The Dunning Kruger Effect and "Better Than Average" Effect

Laura

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I noticed that we didn't have a thread devoted to this topic though there are several threads that mention it and a few that are very close to the topic such as:

https://cassiopaea.org/forum/index.php/topic,19024.0.html

https://cassiopaea.org/forum/index.php/topic,33028.0.html

https://cassiopaea.org/forum/index.php/topic,32026.0.html

Anyway, I came across this today:

[ur=http://www.ncbi.nlm.nih.gov/pubmed/24359153l]Behind bars but above the bar: Prisoners consider themselves more prosocial than non-prisoners.[/url]

Sedikides C1, Meek R, Alicke MD, Taylor S.

Abstract

That people evaluate themselves more favourably than their average peer on desirable characteristics - the better-than-average effect (BTAE) - is one of the most frequently cited instances of motivated self-enhancement. It has been argued, however, that the BTAE can be rational when the distribution of characteristics is skewed such that most people lie above the mean. We addressed whether the BTAE is present even among people liable to be objectively below average on such characteristics. Prisoners compared their standing on pro-social characteristics - such as kindness, morality, law abidingness - with non-prisoners. Prisoners exhibited the BTAE on every characteristic except law abidingness, for which they viewed themselves as average. Given that prisoners are unlikely to be objectively above average on pro-social characteristics, the findings push for a motivational interpretation of the BTAE.

© 2013 The British Psychological Society.

So, I poked around a bit and found this:

Prisoners believe they are just as law abiding as non-prisoners

Date:
January 9, 2014
Source:
University of Southampton

The belief that we consider ourselves better than our peers holds true to convicted criminals as well.

Research from the University of Southampton has shown that prisoners believe themselves to have more pro-social characteristics -- such as kindness, morality, self-control, and generosity -- than non-prisoners.

The research also showed that prisoners did not rate themselves as more law abiding than non-prisoners, but they did rate themselves as equal.

The study, published in the British Journal of Social Psychology, specifically looked at the 'better than average effect' (BTAE), according to which people consistently evaluate themselves more favourably than the average peer on most trait characteristics.

Constantine Sedikides, Professor of Social and Personality Psychology and Director of the Centre for Research on Self and Identity at the University of Southampton, comments: "These findings are some of the most compelling demonstrations of self-enhancement. If the prisoners self-enhanced by considering themselves superior to fellow inmates or community members on "macho" traits, such as toughness, I would not be surprised. However, they self-enhanced on pro-social traits, on which they could demonstrably be inferior to others; that is, they were inferior on those traits to community members and were not necessarily superior to other prisoners. They ignored, to a large degree, reality.

"Virtually by definition, people who are incarcerated have shown a lack of respect for their peers and have violated a legal pact: to adhere to the laws of the community. Although non-incarcerated people do this also, it is highly likely that incarcerated people "cheat" their fellow community members more than the non-incarcerated do. To evaluate themselves more favourably than the non-incarcerated on virtually every social characteristic stretches reality to the breaking point."

During the study, 79 prisoners from a prison in south England filled out a questionnaire, which asked them to rate themselves in comparison to the average prisoner and the average member of the community on nine traits. These were: moral, kind to others, trustworthy, honesty, dependable, compassionate, generous, self-controlled, and law abiding.

Participants rated themselves as superior to the average prisoner on all traits. Surprisingly, they rated themselves superior to the average community member on all traits as well, with one exception. Prisoners considered themselves as law-abiding as the average community member.

Professor Sedikides adds: "Prisoners are strongly influenced by the self-enhancement motive (i.e., the desire to see themselves in positive light). It is because of this motive that they believe they are more law-abiding than other prisoners, and they are equally abiding as community members. Both -- especially the latter -- are unlikely.

"The results showcase how potent the self-enhancement motive is. It is very important for people to consider themselves good, valued, and esteemed no matter what objective circumstances might be. For anyone who doubts this, ask them if they think that their children are perfectly average."

