Tag Archives: QRP

Gino-Colada – 2: The line between fraud and other QRPs

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“It wasn’t fraud. It was other QRPs”

[collaborator] “Francesca and I have done so many studies, a lot of them as part of the CLER lab, the behavioral lab at Harvard. And I’d say 80% of them never worked out.” (Gino, 2023)

Experimental social scientists have considered themselves superior to other social scientists because experiments provide strong evidence about causality that correlational studies cannot provide. Their experimental studies often produced surprising results, but because they were obtained using the experimental method and published in respected, peer-reviewed, journals, they seemed to provide profound novel insights into human behavior.

In his popular book “Thinking: Fast and Slow” Nobel Laureate Daniel Kahneman told readers “disbelief is not an option. The results are not made up, nor are they statistical flukes. You have no choice but to accept that the major conclusions of these studies are true.” He probably regrets writing these words, because he no longer believes these findings (Kahneman, 2017).

What happened between 2011 and 2017? Social scientists started to distrust their own (or at least the results or their colleagues) findings because it became clear that they did not use the scientific method properly. The key problem is that they only published results when they provided evidence for their theories, hypothesis, and predictions, but did not report when their studies did not work. As one prominent experimental social psychologists put it.

“We did run multiple studies, some of which did not work, and some of which worked better than others. You may think that not reporting the less successful studies is wrong, but that is how the field works.” (Roy Baumeister)“

Researchers not only selectively published studies with favorable results. They also used a variety of statistical tricks to increase the chances of obtaining evidence for their claims. John et al. (2012) called these tricks questionable research practices (QRPs) and compared them to doping in sport. The difference is that doping is banned in sports, but the use of many QRPs is not banned or punished by social scientific organizations.

The use of QRPs explains why scientific journals that report the results of experiments with human participants report over 90% of the time that the results confirmed researchers’ predictions. For statistical reasons , this high success rate is implausible even if all predictions were true (Sterling et al., 1995). The selective publishing of studies that worked renders the evidence meaningless (Sterling, 1959). Even clearly false hypotheses like “learning after an exam can increase exam performance” can receive empirical support, when QRPs are being used (Bem, 2011). The use of QRPs also explains why results of experimental social scientists often fail to replicate (Schimmack, 2020).

John et al. (2012) used the term questionable research practices broadly. However, it is necessary to distinguish three types of QRPs that have different implications for the credibility of results.

One QRPs is selective publishing of significant results. In this case, the results are what they are and the data are credible. The problem is mainly that these results are likely to be inflated by sampling bias. This bias would disappear when all studies were published and the results are averaged. However, if non-significant results are not published, the average remains inflated.

The second type of QRPs are various statistical tricks that can be used to “massage” the data to produce a more favorable result. These practices are now often called p-hacking. Presumably, these practices are used mainly after an initial analysis did not produce the desired result, but may be a trend in the expected direction. P-hacking alters the data and it is no longer clear how strong the actual evidence was. While lay people may consider these practices fraud or a type of doping, professional organizations tolerate these practices and even evidence of their use would not lead to disciplinary actions against a researcher.

The third QRP is fraud. Like p-hacking, fraud implies data manipulation with the goal of getting a desirable result, but the difference is …. well, it is hard to say what the difference to p-hacking is except that it is not tolerated by professional organizations. Outright fraud in which a whole data set is made up (as some datasets by disgraced Diederik Stapel) are clear cases of fraud. However, it is harder to distinguish between fraud and p-hacking when one researcher deletes selective outliers from two groups to get significance (p-hacking) or switches extreme cases from one group to another (fraud) (GinoColada1). In both cases, the data are meaningless, but only fraud leads to reputation damage and public outrage, while p-hackers can continue to present their claims as scientific truths.

The distinction between different types of QRPs is important to understand Gino’s latest defense against accusations that she committed fraud that have been widely publicized in newspaper articles and a long article in the New Yorker. In her response, she cites from Harvards’s investigative report to make the point that she is not a data fabricator.

[collaborator] “Francesca and I have done so many studies, a lot of them as part of the CLER lab, the behavioral lab at Harvard. And I’d say 80% of them never worked out.”

The argument is clear. Why would I have so many failed studies, if I could just make up fake data that support my claim. Indeed, Stapel claims that he started faking studies outright because it was clear that p-hacking is a lot of work and making up data is the most efficient QRP (“Why not just make the data up. Same results with less effort”). Gino makes it clear that she did not just fabricate data because she clearly collected a lot of data and has many failed studies that were not p-hacked or manipulated to get significance. She only did what everybody else did; hiding the studies that did not work and lot’s of them.

