 2014 7:14 AM

The R-Index for 18 Multiple Study Articles in Science (Francis et al., 2014)

Dec 13, 2014 10:42 AM

Do it yourself: R-Index Spreadsheet and Manual is now available.

Dec 7, 2014 11:01 AM

Nature Neuroscience: R-Index

Dec 5, 2014 11:44 AM

Dr. Schnall’s R-Index

Dec 4, 2014 11:57 AM

Roy Baumeister’s R-Index

Dec 1, 2014 6:29 PM

The Replicability-Index (R-Index): Quantifying Research Integrity

Nov 30, 2014 10:19 PM


Why the Journal of Personality and Social Psychology Should Retract Article DOI: 10.1037/a0021524 “Feeling the Future: Experimental evidence for anomalous retroactive influences on cognition and affect” by Daryl J. Bem

“I’m all for rigor, but I prefer other people do it. I see its importance—it’s fun for some people—but I don’t have the patience for it. If you looked at all my past experiments, they were always rhetorical devices. I gathered data to show how my point would be made. I used data as a point of persuasion, and I never really worried about, ‘Will this replicate or will this not?” (Daryl J. Bem, in Engber, 2017)

In 2011, the Journal of Personality and Social Psychology published a highly controversial article that claimed to provide evidence for time-reversed causality. Time reversed causality implies that future events have a causal effect on past events. These effects are considered to be anomalous and outside current scientific explanations of human behavior because they contradict fundamental principles of our current understanding of reality.

The article reports 9 experiments with 10 tests of time-reversed causal influences on human behavior with stunning results.  “The mean effect size (d) in psi performance across all 9 experiments was 0.22, and all but one of the experiments yielded statistically significant results. ” (Bem, 2011, p. 407).

The publication of this article rocked psychology and triggered a credibility crisis in psychological science. Unforeseen by Bem, the article did not sway psychologists to believe in time-reversed causality. Rather, it made them doubt other published findings in psychology.

In response to the credibility crisis, psychologists started to take replications more seriously, including replications of Bem’s studies. If Bem’s findings were real, other scientists should be able to replicate them using the same methodology in their labs. After all, independent verification by other scientists is the ultimate test of all empirical sciences.

The first replication studies were published by Ritchie, Wiseman, and French (2012). They conducted three studies with a total sample size of N = 150 and did not obtain a significant effect. Although this finding casts doubt about Bem’s reported results, the sample size is too small to challenge the evidence reported by Bem which was based on over 1,000 participants. A more informative replication attempt was made by Galek et al. (2012). A set of seven studies with a total of N = 3,289 participants produced an average effect size of d = 0.04, which was not significantly different from zero. This massive replication failure raised questions about potential moderators (i.e., variables that can explain inconsistent findings).  The authors found “the only moderator that yields significantly different results is whether the experiment was conducted by Bem or not.” (p. 941).

Galek et al. (2012) also speculate about the nature of the moderating factor that explains Bem’s high success rate. One possible explanation is that Bem’s published results do not represent reality. Published results can only be interpreted at face value, if the reported data and analyses were not influenced by the result. If, however, data or analyzes were selected because they produced evidence for time-reversed causality, and data and analyses that failed to provide evidence for it were not reported, the results cannot be considered empirical evidence for an effect. After all, random numbers can provide evidence for any hypothesis, if they are selected for significance (Rosenthal, 1979; Sterling, 1959). It is irrelevant whether this selection occurred involuntarily (self-deception) or voluntary (other-deception). Both, self-deception and other-deception introduce bias in the scientific record.

Replication studies cannot provide evidence about bias in original studies. A replication study only tells us that other scientists were unable to replicate original findings, but they do not explain how the scientist who conducted the original studies obtained significant results. Seven years after Bem’s stunning results were published, it remains unknown how he obtained significant results in 9 out of 10 studies.

I obtained Bem’s original data (email on February 25, 2015) to examine this question more closely.  Before I present the results of my analysis, I consider several possible explanations for Bem’s surprisingly high success rate.

1. Luck

The simplest and most parsimonious explanation for a stunning original result that cannot be replicate is luck. The outcome of empirical studies is partially determined by factors outside an experimenter’s control. Sometimes these random factors will produce a statistically significant result by chance alone. The probability of this outcome is determined by the criterion for statistical significance. Bem used the standard criterion of 5%. If time-reversed causality does not exist, 1 out of 20 attempts to demonstrate the phenomenon would provide positive evidence for it.

If Bem or other scientists would encounter one successful attempt and 19 unsuccessful attempts, they would not consider the one significant result evidence for the effect. Rather, the evidence would strongly suggest that the phenomenon does not exist. However, if the significant result emerged in the first attempt, Bem could not know (unless he can see into the future) that the next 19 studies will not replicate the effect.

Attributing Bem’s results to luck would be possible, if Bem had reported a significant result in a single study. However, the probability of getting lucky decreases with the number of attempts. Nobody gets lucky every time they try. The luck hypothesis assumes that Bem got lucky 9 out of 10 times with a probability of 5% on each attempt.
The probability of this event is very small. To be exact, it is 0.000000000019 or 1 out of 53,612,565,445.

Given this small probability, it is safe to reject the hypothesis that Bem’s results were merely the outcome of pure chance. If we assume that time-reversed causality does not exist, we are forced to believe that Bem’s published results are biased by involuntarily or voluntarily presenting misleading evidence; that is evidence that strengthens beliefs in a phenomenon that actually does not exist.

2. Questionable Research Practices

The most plausible explanation for Bem’s incredible results is the use of questionable research practices (John et al., 2012). Questionable research practices increase the probability of presenting only supportive evidence for a phenomenon at the risk of providing evidence for a phenomenon that does not exist. Francis (2012) and Schimmack (2012) independently found that Bem reported more significant results than one would expect based on the statistical power of the studies.  This finding suggests that questionable research practices were used, but they do not provide information about the actual research practices that were used.  John et al. listed a number of questionable research practices that might explain Bem’s findings.