Professor Sedikides added that the BTAE could have an impact on a prisoner's common prediction that they are less likely to commit future crimes, when official data indicate that approximately half of them re-offend within a year of release from prison.

"Perhaps a reason for their inaccurate predictions is their overconfidence. Feeling good about themselves relative to others (prisoners or community members) may bias their judgments toward believing that they could stay out of trouble when released from prison," Professor Sedikides adds.

"Prison-based interventions, which rely on efforts to enhance thinking skills, already aim to challenge misconceptions that offenders may have about their offence and the impact their behaviour has had on society. However, prisoners also need to be encouraged to explore the reality of life after release from prison while also being offered support to overcome the individual and societal barriers that can prevent a successful reintegration into the community and the ability to desist from future crime," he adds.

Which led me to look at this:

Understanding the Better Than Average Effect
Motives (Still) Matter

Jonathon D. Brown, Department of Psychology, University of Washington

Abstract

People evaluate themselves more positively than they evaluate most other people. Although this better than average (BTA) effect was originally thought to represent a motivated bias, several cognitively oriented theorists have questioned whether this is the case. In support of a motivational model, the author reports five studies showing that the BTA effect is stronger for important attributes than unimportant ones (all five studies) and that once attribute importance is taken into account, the effect occurs when self-evaluations are compared with a single peer (Study 2) and when self is specified as the referent rather than the target (Study 4). Finally, Study 5 shows that the BTA effect increases in magnitude after participants experience a threat to their feelings of self-worth. Collectively, these findings establish that motivational processes underlie the BTA effect.


And this: http://en.wikipedia.org/wiki/Illusory_superiority

Illusory superiority is a cognitive bias that causes people to overestimate their positive qualities and abilities and to underestimate their negative qualities, relative to others. This is evident in a variety of areas including intelligence, performance on tasks or tests, and the possession of desirable characteristics or personality traits. It is one of many positive illusions relating to the self, and is a phenomenon studied in social psychology.

Illusory superiority is often referred to as the above average effect. Other terms include superiority bias, leniency error, sense of relative superiority, the primus inter pares effect,[1] and the Lake Wobegon effect (named after Garrison Keillor's fictional town where "all the children are above average"). ...

One of the main effects of illusory superiority in IQ is the Downing effect. This describes the tendency of people with a below average IQ to overestimate their IQ, and of people with an above average IQ to underestimate their IQ. ...

The disparity between actual IQ and perceived IQ has also been noted between genders by British psychologist Adrian Furnham, in whose work there was a suggestion that, on average, men are more likely to overestimate their intelligence by 5 points, while women are more likely to underestimate their IQ by a similar margin....

In Kruger and Dunning's experiments participants were given specific tasks...

Results were divided into four groups depending on actual performance and it was found that all four groups evaluated their performance as above average, meaning that the lowest-scoring group (the bottom 25%) showed a very large illusory superiority bias. The researchers attributed this to the fact that the individuals who were worst at performing the tasks were also worst at recognizing skill in those tasks. ...

Subjects describe themselves in positive terms compared to other people, and this includes describing themselves as less susceptible to bias than other people. This effect is called the bias blind spot and has been demonstrated independently. ...

Which leads to: http://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect

The Dunning–Kruger effect is a cognitive bias which can manifest in one of two ways:

Unskilled individuals suffer from illusory superiority, mistakenly rating their ability much higher than is accurate. This bias is attributed to a metacognitive inability of the unskilled to recognize their ineptitude.[1]
Those persons to whom a skill or set of skills come easily may find themselves with weak self-confidence, as they may falsely assume that others have an equivalent understanding. See Impostor syndrome.

David Dunning and Justin Kruger of Cornell University conclude, "the miscalibration of the incompetent stems from an error about the self, whereas the miscalibration of the highly competent stems from an error about others"....

If you’re incompetent, you can’t know you’re incompetent. […] the skills you need to produce a right answer are exactly the skills you need to recognize what a right answer is.
—David Dunning ...