Whether she sometimes did engage in practices that cross the line from p-hacking to fraud is currently being investigated and not my concern. What I find interesting is the frank admission in her defense that 80% of her studies failed to provide evidence for her hypotheses. However, if somebody would look up her published work, they would see mainly the results of studies that worked. And she has no problem of telling us that these published results are just the tip of an iceberg of studies, where many more did not work. She thinks this is totally ok, because she has been trained / brainwashed to believe that this is how science works. Significance testing is like a gold pan.

Get a lot of datasets, look for p < .05, keep the significant ones (gold) and throw away the rest. The more studies, you run, the more gold you find, and the richer you are. Unfortunately, for her and the other experimental social scientists who think every p-value below .05 is a discovery, this is not how science works, as pointed out by Sterling (1959) many, many years before, but nobody wants to listen to people to tell you something is hard work.

Let’s for the moment assume that Gino really runs 100 studies to get 20 significant results (80% do not work, p < .10). Using a formula from Soric (1989), we can compute the risk that one of her 20 significant results is a false positive result (i.e., the significant result is a fluke without a real effect), even if she did not use p-hacking or other QRPs, which would further increase the risk of false claims.

FDR = ((1/.20) – 1)*(.05/.95) = 21%

Based on Gino’s own claim that 80% of her studies fail to produce significant results, we can infer that up to 21% of her published significant results could be false positive results. Moreover, selective publishing also inflates effect sizes and even if a result is not a false positive, the effect size may be in the same direction, but too small to be practically important. In other words, Gino’s empirical findings are meaningless without independent replications, even if she didn’t use p-hacking or manipulated any data. The question whether she committed fraud is only relevant for her personal future. It has no relevance for the credibility of her published findings or those of others in her field like Dan Air-Heady. The whole field is a train wreck. In 2012, Kahneman asked researchers in the field to clean up their act, but nobody listened and Kahneman has lost faith in their findings. Maye it is time to stop nudging social scientists with badges and use some operant conditioning to shape their behavior. But until this happens, if it every happens, we can just ignore this pseudo-science, no matter what happens in the Gino versus Harvard/DataColada case. As interesting as scandals are, it has no practical importance for the evaluation of the work that has been produced by experimental social scientists.

P.S. Of course, there are also researchers who have made real contributions, but unless we find ways to distinguish between credible work that was obtained without QRPs and incredible findings that were obtained with scientific doping, we don’t know which results we can trust. Maybe we need a doping test for scientists to find out.

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

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The term “questionable research practices” (QRPs) was popularized in an article by John, Loewenstein, and Prelec (2012).
The authors distinguish between fraud and QRPs. Fraud is typically limited to cases in which researchers create false data. In contrast, QRPs typically involve the exclusion of data that are inconsistent with a theoretical hypothesis.  QRPs are treated differently than fraud because QRPs can sometimes be used for legitimate purposes.

For example, a data entry error may produce a large outlier that leads to a non-significant result when all data are included in the analysis.  The results are significant when the outlier is removed.  Statistical textbook often advise to exclude outliers for this reason.  However, removal of outliers becomes a QRP when it is used selectively.  That is, outliers are not removed when a result is significant or when the outlier helps to produce a significant result, but outliers are removed when removal of outliers helps to get a significant result.

The use of QRPs is damaging because published results provide false impressions about the replicability of empirical results and misleading evidence about the size of an effect.

Below is a list of QRPs.

Selective reporting of (dependent) variables.  For example, a researcher may include 10 items to measure depression.  Typically, the 10 items are averaged to get the best measure of depression.  However, if this analysis does not produce a significant result, the researcher can conduct analyses of each individual item or average items that trend in the right direction.  By creating different dependent variables after the study is completed, a researcher increases the chances of obtaining a significant result that will not replicate in a replication study with the same dependent variable.

A simple solution to preventing this QRP is to ask authors to use well-established measures as dependent variables and/or to ask for pre-registration of all measures that are relevant to the test of a theoretical hypothesis (i.e., it is not necessary to specify that the study also asked about handedness because handedness is not a measure of depression).

Deciding whether to collect more data after looking to see whether the results will be significant.  It is difficult to distinguish random variation from a true effect in small samples.  At the same time, it can be a costly waste of resources (or even unethical in animal research) to conduct studies with large samples, when the effect can be detected in a smaller sample.  It is also difficult to know a priori how large a sample should be to obtain a significant result.  It therefore seems reasonable to check data while they are being collected for significance.  If an effect does not seem to be present in a reasonably large sample size, it may be better to abandon a study.  None of these practices are problematic unless a researcher constantly checks for significance and stops data collection immediately after the data show a significant result.  This practice capitalizes on sampling error and the experiment will typically stop when sampling error inflates the true effect size.

