Tag Archives: Kahneman

Incidental Anchoring Bites the Dust

Update: 6/10/21

After I posted this post, I learned about a published meta-analysis and new studies of incidental anchoring by David Shanks and colleagues that came to the same conclusion (Shanks et al., 2020).


“The most expensive car in the world costs $5 million. How much does a new BMW 530i cost?”

According to anchoring theory, information about the most expensive car can lead to higher estimates for the cost of a BMW. Anchoring effects have been demonstrated in many credible studies since the 1970s (Kahneman & Tversky, 1973).

A more controversial claim is that anchoring effects even occur when the numbers are unrelated to the question and presented incidentally (Criticher & Gilovich, 2008). In one study, participants saw a picture of a football player and were asked to guess how likely it is that the player will sack the football player in the next game. The player’s number on jersey was manipulated to be 54 or 94. The study produced a statistically significant result suggesting that a higher number makes people give higher likelihood judgments. This study started a small literature on incidental anchoring effects. A variation on this them are studies that presented numbers so briefly on a computer screen that most participants did not actually see the numbers. This is called subliminal priming. Allegedly, subliminal priming also produced anchoring effects (Mussweiler & Englich (2005).

Since 2011, many psychologists are skeptical whether statistically significant results in published articles can be trusted. The reason is that researchers only published results that supported their theoretical claims even when the claims were outlandish. For example, significant results also suggested that extraverts can foresee where pornographic images are displayed on a computer screen even before the computer randomly selected the location (Bem, 2011). No psychologist, except Bem, believes these findings. More problematic is that many other findings are equally incredible. A replication project found that only 25% of results in social psychology could be replicated (Open Science Collaboration, 2005). So, the question is whether incidental and subliminal anchoring are more like classic anchoring or more like extrasensory perception.

There are two ways to assess the credibility of published results when publication bias is present. One approach is to conduct credible replication studies that are published independent of the outcome of a study. The other approach is to conduct a meta-analysis of the published literature that corrects for publication bias. A recent article used both methods to examine whether incidental anchoring is a credible effect (Kvarven et al., 2020). In this article, the two approaches produced inconsistent results. The replication study produced a non-significant result with a tiny effect size, d = .04 (Klein et al., 2014). However, even with bias-correction, the meta-analysis suggested a significant, small to moderate effect size, d = .40.


The data for the meta-analysis were obtained from an unpublished thesis (Henriksson, 2015). I suspected that the meta-analysis might have coded some studies incorrectly. Therefore, I conducted a new meta-analysis, using the same studies and one new study. The main difference between the two meta-analysis is that I coded studies based on the focal hypothesis test that was used to claim evidence for incidental anchoring. The p-values were then transformed into fisher-z transformed correlations and and sampling error, 1/sqrt(N – 3), based on the sample sizes of the studies.

Whereas the old meta-analysis suggested that there is no publication bias, the new meta-analysis showed a clear relationship between sampling error and effect sizes, b = 1.68, se = .56, z = 2.99, p = .003. Correcting for publication bias produced a non-significant intercept, b = .039, se = .058, z = 0.672, p = .502, suggesting that the real effect size is close to zero.

Figure 1 shows the regression line for this model in blue and the results from the replication study in green. We see that the blue and green lines intersect when sampling error is close to zero. As sampling error increases because sample sizes are smaller, the blue and green line diverge more and more. This shows that effect sizes in small samples are inflated by selection for significance.

However, there is some statistically significant variability in the effect sizes, I2 = 36.60%, p = .035. To further examine this heterogeneity, I conducted a z-curve analysis (Bartos & Schimmack, 2021; Brunner & Schimmack, 2020). A z-curve analysis converts p-values into z-statistics. The histogram of these z-statistics shows publication bias, when z-statistics cluster just above the significance criterion, z = 1.96.

Figure 2 shows a big pile of just significant results. As a result, the z-curve model predicts a large number of non-significant results that are absent. While the published articles have a 73% success rate, the observed discovery rate, the model estimates that the expected discovery rate is only 6%. That is, for every 100 tests of incidental anchoring, only 6 studies are expected to produce a significant result. To put this estimate in context, with alpha = .05, 5 studies are expected to be significant based on chance alone. The 95% confidence interval around this estimate includes 5% and is limited at 26% at the upper end. Thus, researchers who reported significant results did so based on studies with very low power and they needed luck or questionable research practices to get significant results.

A low discovery rate implies a high false positive risk. With an expected discovery rate of 6%, the false discovery risk is 76%. This is unacceptable. To reduce the false discovery risk, it is possible to lower the alpha criterion for significance. In this case, lowering alpha to .005 produces a false discovery risk of 5%. This leaves 5 studies that are significant.

One notable study with strong evidence, z = 3.70, examined anchoring effects for actual car sales. The data came from an actual auction of classic cars. The incidental anchors were the prices of the previous bid for a different vintage car. Based on sales data of 1,477 cars, the authors found a significant effect, b = .15, se = .04 that translates into a standardized effect size of d = .2 (fz = .087). Thus, while this study provides some evidence for incidental anchoring effects in one context, the effect size estimate is also consistent with the broader meta-analysis that effect sizes of incidental anchors are fairly small. Moreover, the incidental anchor in this study is still in the focus of attention and in some way related to the actual bid. Thus, weaker effects can be expected for anchors that are not related to the question at all (a player’s number) or anchors presented outside of awareness.