2.1. Multiple Dependent Variables

One practice is to collect multiple dependent variables and to report only dependent variables that produced a significant result. The nature of Bem’s studies reduces the opportunity to collect many dependent variables. Thus, the inclusion of multiple dependent variables cannot explain Bem’s results.

2.2. Failure to report all conditions

This practice applies to studies with multiple conditions. Only Study 1 examined precognition for multiple types of stimuli and found a significant result for only one of them. However, Bem reported the results for all conditions and it was transparent that the significant result was only obtained in one condition, namely with erotic pictures. This weakens the evidence in Study 1, but it does not explain significant results in the other studies that had only one condition or two conditions that both produced significant results.

2.3 Generous Rounding

Sometimes a study may produce a p-value that is close to the threshold value of .05. Strictly speaking a p-value of .054 is not significant. However, researchers may report the p-value rounded to the second digit and claim significance. It is easy to spot this questionable research practice by computing exact p-values for the reported test-statistics or by redoing the statistical analysis from original data. Bem reported his p-values with three digits. Moreover, it is very unlikely that a p-value falls into the range between .05 and .055 and that this could happen in 9 out of 10 studies. Thus, this practice also does not explain Bem’s results.

2.4 HARKing

Hypothesizing after results are known (Kerr, 1998) can be used to make significant results more credible. The reason is that it is easy to find significant results in a series of exploratory analyses. A priori predictions limit the number of tests that are carried out and the risk of capitalizing on chance. Bem’s studies didn’t leave much room for HARKing, except Study 1. The studies build on a meta-analysis of prior studies and nobody has questioned the paradigms used by Bem to test time-reversed causality. Bem did include an individual difference measure and found that it moderated the effect, but even if this moderator effect was HARKed, the main effect remains to be explained. Thus, HARKing can also not explain Bem’s findings.

2.5 Excluding of Data

Sometimes non-significant results are caused by an an inconvenient outlier in the control group. Selective exclusion of these outliers based on p-values is another questionable research practice. There are some exclusions in Bem’s studies. The method section of Study 3 states that 100 participants were tested and three participants were excluded due to a high error rate in responses. The inclusion of these three participants is unlikely to turn a significant result with t(96) = 2.55, p = .006 (one-tailed), into a non-significant result. In Study 4, one participant out of 100 participants was excluded. The exclusion of a single participant is unlikely to change a significant result with t(98) = 2.03, p = .023 into a non-significant result. Across all studies, only 4 participants out of 1075 participants were excluded. Thus, exclusion of data cannot explain Bem’s robust evidence for time-reversed causality that other researchers cannot replicate.

2.6 Stopping Data Collection Early

Bem aimed for a minimum sample size of N = 100 to achieve 80% power in each study. All studies except Study 9 met this criterion before excluding participants (Ns = 100, 150, 97, 99, 100, 150, 200, 125, 50). Bem does not provide a justification for the use of a smaller sample size in Study 9 that reduced power from 80% to 54%. The article mentions that Study 9 was a modified replication of Study 8 and yielded a larger observed effect size, but the results of Studies 8 and 9 are not significantly different. Thus, the smaller sample size is not justified by an expectation of a larger effect size to maintain 80% power.

In a personal communication, Bem also mentioned that the study was terminated early because it was the end of the semester and the time stamp in the data file shows that the last participant was run on December 6, 2009. Thus, it seems that Study 9 was terminated early, but Bem simply got lucky that results were significant at the end of the semester. Even if Study 9 is excluded for this reason, it remains unclear how the other 8 studies could have produced significant results without a real effect.

2.7 Optional Stopping/Snooping

Collecting more data, if the collected data already show a significant effect can be wasteful. Therefore, researchers may conduct statistical significance tests throughout a study and terminate data collection when a significant result is obtained. The problem with this approach is that repeated checking (snooping) increases the risk of a false positive result (Strube, 2006). The increase in the risk of a false positive results depends on how frequently and how often researchers check results. If researchers use optional stopping, sample sizes are expected to vary because sampling error will sometimes produce a significant result quickly and sometimes after a long time. Second, sample size would be negatively correlated with observed effect sizes. The reason is that larger samples are needed to achieve significance with smaller observed effect sizes. If chance produces large effect sizes early on, significance is achieved quickly and the study is terminated with a small sample size and a large effect size. Finally, optional stopping will produce p-values close to the significance criterion because data collection is terminated as soon as p-values reach the criterion value.

The reported statistics in Bem’s article are consistent with optional stopping. First, sample sizes vary from N = 50 to N = 200. Second, sample sizes are strongly correlated with effect sizes, r = -.91 (Alcock, 2011). Third, p-values are bunched up close to the criterion value, which suggests studies may have been stopped as soon as significance was achieved (Schimmack, 2015).

Despite these warning signs, optional stopping cannot explain Bem’s results, if time-reversed causality does not exist. The reason is that the sample sizes are too small for a set of 9 studies to produce significant results. In a simulation study, with a minimum of 50 participants and a maximum of 200 participants, only 30% of attempts produced a significant result. Even 1,000 participants are not enough to guarantee a significant result by simply collecting more data.

2.8 Selective Reporting

The last questionable practice is to report only successful studies that produce a significant result. This practice is widespread and contributes to the presence of publication bias in scientific journals (Fraonco et al., 2014).

Selective reporting assumes that researchers conduct a series of studies and report only studies that produced a significant result. This may be a viable strategy for sets of studies with a real effect, but it does not seem to be a viable strategy, if there is no effect. Without a real effect, a significant result with p < .05 emerges in 1 out of 20 attempts. To obtain 9 significant results, Bem would have had to conduct approximately 9*20 = 180 studies. With a modal sample size of N = 100, this would imply a total sample size of 18,000 participants.

Engber (2017) reports that Bem conducted his studies over a period of 10 years. This may be enough time to collect data from 18,000 participants. However, Bem also paid participants $5 out of his own pocket because (fortunately) this research was not supported by research grants. This would imply that Bem paid $90,000 out of pocket.