A simple solution to this problem is to set some a priori rules about the end of data collection.  For example, a researcher may calculate sample size based on a rough power analysis.  Based on an optimistic assumption that the true effect is large, the data will be checked when the study has 80% power for a large effect (d = .8).  If this does not result in a significant result, the researcher continues with the revised hypothesis that the true effect is moderate and then checks the data again when 80% power for a moderate effect is reached.  If this does not result in a significant result, the researcher may give up or continue with the revised hypothesis that the true effect is small.  This procedure would allow researchers to use an optimal amount of resources.  Moreover, they can state there sampling strategy openly so that meta-analysts can make corrections for the small amount of biases that is still introduced by this reasonable form of optional stopping.

Failing to disclose experimental conditions.   There are no justifiable reasons for the exclusion of conditions.  Evidently, researchers are not going to exclude conditions that are consistent with theoretical predictions. So, the exclusion of conditions can only produce results that are overly consistent with theoretical predictions.  If there are reasonable doubts about a condition (e.g., a manipulation check shows that it did not work), the condition can be included and it can be explained why the results may not conform to predictions).

A simple solution to the problem of conditions with unexpected results is that researchers may include too many conditions in their design.  A 2 x 2 x 2 factorial design has 8 cells, which allows for 28 comparisons of means. What are the chances that all of these 28 comparisons produce results that are consistent with theoretical predictions?

Another simple solution is to avoid the use of statistical methods with low power.  To demonstrate a three-way interaction requires a lot more data than to demonstrate that a pattern of means is consistent with an a priori theoretically predicted pattern.

In a paper reporting selectively studies that worked.

There is no reason for excluding studies that did not work. Excluding studies that were planned as demonstrations of an effect need to be reported. Otherwise the published evidence provides an overly positive picture of the robustness of a phenomenon and effect sizes are inflated.

Just like failed conditions, failed studies can be reported if there is a plausible explanation why it failed whereas other studies worked.  However, to justify this claim, it should be demonstrated that the effects in failed and successful studies are really significantly different (a significant moderator effect).  If this is not the case, there is no reason to treat failed and successful studies as different from each other.

A simple solution to this problem is to conduct studies with high statistical power because the main reason for failed studies is that studies have low power.  If a study has only 30% power, only one out of three studies will produce a significant result. The other two studies are likely to produce a type-II error (not show a significant result when the effect exists).  Rather than throwing away the two failed studies, a researcher should have conducted one study with higher power.  Another solution is to report all three studies and to test for significance only in a meta-analysis across the three studies.

In a paper, rounding off a p-value just above .054 and claim that it is below .05.   This is a minor problem. It is silly to change a p-value, but it does not bias a meta-analysis of effect sizes because researchers do not change effect size information.  Moreover, it would be even more silly not to change the p-value and conclude that there is no effect, which is often the case when results are not significant.  After all, a p-value of .054 means that the effect in this study would have occurred if the true effect is zero or has the opposite sign.

If a type-I error probability of 5.4% is considered too high, it would be possible to collect more data and test again with a larger sample (taking multiple testing into account).

Moreover, this problem should arise very infrequently. Even if a study is underpowered and has only 50% power, only 2% of p-values are expected to fall into the narrow range between .050 and .054.

In a paper, reporting an unexpected finding as having been predicted from the start.   I am sure some statisticians disagree with me and I may be wrong about this one, but I simply do not understand how a statistical analysis of some data cares about the expectations of a researcher.  Say, I analyze some data and find a significant effect in the data.  How can this effect be influenced by the way I report it later?  It may be a type-I error or it is not a type-I error, but my expectations have no influence on the causal processes that produced the empirical data.  I think the practice of writing exploratory studies as if they were conducted an a priori hypothesis is considered questionable because it often requires other QRPs (e.g., excluding additional tests that didn’t work) to produce a story that is concocted to explain unexpected results.  However, if the results are presented honestly and one out of five predictor variables in a multiple-regression is significant at p < .0001, it is likely to be a replicable finding, even if it is presented with a post-hoc prediction.