Although the Dunning–Kruger effect was put forward in 1999, Dunning and Kruger have noted similar historical observations from philosophers and scientists, including Confucius ("Real knowledge is to know the extent of one's ignorance."),[3] Bertrand Russell ("One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision", see Wikiquote),[13] and Charles Darwin, whom they quoted in their original paper ("ignorance more frequently begets confidence than does knowledge").
 

SMM

The Living Force
Results were divided into four groups depending on actual performance and it was found that all four groups evaluated their performance as above average, meaning that the lowest-scoring group (the bottom 25%) showed a very large illusory superiority bias. The researchers attributed this to the fact that the individuals who were worst at performing the tasks were also worst at recognizing skill in those tasks. ...

Subjects describe themselves in positive terms compared to other people, and this includes describing themselves as less susceptible to bias than other people. This effect is called the bias blind spot and has been demonstrated independently. ...

Oddly enough, this BTAE, or pseudo-confidence, made me think of Anna Salter's Predators Among Us book, with regards to spotting predators and feeling safe.

There's this article from Pacific Standard magazine on the subject:

_http://www.psmag.com/navigation/health-and-behavior/people-much-trouble-recognizing-incompetence-72523/

Why People Have So Much Trouble Recognizing Their Own Incompetence said:
“When people are incompetent,” wrote the Cornell University psychologists David Dunning and Justin Kruger in a seminal 1999 paper, “not only do they reach erroneous conclusions and make unfortunate choices, but their incompetence robs them of the ability to realize it.” We are often most confident, in other words, when we are most ignorant.

Here’s what Dunning and Kruger found out in a series of lab tests: If you’re a bad judge of what other people will find funny, you’re more likely to think of yourself as a great comedian; if you perform poorly on tests of basic grammar, you’re more likely to overrate your facility with language. Why? “The skills that engender competence in a particular domain are often the very same skills necessary to evaluate competence in that domain,” the psychologists surmised. And there’s a flip side to Dunning-Kruger as well: People who are genuinely competent tend to sell themselves short, underrating their abilities.

“The best lack all conviction,” wrote the poet W. B. Yeats, “while the worst are full of passionate intensity.” Turns out he wasn’t just describing Europe after World War I. He was describing any given Wednesday. But take heart: With a little negative feedback, people do learn to calibrate their self-assessments. And for most of us—bumbling burglars excepted—that feedback won’t come in the form of several days in the slammer.

Feedback as a yardstick provides a dose of a much needed reality check and reassessment if heeded, yep. Networking works.
 

Seamus

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Ran across this video today and I think its a good introduction to the Dunning Kruger effect:


Its one of those "white board" type videos which illustrates what the speaker is saying and is quite accessible IMO.
 

MikaelYosef

Jedi Master
Feedback as a yardstick provides a dose of a much needed reality check and reassessment if heeded, yep. Networking works.

I think there might be a caveat to networking which is probably obvious to folks in the forum but for the people who would genuinely benefit from networking and feedback - that the people in that network at least collectively have as much or more experience, knowledge, wisdom and goodwill than the self. Surely there's an amplification of the Dunning-Kruger effect when stupid people network with equals, or even worse - yes people.
 

Laura

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I think there might be a caveat to networking which is probably obvious to folks in the forum but for the people who would genuinely benefit from networking and feedback - that the people in that network at least collectively have as much or more experience, knowledge, wisdom and goodwill than the self. Surely there's an amplification of the Dunning-Kruger effect when stupid people network with equals, or even worse - yes people.

You can sure say that again! There is such a thing as "a confederacy of dunces."
 