As a strong believer in ESP, Bem may have paid $90,000 dollars to fund his studies, but any researcher of Bem’s status should realize that obtaining 9 significant results in 180 attempts does not provide evidence for time-reversed causality. Not disclosing that there were over 100 failed studies, would be a breach of scientific standards. Indeed, Bem (2010) warned graduate students in social psychology.

“The integrity of the scientific enterprise requires the reporting of disconfirming results.”

2.9 Conclusion

In conclusion, none of the questionable research practices that have been identified by John et al. seem to be plausible explanations for Bem’s results.

3. The Decline Effect and a New Questionable Research Practice

When I examined Bem’s original data, I discovered an interesting pattern. Most studies seemed to produce strong effect sizes at the beginning of a study, but then effect sizes decreased.  This pattern is similar to the decline effect that has been observed across replication studies of paranormal phenomena (Schooler, 2011).

Figure 1 provides a visual representation of the decline effect in Bem’s studies. The x-axis is the sample size and the y-axis is the cumulative effect size. As sample sizes increase, the cumulative effect size approaches the population effect size. The grey area represents the results of simulation studies with a population effect size of d = .20. As sampling error is random, the grey area is a symmetrical funnel around the population effect size. The blue dotted lines show the cumulative effect sizes for Bem’s studies. The solid blue line shows the average cumulative effect size. The figure shows how the cumulative effect size decreases by more than 50% from the first 5 participants to a sample size of 100 participants.



The selection effect is so strong that Bem could have stopped 9 of the 10 studies after collecting a maximum of 15 participants with a significant result. The average sample size for these 9 studies would have been only 7.75 participants.

Table 1 shows the one-sided p-values for Bem’s datasets separately for the first 50 participants and for participants 51 to 100. For the first 50 participants, 8 out of 10 tests are statistically significant. For the following 50 participants none of the 10 tests is statistically significant. A meta-analysis across the 10 studies does show a significant effect for participants 51 to 100, but the Test of Insufficient Variance also shows insufficient variance, Var(z) = 0.22, p = .013, suggesting that even these trials are biased by selection for significance (Schimmack, 2015).
Table 1.  P-values for Bem’s 10 datasets based on analyses of the first group of 50 participants and the second group of 50 participants.

EXPERIMENT S 1-50 S 51-100
EXP1 p = .004 p = .194
EXP2 p = .096 p = .170
EXP3 p = .039 p = .100
EXP4 p = .033 p = .067
EXP5 p = .013 p = .069
EXP6a p = .412 p = .126
EXP5b p = .023 p = .410
EXP7 p = .020 p = .338
EXP8 p = .010 p = .318
EXP9 p = .003 NA


There are two interpretations of the decrease in effect sizes over the course of an experiment. One explanation is that we are seeing a subset of attempts that showed promising results after peeking at the data. Unlike optional stopping, however, a researcher continuous to collect more data to see whether the effect is real. Although the effect size decreases, the strong effect during the initial trials that motivated a researcher to collect more data is sufficient to maintain statistical significance because sampling error also decreases as more participants are added. These results cannot be replicated because they capitalized on chance during the first trials, but this remains unnoticed because the next study does not replicate the first study exactly. Instead, the researcher makes a small change to the experimental procedure and when he or she peeks at the data of the next study, the study is abandoned and the failure is attributed to the change in the experimental procedure (without checking that the successful finding can be replicated).

In this scenario, researchers are deceiving themselves that slight experimental manipulations apparently have huge effects on their dependent variable because sampling error in small samples is very large. Observed effect sizes in small samples can range from 1 to -1 (see grey area in Figure 1), giving the illusion that each experiment is different, but a random number generator would produce the same stunning differences in effect sizes.  Bem (2011), and reviewers of his article, seem to share the believe that “the success of replications in psychological research often depends on subtle and unknown factors.” (p. 422).  How could Bem reconcile this believe with the reporting of 9 out of 10 successes? The most plausible explanation is that successes are a selected set of findings out of many attempts that were not reported.

There are other hints that Bem peeked at the data to decide whether to collect more data or terminate data collection.  In his 2011 article, he addressed concerns about a file drawer stuffed with failed studies.

“Like most social-psychological experiments, the experiments reported here required extensive pilot testing. As all research psychologists know, many procedures are tried and discarded during this process. This raises the question of how much of this pilot exploration should be reported to avoid the file-drawer problem, the selective suppression of negative or null results.”

Bem does not answer his own question, but the correct answer is clear: all of the so-called pilot studies need to be included if promising pilot studies were included in the actual studies. If Bem had clearly distinguished between promising pilot studies and actual studies, actual studies would be unbiased. However, it appears that he continued collecting data after peeking at the results after a few trials and that the significant results are largely driven by inflated effect sizes in promising pilot studies. This biased the results and can explain how Bem obtained evidence for time-reversed causality that others could not replicate when they did not peek at the data and terminated studies when the results were not promising.

Additional hints come from an interview with Engber (2017).

“I would start one [experiment], and if it just wasn’t going anywhere, I would abandon it and restart it with changes,” Bem told me recently. Some of these changes were reported in the article; others weren’t. “I didn’t keep very close track of which ones I had discarded and which ones I hadn’t,” he said. Given that the studies spanned a decade, Bem can’t remember all the details of the early work. “I was probably very sloppy at the beginning,” he said.

In sum, a plausible explanation of Bem’s successes that others could not replicate is that he stopped studies early when they did not show a promising result, then changed the procedure slightly. He also continued data collection when results looked promising after a few trials. As this research practices capitalizes on chance to produce large effect sizes at the beginning of a study, the results are not replicable.

Although this may appear to be the only hypothesis that is consistent with all of the evidence (evidence of selection bias in Bem’s studies, decline effect over the course of Bem’s studies, failed replications), it may not be the only one.  Schooler (2011) proposed that something more intriguing may cause decline effects.

“Less likely, but not inconceivable, is an effect stemming from some unconventional process. Perhaps, just as the act of observation has been suggested to affect quantum measurements, scientific observation could subtly change some scientific effects. Although the laws of reality are usually understood to be immutable, some physicists, including Paul Davies, director of the BEYOND: Center for Fundamental Concepts in Science at Arizona State University in Tempe, have observed that this should be considered an assumption, not a foregone conclusion.” 