In a paper, claiming that results are unaffected by demographic variables (e.g., gender) when one is actually unsure (or knows that they do).   Again, this is a relatively minor point because it only speaks about potential moderators of a reported effect.  Moderation is important, but the conclusion about the main effect remains unchanged. For example, if an effect exists for men, but not for women, it is still true that on average there is an effect.  Furthermore, a more common mistake is often to claim that gender or other factors did not moderate an effect based on an underpowered comparison of 10 men and 30 women in a study with 40 participants.  Thus, false claims about moderating variables are annoying, but not a threat to the replicability of empirical results.

Falsifying Data. I personally do not include falsifying or fabricating of data in the list of questionable research practices.  I think falsifying and fabrication of data is not a research practice. It is also something that is clearly considered fraudulent and punished when it is discovered.  In contrast, questionable research practices are tolerated in many scientific communities and there are no clear guidelines against the use of these practices.

In conclusion, the most problematic research practices that undermine the replicability of published studies are selective reporting of dependent variables, conditions, or entire studies, and optional stopping when significance is reached.  These practices make it possible to produce significant results when a study has insufficient power.  However, to achieve significance without power, the type-I error rate also increases and replicability decreases.  John et al. (2012) aptly compared these QRPs to the use of doping in sports.  I consider the R-Index a doping test for science because it reveals that researchers used these QRPs.  I hope that the R-Index will discourage the use of QRPs and increase the power and replicability of published studies.

Whether scientific organizations should ban QRPs just like sports organizations ban doping is an interesting question.  Meanwhile the R-Index can be used without draconian consequences.  Researchers can self-examine the replicability of their findings and they can examine the replicability of published results before they invest resources, time, and the future of their graduate students in research projects that fail. Granting agencies can use the R-Index to reward researchers who conduct fewer studies with replicable results rather than researchers with many studies that fail to replicate.  Finally, the R-Index can be used to track how successful current initiatives are to increase the replicability of published studies.

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

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A previous blog examined how and why Dr. Förster’s data showed incredibly improbable linearity.

The main hypothesis was that two experimental manipulations have opposite effects on a dependent variable.

Assuming that the average effect size of a single manipulation is similar to effect sizes in social psychology, a single manipulation is expected to have an effect size of d = .5 (change by half a standard deviation). As the two manipulations are expected to have opposite effects, the mean difference between the two experimental groups should be one standard deviation (0.5 + 0.5 = 1). With N = 40, and d = 1, a study has 87% power to produce a significant effect (p < .05, two-tailed). With power of this magnitude, it would not be surprising to get significant results in 12 comparisonForsterTables (Table 1).

The R-Index for the comparison of the two experimental groups in Table is Ř = 87%
(Success Rate = 100%, Median Observed Power = 94%, Inflation Rate = 6%).

The Test of Insufficient Variance (TIVA) shows that the variance in z-scores is less than 1, but the probability of this event to occur by chance is 10%, Var(z) = .63, Chi-square (df = 11) = 17.43, p = .096.

Thus, the results for the two experimental groups are perfectly consistent with real empirical data and the large effect size could be the result of two moderately strong manipulations with opposite effects.

The problem for Dr. Förster started when he included a control condition and want to demonstrate in each study that the two experimental groups also differed significantly from the experimental group. As already pointed out in the original post, samples of 20 participants per condition do not provide sufficient power to demonstrate effect sizes of d = .5 consistently.

To make matters worse, the three-group design has even less power than two independent studies because the same control group is used in a three-group comparison. When sampling error inflates the mean in the control group (e.g, true mean = 33, estimated mean = 36), it benefits the comparison for the experimental group with the lower mean, but it hurts the comparison for the experimental group with the higher mean (e.g., M = 27, M = 33, M = 39 vs. M = 27, M = 36, M = 39). When sampling error leads to an underestimation of the true mean in the control group (e.g., true mean = 33, estimated mean = 30), it benefits the comparison of the higher experimental group with the control group, but it hurts the comparison of the lower experimental group and the control group.

Thus, total power to produce significant results for both comparisons is even lower than for two independent studies.

It follows that the problem for a researcher with real data was the control group. Most studies would have produced significant results for the comparison of the two experimental groups, but failed to show significant differences between one of the experimental groups and the control group.

At this point, it is unclear how Jens Förster achieved significant results under the contested assumption that real data were collected. However, it seems most plausible that QRPs would be used to move the mean of the control group to the center so that both experimental groups show a significant difference. When this was impossible, the control group could be dropped, which may explain why 3 studies in Table 1 did not report results for a control group.