R

Resistense

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*Starts scrambling around the pig-sty looking for the tablet of Big Chief with his notes*

I haven't watched the videos yet, or really vetted the material, but would like to make input:
Laura:
We addressed whether the BTAE is present even among people liable to be objectively below average on such characteristics. Prisoners compared their standing on pro-social characteristics - such as kindness, morality, law abidingness - with non-prisoners. Prisoners exhibited the BTAE on every characteristic except law abidingness, for which they viewed themselves as average. Given that prisoners are unlikely to be objectively above average on pro-social characteristics, the findings push for a motivational interpretation of the BTAE.
There is a heuristic being used: assume that prisoners, objectively, are below non-imprisoned peers in pro-social traits, because they are imprisoned. Given the unusual circumstances of being in prison (which I imagine requires a unique development of social skills alongside a baseline of overconfidence) makes it hard to control for environmental stressors influencing the self-reporting.
"Virtually by definition, people who are incarcerated have shown a lack of respect for their peers and have violated a legal pact: to adhere to the laws of the community. Although non-incarcerated people do this also, it is highly likely that incarcerated people "cheat" their fellow community members more than the non-incarcerated do. To evaluate themselves more favourably than the non-incarcerated on virtually every social characteristic stretches reality to the breaking point."
Again, it reads to me like there are short-cuts being taken.
Although the Dunning–Kruger effect was put forward in 1999, Dunning and Kruger have noted similar historical observations from philosophers and scientists, including Confucius ("Real knowledge is to know the extent of one's ignorance."),[...]
To paraphrase a loose-end I can't verify currently, summa sciencia nihil est, or the summit of all science is to know you know nothing, paraphrasing that Christian Rosenkruez fellow, iirc.

From a Work perspective, the return to remembering that one does not have properly developed consciousness can help to continue to spur good work. If you falsely believe you have got something, there will be no motivation to work for it; we overestimate ourselves, we lie to ourselves.


SMM:
Subjects describe themselves in positive terms compared to other people, and this includes describing themselves as less susceptible to bias than other people.
Quite a bind to be in! The Thinking Fast and Slow book comes to mind.
“The skills that engender competence in a particular domain are often the very same skills necessary to evaluate competence in that domain,” the psychologists surmised.
This speaks to the need for objectivity.


Mikael Yosef:
SMM said:
Feedback as a yardstick provides a dose of a much needed reality check and reassessment if heeded, yep. Networking works.
I think there might be a caveat to networking which is probably obvious to folks in the forum but for the people who would genuinely benefit from networking and feedback - that the people in that network at least collectively have as much or more experience, knowledge, wisdom and goodwill than the self. Surely there's an amplification of the Dunning-Kruger effect when stupid people network with equals, or even worse - yes people.
There are two ends to this Dunning-Kruger effect. People might tend to overestimate their abilities if imcompetent because it's hard to measure themselves accurately. If everyone in the network is imcompetent, too, then let's assume noone is measuring anything properly and no work is being done.

On the other side of it, what are the downsides to underestimating yourself? Of operating from under the "imposter syndrome" side of this? If you're aware that you're using this, perhaps you can avoid the "negative symptoms" that are ascribed to this "syndrome".


P.S. A Confederacy of Dunces might give a portrait of the BTAE taken to an extreme, in some respects. I second the mention of this book.
 

psychegram

The Living Force
So it turns out the Dunning-Kruger effect might not actually exist, but could be simply an artifact of noise in the data combined with the rather curious way in which the putative effect was originally measured.


Take-home message:
- The Dunning-Kruger effect was originally described in 1999 as the observation that people who are terrible at a particular task think they are much better than they are, while people who are very good at it tend to underestimate their competence
- The Dunning-Kruger effect was never about “dumb people not knowing they are dumb” or about “ignorant people being very arrogant and confident in their lack of knowledge.”
- Because the effect can be seen in random, computer-generated data, it may not be a real flaw in our thinking and thus may not really exist
 
R

Resistense

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So it turns out the Dunning-Kruger effect might not actually exist, but could be simply an artifact of noise in the data combined with the rather curious way in which the putative effect was originally measured.