Researchers who are willing to believe in time-reversed causality are probably also open to the idea that the process of detecting these processes is subject to quantum effects that lead to a decline in the effect size after attempts to measure it. They may consider the present findings of decline effects within Bem’s experiment a plausible explanation for replication failures. If a researcher collects too many data, the weak effects in the later trials wash out the strong effects during the initial trials. Moreover, quantum effect may not be observable all the time. Thus, sometimes initial trials will also not show the effect.

I have little hope that my analyses of Bem’s data will convince Bem or other parapsychologists to doubt supernatural phenomena. However, the analysis provides skeptics with rational and scientific arguments to dismiss Bem’s findings as empirical evidence that requires a supernatural explanation. Bad research practices are sufficient to explain why Bem obtained statistically significant results that could not be replicated in honest and unbiased replication attempts.


Bem’s 2011 article “Feeling the Future” has had a profound effect on social psychology. Rather than revealing a supernatural phenomenon, the article demonstrated fundamental flaws in the way social psychologists conducted and reported empirical studies. Seven years later, awareness of bad research practices is widespread and new journal editors are implementing reforms in the evaluation of manuscripts. New statistical tools have been developed to detect practices that produce significant results by capitalizing on chance. It is unlikely that Bem’s article would be accepted for publication these days.

The past seven years have also revealed that Bem’s article is not an exception. The only difference is that the results contradicted researchers’ a priori beliefs, whereas other studies with even more questionable evidence were not scrutinized because the claims were consistent with researchers a priori beliefs (e.g., the glucose theory of will-power; cf. Schimmack, 2012).

The ability to analyze the original data of Bem’s studies offered a unique opportunity to examine how social psychologists deceived themselves and others into believing that they tested theories of human behavior when they were merely confirming their own beliefs, even if these beliefs defied basic principles of causality.  The main problem appears to be a practice to peek at results in small samples with different procedures and to attribute differences in results to the experimental procedures, while ignoring the influence of sampling error.

Conceptual Replications and Hidden Moderators

In response to the crisis of confidence about social psychology, social psychologists have introduced the distinction between conceptual and exact replications and the hidden moderator hypothesis. The distinction between conceptual and exact replications is important because exact replications make a clear prediction about the outcome. If a theory is correct and an original study produced a result that is predicted by the theory, then an exact replication of the original study should also produce a significant result. At least, exact replications should be successful more often than fail (Tversky and Kahneman, 1971).

Social psychologists also realize that not reporting the outcome of failed exact replications distorts the evidence and that this practice violates research ethics (Bem, 2000).

The concept of a conceptual replication provides the opportunity to dismiss studies that fail to support a prediction by attributing the failure to a change in the experimental procedure, even if it is not clear, why a small change in the experimental procedure would produce a different result. These unexplained factors that seemingly produced a success in one study and a failure in the other studies are called hidden moderator.

Social psychologists have convinced themselves that many of the phenomena that they study are sensitive to minute changes in experimental protocols (Bem, 2011). This belief sustains beliefs in a theory despite many failures to obtain evidence for a predicted effect and justifies not reporting disconfirming evidence.

The sensitivity of social psychological effects to small changes in experimental procedures also justifies that it is necessary to conduct many studies that are expected to fail, just like medieval alchemists expected many failures in their attempts to make gold. These failures are not important. They are simply needed to find the conditions that produce the desired outcome; a significant result that supports researchers’ predictions.

The attribution of failures to hidden moderators is the ultimate attribution error of social psychologists. It makes them conduct study after study in the search for a predicted outcome without realizing that a few successes among many failures are expected simply due to chance alone. To avoid realizing the fragility of these successes, they never repeat the same study twice. The ultimate attribution error has enabled social psychologist to deceive themselves and others for decades.

Since Bem’s 2011 article was published, it has become apparent that many social psychological articles report results that fail to provide credible evidence for theoretical claims because they do not report results from an unknown number of failed attempts. The consequences of this inconvenient realization are difficult to exaggerate. Entire textbooks covering decades of research will have to be rewritten.


Another important article for the replication crisis in psychology examined the probability that questionable research practices can produce false positive results (Simmons, Nelson, & Simonsohn, 2011).  The article presents simulation studies that examine the actual risk of a type-I error when questionable research practices are used.  They find that a single questionable practice can increase the chances of obtaining a false positive result from the nominal 5% to 12.6%.  A combination of four questionable research practices increased the risk to 60.7%.  The massive use of questionable research practices is called p-hacking. P-hacking may work for a single study, if a researcher is lucky.  But it is very unlikely that a researcher can p-hack a series of 9 studies to produce 9 false positive results,  (p = .6= 1%).

The analysis of Bem’s data suggest that a perfect multiple-study article requires omitting failed studies from the record, and hiding disconfirming evidence violates basic standards of research ethics. If there is a known moderator, the non-significant results provide important information about boundary conditions (time-reversed causality works with erotic pictures, but not with pictures of puppies).  If the moderator is not known, it is still important to report this finding to plan future studies. There is simply no justification for excluding non-significant results from a series of studies that are reported in a single article.

To reduce bias and increase credibility, pilot studies or other failed studies could be included in a meta-analysis at the end of a multiple-study article. The meta-analysis could show that the effect is significant across an unbiased sample of studies that produced significant and nonsignificant results. This overall effect is functionally equivalent to the test of the hypothesis in a single study with high power. Importantly, the meta-analysis is only credible if it includes nonsignificant results (Schimmack, 2012, p. 563).

Thus, a simple way to improve the credibility of psychological science is to demand that researchers submit all studies that tested relevant hypotheses for publication and to consider selection of significant results scientific misconduct.  Ironically, publishing failed studies will provide stronger evidence than seemingly flawless results that were obtained by omitting nonsignificant results. Moreover, allowing for the publication of non-significant results reduces the pressure to use p-hacking, which only serves the goal to obtain significant results in all studies.