The influence of QRPs on the control group can be detected by examining the variation of means in Table 1 across the 12(9) studies. Sampling error should randomly increase or decrease means relative to the overall mean of an experimental condition. Thus, there is no reason to expect a correlation in the pattern of means. Consistent with this prediction, the means of the two experimental groups are unrelated, r(12) = .05, p = .889; r(9) = .36, p = .347. In contrast, the means of the control group are correlated with the means of the two experimental groups, r(9) = .73, r(9) = .71. If the means in the control group are the result of the unbiased means in the experimental groups, it makes sense to predict the means in the control group from the means in the two experimental groups. A regression equation shows that 77% of the variance in the means of the control group is explained by the variation in the means in the experimental groups, R = .88, F(2,6) = 10.06, p = .01.

This analysis clarifies the source of the unusual linearity in the data. Studies with n = 20 per condition have very low power to demonstrate significant differences between a control group and opposite experimental groups because sampling error in the control group is likely to move the mean of the control group too close to one of the experimental groups to produce a significant difference.

This problem of low power may lead researchers to use QRPs to move the mean of the control group to the center. The problem for users of QRPs is that this statistical boost of power leaves a trace in the data that can be detected with various bias tests. The pattern of the three means will be too linear, there will be insufficient variance in the effect sizes, p-values, and observed power in the comparisons of experimental groups and control groups, the success rate will exceed median observed power, and, as shown here, the means in the control group will be correlated with the means in the experimental group across conditions.

In a personal email Dr. Förster did not comment on the statistical analyses because his background in statistics is insufficient to follow the analyses. However, he rejected this scenario as an account for the unusual linearity in his data; “I never changed any means.” Another problem for this account of what could have happened is that dropping cases from the middle group would lower the sample size of this group, but the sample size is always close to n = 20. Moreover, oversampling and dropping of cases would be a QRP that Dr. Förster would remember and could report. Thus, I now agree with the conclusion of the LOWI commission that the data cannot be explained by using QRPs, mainly because Dr. Förster denies having used any plausible QRPs that could have produced his results.

Some readers may be confused about this conclusion because it may appear to contradict my first blog. However, my first blog merely challenged the claim by the LOWI commission that linearity cannot be explained by QRPs. I found a plausible way in which QRPs could have produced linearity, and these new analyses still suggest that secretive and selective dropping of cases from the middle group could be used to show significant contrasts. Depending on the strength of the original evidence, this use of QRPs would be consistent with the widespread use of QRPs in the field and would not be considered scientific misconduct. As Roy F. Baumeister, a prominent social psychologist put it, “this is just how the field works.” However, unlike Roy Baumeister, who explained improbable results with the use of QRPs, Dr. Förster denies any use of QRPs that could potentially explain the improbable linearity in his results.

In conclusion, the following facts have been established with sufficient certainty:
(a) the reported results are too improbable to reflect just true effects and sampling error; they are not credible.
(b) the main problem for a researcher to obtain valid results is the low power of multiple-study articles and the difficulty of demonstrating statistical differences between one control group and two opposite experimental groups.
(c) to avoid reporting non-significant results, a researcher must drop failed studies and selectively drop cases from the middle group to move the mean of the middle group to the middle.
(d) Dr. Förster denies the use of QRPs and he denies data manipulation.
Evidently, the facts do not add up.

The new analyses suggest that there is one simple way for Dr. Förster to show that his data have some validity. The reason is that the comparison of the two experimental groups shows an R-Index of 87%. This implies that there is nothing statistically improbable about the comparison of these data. If these reported results are based on real data, a replication study is highly likely to replicate the mean difference between the two experimental groups. With n = 20 in each cell (N = 40), it would be relatively easy to conduct a preregistered and transparent replication study. However, without further credible evidence the published data lack credible scientific evidence and it would be prudent to retract all articles that show unusual statistical patterns that cannot be explained by the author.

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

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[further information can be found in a follow up blog]

Background

In 2011, Dr. Förster published an article in Journal of Experimental Psychology: General. The article reported 12 studies and each study reported several hypothesis tests. The abstract reports that “In all experiments, global/local processing in 1 modality shifted to global/local processing in the other modality”.

For a while this article was just another article that reported a large number of studies that all worked and neither reviewers nor the editor who accepted the manuscript for publication found anything wrong with the reported results.

In 2012, an anonymous letter voiced suspicion that Jens Forster violated rules of scientific misconduct. The allegation led to an investigation, but as of today (January 1, 2015) there is no satisfactory account of what happened. Jens Förster maintains that he is innocent (5b. Brief von Jens Förster vom 10. September 2014) and blames the accusations about scientific misconduct on a climate of hypervigilance after the discovery of scientific misconduct by another social psychologist.