There is clear evidence that evidence for incidental anchoring cannot be trusted at face value. Consistent with research practices in general, studies on incidental and subliminal anchoring suffer from publication bias that undermines the credibility of the published results. Unbiased replication studies and meta-analysis suggest that incidental anchoring effects are either very small or zero. Thus, there exists currently no empirical support for the notion that irrelevant numeric information can bias numeric judgments. More research on anchoring effects that corrects for publication bias is needed.

Thinking Too Fast About Life-Satisfaction Judgments

In 2002, Daniel Kahneman was awarded the Nobel Prize for Economics.   He received the award for his groundbreaking work on human irrationality in collaboration with Amos Tversky in the 1970s. 

In 1999, Daniel Kahneman was the lead editor of the book “Well-Being: The foundations of Hedonic Psychology.”   Subsequently, Daniel Kahneman conducted several influential studies on well-being. 

The aim of the book was to draw attention to hedonic or affective experiences as an important, if not the sole, contributor to human happiness.  He called for a return to Bentham’s definition of a good life as a life filled with pleasure and devoid of pain a.k.a displeasure. 

The book was co-edited by Norbert Schwarz and Ed Diener, who both contributed chapters to the book.  These chapters make contradictory claims about the usefulness of life-satisfaction judgments as an alternative measure of a good life. 

Ed Diener is famous for his conception of wellbeing in terms of a positive hedonic balance (lot’s of pleasure, little pain) and high life-satisfaction.   In contrast, Schwarz is known as a critic of life-satisfaction judgments.  In fact, Schwarz and Strack’s contribution to the book ended with the claim that “most readers have probably concluded that there is little to be learned from self-reports of global well-being” (p. 80).   

To a large part, Schwarz and Strack’s pessimistic view is based on their own studies that seemed to show that life-satisfaction judgments are influenced by transient factors such as current mood or priming effects.

the obtained reports of SWB are subject to pronounced question-order- effects because the content of preceding questions influences the temporary accessibility of relevant information” (Schwarz & Strack, p. 79). 

There is only one problem with this claim; it is only true for a few studies conducted by Schwarz and Strack.  Studies by other researchers have produced much weaker and often not statistically reliable context effects (see Schimmack & Oishi, 2005, for a meta-analysis). 
In fact, a recent attempt to replicate Schwarz and Strack’s results in a large sample of over 7,000 participants failed to show the effect and even found a small, but statistically significant effect in the opposite direction (ManyLabs2).   

Figure 1 summarizes the results of the meta-analysis from Schimmack and Oishi 2005), but it is enhanced by new developments in meta-analysis. The blue line in the graph regresses effect sizes (converted into Fisher-z scores) onto sampling error (1/sqrt(N -3). Publication bias and other statistical tricks produce a correlation between effect size and sampling error. The slope of the blue line shows clear evidence of publication bias, z = 3.85, p = .0001. The intercept (where the line meets zero on the x-axis) can be interpreted as a bias-corrected estimate of the real effect size. The value is close to zero and not statistically significant, z = 1.70, p = .088. The green line shows the effect size in the replication study, which was also close to zero, but statistically significant in the opposite direction. The orange vertical red line shows the average effect size without controlling for publication bias. We see that this naive meta-analysis overestimates the effect size and falsely suggests that item-order effects are a robust phenomenon. Finally, the graph highlights the three results from studies by Strack and Schwarz. These results are clear outliers and even above the biased blue regression line. The biggest outlier was obtained by Strack et al. (1991) and this is the finding that is featured in Kahneman’s book, even though it is not reproducible and clearly inflated by sampling error. Interestingly, sampling error is also called noise and Kahneman wrote a whole new book about the problems of noise in human judgments.

While the figure is new, the findings were published in 2005, several years before Kahneman wrote his book “Thinking Fast and Slow). He was simply to lazy to use the slow process of a thorough literature research to write about life-satisfaction judgments. Instead, he relied on a fast memory search that retrieved a study by his buddy. Thus, while the chapter is a good example of biases that result from fast information processing, it is not a good chapter to tell readers about life-satisfaction judgments.

To be fair, Kahneman did inform his readers that he is biased against life-satisfaction judgments.  Having come to the topic of well-being from the study of the mistaken memories of colonoscopies and painfully cold hands, I was naturally suspicious of global satisfaction with life as a valid measure of well-being (Kindle Locations 6796-6798). Later on, he even admits to his mistake.  Life satisfaction is not a flawed measure of their experienced well-being, as I thought some years ago. It is something else entirely (Kindle Location 6911-6912)

However, insight into his bias was not enough to motivate him to search for evidence that may contradict his bias. This is known as confirmation bias. Even ideal-prototypes of scientists like Nobel Laureates are not immune to this fallacy. Thus, this example shows that we cannot rely on simple cues like “professor at Ivy League,” “respected scientists,” or “published in prestigious journals.” to trust scientific claims. Scientific claims need to be backed up by credible evidence. Unfortunately, social psychology has produced a literature that is not trustworthy because studies were only published if they confirmed theories. It will take time to correct these mistakes of the past by carefully controlling for publication bias in meta-analyses and by conducting pre-registered studies that are published even if they falsify theoretical predictions. Until then, readers should be skeptical about claims based on psychological ‘science,’ even if they are made by a Nobel Laureate.