Link to article (abstract only, http_s://psycnet.apa...) linked to within the McGill U. article, from 2002:

What we really know about our abilities and our knowledge. Personality and Individual Differences, 33(4), 587–605.
Ackerman, P. L., Beier, M. E., & Bowen, K. R. (2002). What we really know about our abilities and our knowledge. Personality and Individual Differences, 33(4), 587–605. https://doi.org/10.1016/S0191-8869(01)00174-X (<--- the actual link from McGill; Jarry, J., article)
Abstract

Recent research has only documented the experimental side of the scientific divide (which focuses on means and ignores individual differences) regarding what individuals know about their abilities and knowledge level. The current paper shows that research from the other side of the scientific divide, namely the correlational approach (which focuses on individual differences), provides a very different perspective for people's views of their own intellectual abilities and knowledge. Previous research is reviewed, and an empirical study of 228 adults (aged 21-62 yrs) is described where self-report assessments of abilities and knowledge are compared with objective [Ed.:no in-road to see how the M&M purportedly does this...] measures. Correlations of self-rating and objective-score pairings show both substantial convergent and discriminant validity, indicating that individuals have both generally accurate and differentiated views of their relative standing on abilities and knowledge. (PsycInfo Database Record (c) 2020 APA, all rights reserved)
On point, Psychegram, that article is worth the read. Apparently we needed to do a literature search, or search for data that speaks to alternate explanations.

From the Jarry, J. article, "The Dunning-Kruger Effect Is Probably [mathematicians' hedging?] Not Real":
This story is not over. There will undoubtedly be more ink spilled in academic journals over this issue, which is a healthy part of scientific research [for ink and solvent makers] after all. Studying protons and electrons is relatively easy as these particles don’t have a mind of their own; studying human psychology, by comparison, is much harder because the number of variables [define one?] being juggled [like, by a clown, on a penny-farthing,] is incredibly high. It is thus really easy for findings in psychology to appear real when they are not.
"Hard science is easy. Squishy science, building rat's nests; very difficult! Do not study yourself or others! We'll take care of that."
IMO it can be part of the design for the psychology/psychiatry/sociology sciences to yield results that can be fashioned into a cudgel.


Going off on a tangent, but if the intention and study design are otherwise directed (and please do suss that under your own auspices), maybe the results that appear will be sounder; but then, for that reason, they'd be likely to be obfuscated, covered, and/or go unfunded.
Does reading make you smarter? Literacy and the development of verbal intelligence
K E Stanovich 1
Affiliations
Affiliation
1Ontario Institute for Studies in Education, Toronto, Canada.
PMID: 8447247 DOI: 10.1016/s0065-2407(08)60302-x
[Again, only the abstract is readily available, from 1993]
Abstract

The studies reported here represent the first steps in the development of a new research paradigm for studying the unique cognitive correlates of literacy. Reading experience exhibits enough isolable [!] variance within a generally literate society to be reliably linked with cognitive differences. Research on such links is therefore facilitated because the consequences of engaging in literacy activities can be studied without necessarily obtaining totally illiterate samples or setting up cross-cultural comparisons [means vs. individual differences?]. Issues that are at least analogous issues to those raised in cross-cultural research can be studied within literate societies with a paradigm such as this, and therefore the speed with which we can answer questions about the cognitive consequences of literacy may be greatly increased because more studies can be carried out, larger samples can be studied, and the range of the cognitive domains tapped can be widened. Research in this area appears to have been stifled because of the widespread acceptance of the most extreme interpretations of the outcome of Scribner and Cole's (1981) investigation--interpretations that have slowly diffused throughout the literature without being accompanied by any new data. These conclusions are fueled by a powerful social critique that advances the argument that the positive cultural and economic effects of literacy have been overstated--indeed, that literacy is, if anything, a repressive force (Auerbach, 1992; Street, 1984, 1988; Stuckey, 1991). Educational theorists such as Frank Smith accused the educational establishment of "overselling" literacy and have argued that "Literacy doesn't generate finer feelings or higher values. It doesn't even make anyone smarter" (1989, p. 354). The data reported herein appear to indicate that these theorists could well be wrong in this conclusion. If "smarter" means having a larger vocabulary and more world knowledge in addition to the abstract reasoning skills encompassed within the concept of intelligence, as it does in most laymen's definitions of intelligence (Stanovich, 1989; Sternberg, 1990), then reading may well make people smarter. Certainly our data demonstrate time and again that print exposure is associated with vocabulary, general knowledge, and verbal skills even after controlling for abstract reasoning abilities (as measured by such indicators as the Raven).(ABSTRACT TRUNCATED AT 400 WORDS):referee:


It'd seem that the DK effect should have been squashed by the 2002 study, but that it itself was likely squashed, so DK could be bandied about for 20 years... to discourage education?
from The Dunning-Kruger Effect is Probably Not Real, by Johnathan Jarry, M.Sc.
[...]
The most important mistake people make about the Dunning-Kruger effect, according to Dr. Dunning, has to do with who falls victim to it. “The effect is about us [and our unbelievable design errors...], not them,” he wrote to me. “The lesson of the effect was always about how we should be humble and cautious about ourselves.” The Dunning-Kruger effect is not about dumb people. It’s mostly about all of us when it comes to things we are not very competent at. [Dr. D.'s image should be so easy to rehabilitate with such soft strokes. The dripping irony of finishing a sentence with a preposition(?) by a science writer, so touching...]
[...]
Since then, many studies have been done that have reported this effect in other domains of knowledge. Dr. Dunning tells me he believes the effect “has more to do with being misinformed [by study designs like mine, with which I've become eponymous] rather than uninformed."
[...]
”The effect as originally described in 1999 makes use of a very peculiar type of graph. “This graph, to my knowledge, is quite unusual for most areas of science,” Patrick McKnight told me. [...] ... each student had two data points: ... In order to visualize these results, Dunning and Kruger separated everybody into quartiles: those who performed in the bottom 25%, those who scored in the top 25%, and the two quartiles in the middle. For each quartile, the average performance score and the average self-assessed score was plotted. This resulted in the famous Dunning-Kruger graph.
[...]
“Scores of books, articles, and chapters highlight the problem with measurement error and attenuated effects,” Patrick McKnight wrote to me. In his simulation with random measurements, the so-called [trying to create distance?] Dunning-Kruger effect actually becomes more visible as the measurement error increases. “We have no instance in the history of scientific discovery,” he continued, “where a finding improves by increasing measurement error. None.”
Oh, I think the Dr's. McKnight could find plenty of similar malfeasance in psychology, psychiatrics, sociology, behavioral science.
The above Dunning-Kruger graph was created by Patrick McKnight using computer-generated results for both self-assessment and performance. The numbers were random. There was no bias in the coding that would lead these fictitious students to guess they had done really well when their actual score was very low. And yet we can see that the two lines look eerily similar to those of Dunning and Kruger’s seminal experiment. A similar simulation was done by Dr. Phillip Ackerman and colleagues three years after the original Dunning-Kruger paper, and the results were similar.
They got essentially random data as results, and then graphed it. And I'm sure Mr. Humble-Pie Dunning was unawares of these refutations or the way his work was being portrayed in popular science.