The Accusation

The accusation is based on an unusual statistical pattern in three publications. The 3 articles reported 40 experiments with 2284 participants, that is an average sample size of N = 57 participants in each experiment. The 40 experiments all had a between-subject design with three groups: one group received a manipulation design to increase scores on the dependent variable. A second group received the opposite manipulation to decrease scores on the dependent variable. And a third group served as a control condition with the expectation that the average of the group would fall in the middle of the two other groups. To demonstrate that both manipulations have an effect, both experimental groups have to show significant differences from the control group.

The accuser noticed that the reported means were unusually close to a linear trend. This means that the two experimental conditions showed markedly symmetrical deviations from the control group. For example, if one manipulation increased scores on the dependent variables by half a standard deviation (d = +.5), the other manipulation decreased scores on the dependent variable by half a standard deviation (d = -.5). Such a symmetrical pattern can be expected when the two manipulations are equally strong AND WHEN SAMPLE SIZES ARE LARGE ENOUGH TO MINIMIZE RANDOM SAMPLING ERROR. However, the sample sizes were small (n = 20 per condition, N = 60 per study). These sample sizes are not unusual and social psychologists often use n = 20 per condition to plan studies. However, these sample sizes have low power to produce consistent results across a large number of studies.

The accuser computed the statistical probability of obtaining the reported linear trend. The probability of obtaining the picture-perfect pattern of means by chance alone was incredibly small.

Based on this finding, the Dutch National Board for Research Integrity (LOWI) started an investigation of the causes for this unlikely finding. An English translation of the final report was published on retraction watch. An important question was whether the reported results could have been obtained by means of questionable research practices or whether the statistical pattern can only be explained by data manipulation. The English translation of the final report includes two relevant passages.

According to one statistical expert “QRP cannot be excluded, which in the opinion of the expert is a common, if not “prevalent” practice, in this field of science.” This would mean that Dr. Förster acted in accordance with scientific practices and that his behavior would not constitute scientific misconduct.

In response to this assessment the Complainant “extensively counters the expert’s claim that the unlikely patterns in the experiments can be explained by QRP.” This led to the decision that scientific misconduct occurred.

Four QRPs were considered.

  1. Improper rounding of p-values. This QRP can only be used rarely when p-values happen to be close to .05. It is correct that this QRP cannot produce highly unusual patterns in a series of replication studies. It can also be easily checked by computing exact p-values from reported test statistics.
  2. Selecting dependent variables from a set of dependent variables. The articles in question reported several experiments that used the same dependent variable. Thus, this QRP cannot explain the unusual pattern in the data.
  3. Collecting additional research data after an initial research finding revealed a non-significant result. This description of an QRP is ambiguous. Presumably it refers to optional stopping. That is, when the data trend in the right direction to continue data collection with repeated checking of p-values and stopping when the p-value is significant. This practices lead to random variation in sample sizes. However, studies in the reported articles all have more or less 20 participants per condition. Thus, optional stopping can be ruled out. However, if a condition with 20 participants does not produce a significant result, it could simply be discarded, and another condition with 20 participants could be run. With a false-positive rate of 5%, this procedure will eventually yield the desired outcome while holding sample size constant. It seems implausible that Dr. Förster conducted 20 studies to obtain a single significant result. Thus, it is even more plausible that the effect is actually there, but that studies with n = 20 per condition have low power. If power were just 30%, the effect would appear in every third study significantly, and only 60 participants were used to produce significant results in one out of three studies. The report provides insufficient information to rule out this QRP, although it is well-known that excluding failed studies is a common practice in all sciences.
  4. Selectively and secretly deleting data of participants (i.e., outliers) to arrive at significant results. The report provides no explanation how this QRP can be ruled out as an explanation. Simmons, Nelson, and Simonsohn (2011) demonstrated that conducting a study with 37 participants and then deleting data from 17 participants can contribute to a significant result when the null-hypothesis is true. However, if an actual effect is present, fewer participants need to be deleted to obtain a significant result. If the original sample size is large enough, it is always possible to delete cases to end up with a significant result. Of course, at some point selective and secretive deletion of observation is just data fabrication. Rather than making up data, actual data from participants are deleted to end up with the desired pattern of results. However, without information about the true effect size, it is difficult to determine whether an effect was present and just embellished (see Fisher’s analysis of Mendel’s famous genetics studies) or whether the null-hypothesis is true.