Should the Journal of Personality and Social Psychology Retract Bem’s Article?

Journals have a high threshold for retractions. Typically, articles are retracted only if there are doubts about the integrity of the published data. If data were manipulated by fabricating them entirely or by swapping participants from one condition to another to exaggerate mean differences, articles are retracted. In contrast, if researchers collected data and selectively reported only successful studies, articles are not retracted. The selective publishing of significant results is so widespread that it seems inconceivable to retract every article that used this questionable research practice. Francis (2014) estimated that at least 80% of articles published in the flagship journal Psychological Science would have to be retracted (Francis, 2014). This seems excessive.

However, Bem’s article is unique in many ways, and the new analyses of original data presented here suggest that bad research practices, inadvertently or not, produced Bem’s results. Moreover, the results could not be replicated in other studies. Retracting the article would send a clear signal to the scientific community and other stakeholders in psychological science that psychologists are serious about learning from mistakes by flagging the results reported in Bem as erroneous. Unless the article is retracted, uniformed researchers will continue to cite the article as evidence for supernatural phenomena like time-reversed causality.

“Experimentally, such precognitive effects have manifested themselves in a variety of ways. … as well as precognitive priming, where behaviour can be influenced by primes that are shown after the target stimulus has been seen (e.g. Bem, 2011; Vernon, 2015).” (Vernon, 2017, p. 217).

Vernon (2017) does cite failed replication studies, but interprets these failures as evidence for some hidden moderator that could explain inconsistent findings that require further investigation. A retraction would make it clear that there are no inconsistent findings because Bem’s findings do not provide credible evidence for the effect. Thus, it is unnecessary and maybe unethical to recruit human participants to further replication studies of Bem’s paradigms.

This does not mean that future research on paranormal phenomena should be banned. However, future studies cannot be based on Bem’s paradigms or results to plan future studies. For example, Vernon (2017) studied a small sample of 107 participants, which would be sufficient based on Bem’s effect sizes, but these effect sizes are not trustworthy and cannot be used to plan future studies.

A main objection to retractions is that Bem’s study made an inadvertent important contribution to the history of social psychology that triggered a method revolution and changes in the way social psychologist conduct research. Such an important article needs to remain part of the scientific record and needs to be cited in meta-psychological articles that reflect on research practices. However, a retraction does not eradicate a published article. Retracted articles remain available and can be cited (RetractionWatch, 2018). Thus, it is possible to retract an article without removing it from the scientific record. A retraction would signal clearly that the article should not be cited as evidence for time-reversed causality and that the studies should not be included in meta-analyses because the bias in Bem’s studies also biases all meta-analytic findings that include Bem’s studies (Bem, Ressoldi, Rabeyron, & Duggan (2015).

[edited January, 8, 2018]
It is not clear how Bem (2011) thinks about his article these days, but one quote in Enbger’s article suggests that Bem realizes now that he provided false evidence for a phenomenon that does not exist.

When Bem started investigating ESP, he realized the details of his research methods would be scrutinized with far more care than they had been before. In the years since his work was published, those higher standards have increasingly applied to a broad range of research, not just studies of the paranormal. “I get more credit for having started the revolution in questioning mainstream psychological methods than I deserve,” Bem told me. “I was in the right place at the right time. The groundwork was already pre-prepared, and I just made it all startlingly clear.”

If Bem wants credit for making it startlingly clear that his evidence was obtained with questionable research practices that can mislead researchers and readers, he should make it startlingly clear that this was the case by retracting the article.


Alcock, J. E. (2011). Back from the future: Parapsychology and the Bem affair. Skeptical Inquirer, 35(2). Retrieved from

Bem, D. J. (2000). Writing an empirical article. In R. J. Sternberg (Ed.), Guide to publishing in psychological journals (pp. 3–16). Cambridge, England: Cambridge University Press. doi:10.1017/CBO9780511807862.002

Bem, D. J. (2011). Feeling the future: Experimental evidence for anomalous retroactive influences on cognition and affect. Journal of Personality and Social Psychology, 100, 407–425. doi:10.1037/a0021524

Bem, D.J., Tressoldi, P., Rabeyron, T. & Duggan, M. (2015) Feeling the future: A meta-analysis of 90 experiments on the anomalous anticipation of random future events, F1000 Research, 4, 1–33.

Engber, D. (2017). Daryl Bem proved ESP Is real: Which means science is broken.

Francis, G. (2012). Too good to be true: Publication bias in two prominent
studies from experimental psychology. Psychonomic Bulletin & Review,
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Francis, G. (2014). The frequency of excess success for articles in Psychological Science. Psychonomic Bulletin & Review, 21, 1180-1187.

Franco, A., Malhotra, N., & Simonovits, G. (2014). Publication bias in the social sciences: Unlocking the file drawer. Science, 345, Issue 6203, 502-1505, DOI: 10.1126/science.1255484

Galak, J., Leboeuf, R.A., Nelson, L. D., & Simmons, J.P. (2012). Journal of Personality and Social Psychology, 103, 933-948, doi: 10.1037/a0029709.

John, L. K. Loewenstein, G., & Prelec, D. (2012). Measuring the prevalence of questionable research practices with incentives for truth telling. Psychological Science, 23, 524-532. DOI: 10.1177/0956797611430953

RetractionWatch (2018). Ask retraction watch: Is it OK to cite a retracted paper?

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Schimmack, U. (2015). The Test of Insufficient Variance: A New Tool for the Detection of Questionable Research Practices.

Simmons, J. P., Nelson, L. D., & Simonsohn, U. (2011). False-positive psychology: Undisclosed flexibility in data collection and analysis allows presenting anything as significant. Psychological Science, 22, 1359–1366. doi:10.1177/0956797611417632

Strube, M. J. (2006). SNOOP: A program for demonstrating the consequences
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Schooler, J. (2011). Unpublished results hide the decline effect. Nature, 470, 437.