The two papers cited from Numeracy [which they bill as: "quantitative literacy"] are from 2017:
How Random Noise and a Graphical Convention Subverted Behavioral Scientists' Explanations of Self-Assessment Data: Numeracy Underlies Better Alternatives
...the Kruger-Dunning type graphical format or closely related (y - x) vs. (x) graphical conventions. Our data show that peoples' self-assessments of competence, in general, reflect a genuine competence that they can demonstrate. That finding contradicts the current consensus about the nature of self-assessment. Our results further confirm that experts are more proficient in self-assessing their abilities than novices and that women, in general, self-assess more accurately than men. The validity of interpretations of data depends strongly upon how carefully the researchers consider the numeracy that underlies graphical presentations and conclusions.
Nuhfer, Edward, Steven Fleisher, Christopher Cogan, Karl Wirth, and Eric Gaze. "How Random Noise and a
Graphical Convention Subverted Behavioral Scientists' Explanations of Self-Assessment Data: Numeracy
Underlies Better Alternatives." Numeracy 10, Iss. 1 (2017): Article 4. DOI: http://dx.doi.org/10.5038/
1936-4660.10.1.4
and 2016:
Random Number Simulations Reveal How Random Noise Affects the Measurements and Graphical Portrayals of Self-Assessed Competency
Abstract
Self-assessment measures of competency are blends of an authentic self-assessment signal that researchers seek to measure and random disorder or "noise" that accompanies that signal. In this study, we use random number simulations to explore how random noise affects critical aspects of self-assessment investigations: reliability, correlation, critical sample size, and the graphical representations of self-assessment data. We show that graphical conventions common in the self-assessment literature introduce artifacts that invite misinterpretation. Troublesome conventions include: (y minus x) vs. (x) scatterplots; (y minus x) vs. (x) column graphs aggregated as quantiles; line charts that display data aggregated as quantiles; and some histograms. Graphical conventions that generate minimal artifacts include scatterplots with a best-fit line that depict (y) vs. (x) measures (self-assessed competence vs. measured competence) plotted by individual participant scores, and (y) vs. (x) scatterplots of collective average measures of all participants plotted item-by-item. This last graphic convention attenuates noise and improves the definition of the signal. To provide relevant comparisons across varied graphical conventions, we use a single dataset derived from paired measures of 1154 participants' self-assessed competence and demonstrated competence in science literacy. Our results show that different numerical approaches employed in investigating and describing self-assessment accuracy are not equally valid. By modeling this dataset with random numbers, we show how recognizing the varied expressions of randomness in self-assessment data can improve the validity of numeracy-based descriptions of self-assessment.

Nuhfer, Edward, Christopher Cogan, Steven Fleisher, Eric Gaze, and Karl Wirth. "Random Number Simulations Reveal How Random Noise Affects the Measurements and Graphical Portrayals of SelfAssessed Competency." Numeracy 9, Iss. 1 (2016): Article 4. DOI: http://dx.doi.org/10.5038/ 1936-4660.9.1.4
I should try to read through these since they're available, and struggle with my tendency for cursorily reading abstracts, then : "Oh-Oh, I make copy-pasta!".
I have never formally studied statistics, but Leonard Mlodinow's The Drunkard's Walk had me struggling to get to the end, wondering what they were modeling with randomness, and inferring the implications to be. I would recommend that book to any other set of eyes as we should probably be wary of such math modelers, whose intent got across as "it's all random (and meaningless)... now, let's model game theory for applications."
A MUCH STRONGER RECOMMENDATION FOR NUMERACY [or being able to use numbers and do math operations] IS: THE GRAPES OF MATH: How Life Reflects Numbers and Numbers Reflect Life, by Alex Bellos,
...
"…Bellos introduces fascinating characters, from the retired cab driver in Tucson whose hobby is factoring prime numbers, to swashbuckling astronomer Tycho Brahe, who lost his nose in a duel over a math formula. Through intriguing characters, lively prose, and thoroughly accessible mathematics, Bellos deftly shows readers why math is so important, and why it can be so much fun” (Publishers Weekly, starred review). Get hooked on math as Bellos delves deep into humankind’s turbulent relationship with numbers, revealing how they have shaped the world we live in."
Simon & Schuster's blurb from link
a well done survey of math up to calculus which is comprehensible, and entertaining(!), as it builds up concepts through narrative and anecdote, with some equations, some difficulty, but no problem-set slogging, unless you put that on yourself. 350pgs.



The Jarry-Dunning effect: designing a study with rigged up maths/methods which perpetuates social control maneuvers, then washing it as being a misunderstanding. Although, to try and be fair, maybe it's being moth-balled with still incomplete understanding, to try to introduce the numeracy supremacy of randomness-modelers who presume a closed system; trying to be fair but cynicism is tough to shake.
Remember the so-called Dunning-Kruger Kruger-Dunning graph.
 
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