The English translation of the report does not contain any statements about questionable research practices from Dr. Förster. In an email communication on January 2, 2014, Dr. Förster revealed that he in fact ran multiple studies, some of which did not produce significant results, and that he only reported his best studies. He also mentioned that he openly admitted to this common practice to the commission. The English translation of the final report does not mention this fact. Thus, it remains an open question whether QRPs could have produced the unusual linearity in Dr. Förster’s studies.

A New Perspective: The Curse of Low Powered Studies

One unresolved question is why Dr. Förster would manipulate data to produce a linear pattern of means that he did not even mention in his articles. (Discover magazine).

One plausible answer is that the linear pattern is the by-product of questionable research practices to claim that two experimental groups with opposite manipulations are both significantly different from a control group. To support this claim, the articles always report contrasts of the experimental conditions and the control condition (see Table below). ForsterTable

In Table 1 the results of these critical tests are reported with subscripts next to the reported means. As the direction of the effect is theoretically determined, a one-tailed test was used. The null-hypothesis was rejected when p < .05.

Table 1 reports 9 comparisons of global processing conditions and control groups and 9 comparisons of local processing conditions with a control group; a total of 18 critical significance tests. All studies had approximately 20 participants per condition. The average effect size across the 18 studies is d = .71 (median d = .68).   An a priori power analysis with d = .7, N = 40, and significance criterion .05 (one-tailed) gives a power estimate of 69%.

An alternative approach is to compute observed power for each study and to use median observed power (MOP) as an estimate of true power. This approach is more appropriate when effect sizes vary across studies. In this case, it leads to the same conclusion, MOP = 67.

The MOP estimate of power implies that a set of 100 tests is expected to produce 67 significant results and 33 non-significant results. For a set of 18 tests, the expected values are 12.4 significant results and 5.6 non-significant results.

The actual success rate in Table 1 should be easy to infer from Table 1, but there are some inaccuracies in the subscripts. For example, Study 1a shows no significant difference between means of 38 and 31 (d = .60, but it shows a significant difference between means 31 and 27 (d = .33). Most likely the subscript for the control condition should be c not a.

Based on the reported means and standard deviations, the actual success rate with N = 40 and p < .05 (one-tailed) is 83% (15 significant and 3 non-significant results).

The actual success rate (83%) is higher than one would expect based on MOP (67%). This inflation in the success rate suggests that the reported results are biased in favor of significant results (the reasons for this bias are irrelevant for the following discussion, but it could be produced by not reporting studies with non-significant results, which would be consistent with Dr. Förster’s account ).

The R-Index was developed to correct for this bias. The R-Index subtracts the inflation rate (83% – 67% = 16%) from MOP. For the data in Table 1, the R-Index is 51% (67% – 16%).

Given the use of a between-subject design and approximately equal sample sizes in all studies, the inflation in power can be used to estimate inflation of effect sizes. A study with N = 40 and p < .05 (one-tailed) has 50% power when d = .50.

Thus, one interpretation of the results in Table 1 is that the true effect sizes of the manipulation is d = .5, that 9 out of 18 tests should have produced a significant contrast at p < .05 (one-tailed) and that questionable research practices were used to increase the success rate from 50% to 83% (15 vs. 9 successes).

The use of questionable research practices would also explain unusual linearity in the data. Questionable research practices will increase or omit effect sizes that are insufficient to produce a significant result. With a sample size of N = 40, an effect size of d = .5 is insufficient to produce a significant result, d = .5, se = 32, t(38) = 1.58, p = .06 (one-tailed). Random sampling error that works against the hypothesis can only produce non-significant results that have to be dropped or moved upwards using questionable methods. Random error that favors the hypothesis will inflate the effect size and start producing significant results. However, random error is normally distributed around the true effect size and is more likely to produce results that are just significant (d = .8) than to produce results that are very significant (d = 1.5). Thus, the reported effect sizes will be clustered more closely around the median inflated effect size than one would expect based on an unbiased sample of effect sizes.

The clustering of effect sizes will happen for the positive effects in the global processing condition and for the negative effects in the local processing condition. As a result, the pattern of all three means will be more linear than an unbiased set of studies would predict. In a large set of studies, this bias will produce a very low p-value.

One way to test this hypothesis is to examine the variability in the reported results. The Test of Insufficient Variance (TIVA) was developed for this purpose. TIVA first converts p-values into z-scores. The variance of z-scores is known to be 1. Thus, a representative sample of z-scores should have a variance of 1, but questionable research practices lead to a reduction in variance. The probability that a set of z-scores is a representative set of z-scores can be computed with a chi-square test and chi-square is a function of the ratio of the expected and observed variance and the number of studies. For the set of studies in Table 1, the variance in z-scores is .33. The chi-square value is 54. With 17 degrees of freedom, the p-value is 0.00000917 and the odds of this event occurring by chance are 1 out of 109,056 times.