Sterling, T. D. (1959). Publication decisions and their possible effects on inferences drawn from tests of significance— or vice versa. Journal of the American Statistical Association, 54(285), 30–34. doi:10.2307/2282137

Tversky, A. & Kahneman, D. (1971). Belief in the law of small numbers. Psychological Bulletin, 76, 105-110.


Hidden Figures: Replication Failures in the Stereotype Threat Literature

In the past five years, it has become apparent that many classic and important findings in social psychology fail to replicate (Schimmack, 2016).  The replication crisis is often considered a new phenomenon, but failed replications are not entirely new.  Sometimes these studies have simply been ignored.  These studies deserve more attention and need to be reevaluated in the context of the replication crisis in social psychology.

In the past, failed replications were often dismissed because seminal articles were assumed to provide robust empirical support for a phenomenon, especially if an article presented multiple studies. The chance of reporting a false positive results in a multiple study article is low because the risk of a false positive decreases exponentially (Schimmack, 2012). However, the low risk of a false positive is illusory if authors only publish studies that worked. In this case, even false positives can be supported by significant results in multiple studies, as demonstrated in the infamous ESP study by Bem (2011).  As a result, publication bias undermines the reporting of statistical significance as diagnostic information about the risk of false positives (Sterling, 1959) and many important theories in social psychology rest on shaky empirical foundations that need to be reexamined.

Research on stereotype threat and women’s performance on math tests is one example where publication bias undermines the findings in a seminal study that produced a large literature of studies on gender differences in math performance. After correcting for publication bias, this literature shows very little evidence that stereotype threat has a notable and practically significant effect on women’s math performance (Flore & Wicherts, 2014).

Another important line of research has examined the contribution of stereotype threat to differences between racial groups on academic performance tests.  This blog post examines the strength of the empirical evidence for stereotype threat effects in the seminal article by Steele and Aronson (1995). This article is currently the 12th most cited article in the top journal for social psychology, Journal of Personality and Social Psychology (2,278 citations so far).

According to the abstract, “stereotype threat is being at risk of confirming, as self-characteristic, a negative stereotype about one’s group.” Studies 1 and 2 showed that “reflecting the pressure of this vulnerability, Blacks underperformed in relation to Whites in the ability-diagnostic condition but not in the nondiagnostic condition (with Scholastic Aptitude Tests controlled).”  “Study 3 validated that ability-diagnosticity cognitively activated the racial stereotype in these participants and motivated them not to conform to it, or to be judged by it.”  “Study 4 showed that mere salience of the stereotype could impair Blacks’ performance even when the test was not
ability diagnostic.”

The results of Study 4 motivated Stricker and colleagues to examine the influence of stereotype-treat on test performance in a real-world testing situation.  These studies had large samples and were not limited to students at Stanford. One study was reported in a College Board Report (Stricker and Ward, 1998).   Another two studies were published in the Journal of Applied Social Psychology (Stricker & Ward, 2004).  This article received only 52 citations, although it reported two studies with an experimental manipulation of stereotype threat in a real assessment context.  One group of participants were asked about their gender or ethnicity before the text, the other group did not receive these questions.  As noted in the abstract, neither the inquiry about race, nor about gender, had a significant effect on test performance. In short, this study failed to replicate Study 4 of the classic and widely cited article by Steele and Aronson.

Stricker and Ward’s Abstract
Steele and Aronson (1995) found that the performance of Black research participants on
ability test items portrayed as a problem-solving task, in laboratory experiments, was affected adversely when they were asked about their ethnicity. This outcome was attributed to stereotype threat: Performance was disrupted by participants’ concerns about fulfilling the negative stereotype concerning Black people’s intellectual ability. The present field experiments extended that research to other ethnic groups and to males and females taking operational tests. The experiments evaluated the effects of inquiring about ethnicity and gender on the performance of students taking 2 standardized tests-the Advanced Placement Calculus AB Examination, and the Computerized Placement Tests-in actual test administrations. This inquiry did not have any effects on the test performance of Black, female, or other subgroups of students that were both statistically and practically significant.

The article also mentions a personal communication with Steele, in which Steele mentions an unpublished study that also failed to demonstrate the effect under similar conditions.

“In fact, Steele found in an unpublished pilot study that inquiring about ethnicity did not affect Black participants’ performance when the task was described as diagnostic of their ability (C. M. Steele, personal communication, May 2 1, 1997), in contrast to the
substantial effect of inquiring when the task was described as nondiagnostic.”

A substantive interpretation of this finding is that inquires about race or gender do not produce stereotype threat effects when a test is diagnostic because a diagnostic test already activates stereotype threat.  However, if this were a real moderator, it would be important to document this fact and it is not clear why this finding obtained in an earlier study by Steele remained unpublished. Moreover, it is premature to interpret the significant result in the published study with a non-diagnostic task and the non-significant result in an unpublished study with a diagnostic task as evidence that diagnosticity moderates the effect of the stereotype-threat manipulation. A proper test of this moderator hypothesis would require the demonstration of a three-way interaction between race, inquiry about race, and diagnosticity. Absent this evidence, it remains possible that diagnosticity is not a moderator and that the published result is a false positive (or a positive result with an inflated effect size estimate). In contrast, there appears to be consistent evidence that inquiries about race or gender before a real assessment of academic performance does not influence performance. This finding is not widely publicized, but is important for a better understanding of performance differences in real world settings.

The best way to examine the replicability of Steele and Aronson’s seminal finding with non-diagnostic tasks would be to conduct an exact replication study.  However, exact replication studies are difficult and costly.  An alternative is to examine the robustness of the published results by taking a closer look at the strength of the statistical results reported by Steele and Aronson, using modern statistical tests of publication bias and statistical power like the R-Index (Schimmack, 2014) and the Test of Insufficient Variance (TIVA, Schimmack, 2014).