Conclusion

Previous discussions about abnormal linearity in Dr. Förster’s studies have failed to provide a satisfactory answer. An anonymous accuser claimed that the data were fabricated or manipulated, which the author vehemently denies. This blog proposes a plausible explanation of what could have [edited January 19, 2015] happened. Dr. Förster may have conducted more studies than were reported and included only studies with significant results in his articles. Slight variation in sample sizes suggests that he may also have removed a few outliers selectively to compensate for low power. Importantly, neither of these practices would imply scientific misconduct. The conclusion of the commission that scientific misconduct occurred rests on the assumption that QRPs cannot explain the unusual linearity of means, but this blog points out how selective reporting of positive results may have inadvertently produced this linear pattern of means. Thus, the present analysis support the conclusion by an independent statistical expert mentioned in the LOWI report: “QRP cannot be excluded, which in the opinion of the expert is a common, if not “prevalent” practice, in this field of science.”

How Unusual is an R-Index of 51?

The R-Index for the 18 statistical tests reported in Table 1 is 51% and TIVA confirms that the reported p-values have insufficient variance. Thus, it is highly probable that questionable research practices contributed to the results and in a personal communication Dr. Förster confirmed that additional studies with non-significant results exist. However, in response to further inquiries [see follow up blog] Dr. Förster denied having used QRPs that could explain the linearity in his data.

Nevertheless, an R-Index of 51% is not unusual and has been explained with the use of QRPs.  For example, the R-Index for a set of studies by Roy Baumeister was 49%, . and Roy Baumeister stated that QRPs were used to obtain significant results.

“We did run multiple studies, some of which did not work, and some of which worked better than others. You may think that not reporting the less successful studies is wrong, but that is how the field works.”

Sadly, it is quite common to find an R-Index of 50% or lower for prominent publications in social psychology. This is not surprising because questionable research practices were considered good practices until recently. Even at present, it is not clear whether these practices constitute scientific misconduct (see discussion in Dialogue, Newsletter of the Society for Personality and Social Psychology).

How to Avoid Similar Sad Stories in the Future

One way to avoid accusations of scientific misconduct is to conduct a priori power analyses and to conduct only studies with a realistic chance to produce a significant result when the hypothesis is correct. When random error is small, true patterns in data can emerge without the help of QRPs.

Another important lesson from this story is to reduce the number of statistical tests as much as possible. Table 1 reported 18 statistical tests with the aim to demonstrate significance in each test. Even with a liberal criterion of .1 (one-tailed), it is highly unlikely that so many significant tests will produce positive results. Thus, a non-significant result is likely to emerge and researchers should think ahead of time how they would deal with non-significant results.

For the data in Table 1, Dr. Förster could have reported the means of 9 small studies without significance tests and conduct significance tests only once for the pattern in all 9 studies. With a total sample size of 360 participants (9 * 40), this test would have 90% power even if the effect size is only d = .35. With 90% power, the total power to obtain significant differences from the control condition for both manipulations would be 81%. Thus, the same amount of resources that were used for the controversial findings could have been used to conduct a powerful empirical test of theoretical predictions without the need to hide inconclusive, non-significant results in studies with low power.

Jacob Cohen has been trying to teach psychologists the importance of statistical power for decades and psychologists stubbornly ignored his valuable contribution to research methodology until he died in 1998. Methodologists have been mystified by the refusal of psychologists to increase power in their studies (Maxwell, 2004).

One explanation is that small samples provided a huge incentive. A non-significant result can be discarded with little cost of resources, whereas a significant result can be published and have the additional benefit of an inflated effect size, which allows boosting the importance of published results.

The R-Index was developed to balance the incentive structure towards studies with high power. A low R-Index reveals that a researcher is reporting biased results that will be difficult to replicate by other researchers. The R-Index reveals this inconvenient truth and lowers excitement about incredible results that are indeed incredible. The R-Index can also be used by researchers to control their own excitement about results that are mostly due to sampling error and to curb the excitement of eager research assistants that may be motivated to bias results to please a professor.

Curbed excitement does not mean that the R-Index makes science less exciting. Indeed, it will be exciting when social psychologists start reporting credible results about social behavior that boost a high R-Index because for a true scientist nothing is more exciting than the truth.