Replicability Analysis of Steele and Aronson’s four studies

Study 1. The first study had a relatively large sample of N = 114 participants, but it is not clear how many of the participants were White or Black.  The study also had a 2 x 3 design, which leaves less than 20 participants per condition.   The study produced a significant main effect of condition, F(2, 107) = 4.74, and race, F(1,107) = 5.22, but the critical condition x race interaction was not significant (reported as p > .19).   However, a specific contrast showed significant differences between Black participants in the diagnostic condition and the non-diagnostic condition, t(107) = 2.88, p = .005, z = 2.82.  The authors concluded “in sum, then, the hypothesis was supported by the pattern of contrasts, but when tested over the whole design, reached only marginal significance” (p. 800).  In other words, Study 1 provided only weak support for the stereotype threat hypothesis.

Study 2. Study 2 eliminated one of the three experimental conditions. Participants were 20 Black and 20 White participants. This means there were only 10 participants in each condition of a 2 x 2 design. The degrees of freedom further indicate that the actual sample size was only 38 participants. Given the weak evidence in Study 1, there is no justification for a reduction in the number of participants per cell, although the difficulty of recruiting Black participants at Stanford may explain this inadequate sample size. Nevertheless, the study showed a significant interaction between race and test description, F(1,35) = 8.07, p = .007. The study also replicated the contrast from Study 1 that Black participants in the diagnostic condition performed significantly worse than Black participants in the non-diagnostic group, t(35) = 2.38, p = .023, z = 2.28.

Studies 1 and 2 are close replications of each other.  The consistent finding across the two studies that supports stereotype-treat theory is the finding that merely changing the description of an assessment task changes Black participants performance, as revealed by significant differences between the diagnostic and non-diagnostic condition in both studies.  The problem is that both studies had small numbers of Black participants and that small samples have low power to produce significant results. As a result, it is unlikely that a pair of studies would produce significant results in both studies.

Observed power  in the two studies is .81 and .62 with median observed power of .71. Thus, the actual success rate of 100% (2 out of 2 significant results) is 29 percentage points higher than the expected success rate. Moreover, when inflation is evident, median observed power is also inflated. To correct for this inflation, the Replicability-Index (R-Index) subtracts inflation from median observed power, which yields an R-Index of 42.  Any value below 50 is considered unacceptably low and I give it a letter grade F, just like students at American Universities receive an F for exams with less than 50% correct answers.  This does not mean that stereotype threat is not a valid theory or that there was no real effect in this pair of studies. It simply means that the evidence in this highly cited article is insufficient to make strong claims about the causes of Black’s performance on academic tests.

The Test of Insufficient Variance (TIVA) provides another way to examine published results.  Test statistics like t-values vary considerably from study to study even if the exact same study is conducted twice (or if one larger sample is randomly split into two sub-samples).  When test-statistics are converted into z-scores, sampling error (the random variability from sample to sample) follows approximately a standard normal distribution with a variance of 1.  If the variance is considerably smaller than 1, it suggests that the reported results represent a selected sample. Often the selection is a result of publication bias.  Applying TIVA to the pair of studies, yields a variance of Var(z) = 0.15.  As there are only two studies, it is possible that this outcome occurred by chance, p = .300, and it does not imply intentional selection for significance or other questionable research practices.  Nevertheless, it suggests that future replication studies will be more variable and produce some non-significant results.

In conclusion, the evidence presented in the first two studies is weaker than we might assume if we focused only on the fact that both studies produced significant contrasts. Given publication bias, the fact that both studies reported significant results provides no empirical evidence because virtually all published studies report significant results. The R-Index quantifies the strength of evidence for an effect while taking the influence of publication bias into account and it shows that the two studies with small samples provide only weak evidence for an effect.

Study 3.  This study did not examine performance. The aim was to demonstrate activation of stereotype threat with a sentence completion task.  The sample size of 68 participants  (35 Black, 33 White) implied that only 11 or 12 participants were assigned to one of the six cells in a 2 (race) by 3 (task description) design. The study produced main effects for race and condition, but most importantly it produced a significant interaction effect, F(2,61) = 3.30, p = .044.  In addition, Black participants in the diagnostic condition had more stereotype-related associations than Black participants in the non-diagnostic condition, t(61) = 3.53,

Study 4.  This study used inquiry about race to induce stereotype-threat. Importantly, the task was described as non-diagnostic (as noted earlier, a similar study produced no significant results when the task was described as diagnostic).  The design was a 2 x 2 design with 47 participants, which means only 11 or 12 participants were allocated to the four conditions.  The degrees of freedom indicated that cell frequencies were even lower. The study produced a significant interaction effect, F(1,39) = 7.82, p = .008.  The study also produced a significant contrast between Blacks in the race-prime condition and the no-prime condition, t(39) = 2.43, p = .020.

The contrast effect in Study 3 is strong, but it is not a performance measure.  If stereotype threat mediates the effect of task characteristics and performance, we would expect a stronger effect on the measure of the mediator than on the actual outcome of interest, task performance.  The key aim of stereotype threat theory is to explain differences in performance.  With a focus on performance outcomes, it is possible to examine the R-Index and TIVA of Studies 1, 2, and 4.  All three studies reported significant contrasts between Black students randomly assigned to two groups that were expected to show performance differences (Table 1).

Table 1

Study Test Statistic p-value z-score obs.pow
Study 1 t(107) = 2.88 0.005 2.82 0.81
Study 2 t(35)=2.38 0.023 2.28 0.62
Study 4 t(39) = 2.43 0.020 2.33 0.64

Median observed power is 64 and the R-Index is well below 50, 64 – 36 = 28 (F).  The variance in z-scores is Var(z) = 0.09, p = .086.  These results cast doubt about the replicability of the performance effects reported in Steele and Aronson’s seminal stereotype threat article.


Racial stereotypes and racial disparities are an important social issue.  Social psychology aims and promises to contribute to the understanding of this issue by conducting objective, scientific studies that can inform our understanding of these issues.  In order to live up to these expectations, social psychology has to follow the rules of science and listen to the data.  Just like it is important to get the numbers right to send men and women into space (and bring them back), it is important to get the numbers right when we use science to understand women and men on earth.  Unfortunately, social psychologists have not followed the examples of astronomers and the numbers do not add up.

The three African American women, features in this years movie “Hidden Figures”***,  Katherine Johnson, Dorothy Vaughan, and Mary Jackson might not approve of the casual way social psychologists use numbers in their research, especially the wide-spread practice of hiding numbers that do not match expectations.  No science that wants to make a real-world contribution can condone this practice.  It is also not acceptable to simply ignore published results from well-conducted studies with large samples that challenge a prominent theory.

Surely, the movie Hidden Figures dramatized some of the experiences of Black women at NASA, but there is little doubt that Katherine Johnson, Dorothy Vaughan, and Mary Jackson encountered many obstacles that might be considered stereotype threatening situations.  Yet, they prevailed and they paved the way for future generations of stereotyped groups.  Understanding racial and gender bias and performance differences remains an important issue and that is the reason why it is important to shed a light on hidden numbers and put simplistic theories under the microscope. Stereotype threat is too often used as a simple explanation that avoids tackling deeper and more difficult issues that cannot be easily studied in a quick laboratory experiment with undergraduate students at top research universities.  It is time for social psychologists to live up to its promises by tackling real world issues with research designs that have real world significance that produce real evidence using open and transparent research practices.


*** If you haven’t seen the movie, I highly recommend it.


How did Diedrik Stapel Create Fake Results? A forensic analysis of “From Seeing to Being: Subliminal Social Comparisons Affect Implicit and Explicit Self-Evaluations”

Diederik Stapel represents everything that has gone wrong in social psychology.  Until 2011, he was seen as a successful scientists who made important contributions to the literature on social priming.  In the article “From Seeing to Being: Subliminal Social Comparisons Affect Implicit and Explicit Self-Evaluations” he presented 8 studies that showed that social comparisons can occur in response to stimuli that were presented witout awareness (subliminally).  The results were published in the top journal of social psychology published by the American Psychological Association (APA) and APA published a press-release for the general public about this work.  
In 2011, an investigation into Diedrik Stapel’s reserach practices revealed scientific fraud, which resulted in over 50 retractions (Retraction Watch), including the article on unconscious social comparisons (Retraction Notice).  In a book, Diederik Stapel told his story about his motives and practices, but the book is not detailed enough to explain how particular datasets were fabricated.  All we know, is that he used a number of different methods that range from making up datasets to the use of questionable research practices that increase the chance of producing a significant result.  These practices are widely used and are not considered scientific fraud, although the end result is the same. Published results no longer provide credible empirical evidence for the claims made in a published article.
I had two hypothesis. First, the data could be entirely made up. When researchers make up fake data they are likely to overestimate the real effect sizes and produce data that show the predicted pattern much more clearly than real data would. In this case, bias tests would not show a problem with the data.  The only evidence that the data are fake would be that the evidence is stronger than in other studies that relied on real data. 
In contrast, a researcher who starts with real data and then uses questionable practices is likely to use as little dishonest practices as possible because this makes it easier to justify the questionable decisions.  For example, removing 10% of data may seem justified, especially if some rational for exclusion can be found.  However, removing 60% of data cannot be justified.  The researcher will need to use these practices to produce the desired outcome, namely a p-value below .05 (or at least very close to .05).  As more use of questionable practices is not needed and harder to justify, the researcher will stop producing stronger evidence.  As a result, we would expect a large number of just significant results.
There are two bias tests that detect the latter form of fabricating significant results by means of questionable statistical methods; the Replicability-Index (R-Index) and the Test of Insufficient Variance (TIVA).   If Stapel used questionable statistical practices to produce just significant results, R-Index and TIVA would show evidence of bias.
The article reported 8 studies. The table shows the key finding of each study.
Study Statistic p z OP
1 F(1,28)=4.47 0.044 2.02 0.52
2A F(1,38)=4.51 0.040 2.05 0.54
2B F(1,32)=4.20 0.049 1.97 0.50
2C F(1,38)=4.13 0.049 1.97 0.50
3 F(1,42)=4.46 0.041 2.05 0.53
4 F(2,49)=3.61 0.034 2.11 0.56
5 F(1,29)=7.04 0.013 2.49 0.70
6 F(1,55)=3.90 0.053 1.93 0.49
All results were interpreted as evidence for an effect and the p-value for Study 6 was reported as p = .05.
All p-values are below .053 but greater than .01.  This is an unlikely outcome because sampling error should produce more variability in p-values.  TIVA examines whether there is insufficient variability.  First, p-values are converted into z-scores.  The variance of z-scores due to sampling error alone is expected to be approximately 1.  However, the observed variance is only Var(z) = 0.032.  A chi-square test shows that this observed variance is unlikely to occur by chance alone,  p = .00035. We would expect such an extremely small variabilty or even less variability in only 1 out of 28,458 sets of studies by chance alone.
The last column transforms z-scores into a measure of observed power. Observed power is an estimate of the probability of obtaining a significant result under the assumption that the observed effect size matches the population effect size.  These estimates are influenced by sampling error.  To get a more reliable estimate of the probability of a successful outcome, the R-Index uses the median. The median is 53%.  It is unlikely that a set of 8 studies with a 53% chance of obtaining a significant result produced significant results in all studies.  This finding shows that the reported success rate is not credible. To make matters worse, the probability of obtaining a significant result is inflated when a set of studies contains too many significant results.  To correct for this bias, the R-Index computes the inflation rate.  With 53% probability of success and 100% success rate, the inflation rate is 47%.  To correct for inflation, the inflation rate is subtracted from median observed probability, which yields an R-Index of 53% – 47% = 6%.  Based on this value, it is extremely unlikely that a researcher would obtain a significant result, if they would actually replicate the original studies exactly.  The published results show that Stapel could not have produced these results without the help of questionable methods, which also means nobody else can reproduce these results.
In conclusion, bias tests suggest that Stapel actually collected data and failed to find supporting evidence for his hypotheses.  He then used questionable practices until the results were statistically significant.  It seems unlikely that he outright faked these data and intentionally produced a p-value of .053 and reported it as p = .05.  However, statistical analysis can only provide suggestive evidence and only Stapel knows what he did to get these results.