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Personal top 10 fallacies and paradoxes in statistics
1. Absence of evidence fallacy
2. Ecological fallacy
3. Stein’s paradox
4. Lord’s paradox
5. Simpson’s paradox
6. Berkson’s paradox
7. Prosecutors fallacy
8. Gambler’s fallacy
9. Lindsey’s paradox
10. Low birthweight paradox
1. Absence of evidence fallacy
2. Ecological fallacy
3. Stein’s paradox
4. Lord’s paradox
5. Simpson’s paradox
6. Berkson’s paradox
7. Prosecutors fallacy
8. Gambler’s fallacy
9. Lindsey’s paradox
10. Low birthweight paradox
1. Absence of evidence fallacy
Absence of evidence is not the same as evidence of absence. Wouldn't it be great if not statistically significant would just mean "no effect"? https://www.bmj.com/content/311/7003/485.long
Absence of evidence is not the same as evidence of absence. Wouldn't it be great if not statistically significant would just mean "no effect"? https://www.bmj.com/content/311/7003/485.long
2. Ecological fallacy
Hard to resist those sweet population level data to make inferences about health effects on the individual level https://web.stanford.edu/class/ed260/freedman549.pdf
Hard to resist those sweet population level data to make inferences about health effects on the individual level https://web.stanford.edu/class/ed260/freedman549.pdf
3. Stein's paradox
If your goal is prediction, you may *not* be after unbiased predictor effects in your prediction model
http://scholar.google.nl/scholar_url?url=https://www.researchgate.net/profile/Carl_Morris/publication/247647698_Stein%27s_Paradox_in_Statistics/links/53da1fe60cf2631430c7f8ed.pdf&hl=nl&sa=X&ei=m7YXYK3sPOPKsQLKtYWYBw&scisig=AAGBfm299RJEZV-VWCdNETwpmsjPalO4xg&nossl=1&oi=scholarr
If your goal is prediction, you may *not* be after unbiased predictor effects in your prediction model
http://scholar.google.nl/scholar_url?url=https://www.researchgate.net/profile/Carl_Morris/publication/247647698_Stein%27s_Paradox_in_Statistics/links/53da1fe60cf2631430c7f8ed.pdf&hl=nl&sa=X&ei=m7YXYK3sPOPKsQLKtYWYBw&scisig=AAGBfm299RJEZV-VWCdNETwpmsjPalO4xg&nossl=1&oi=scholarr
4. Lord’s paradox
Between group comparisons with baseline and follow-up: analysis of change scores or ANCOVA? Doesn't matter? Well it does... https://errorstatistics.com/2019/08/02/s-senn-red-herrings-and-the-art-of-cause-fishing-lords-paradox-revisited-guest-post/
Between group comparisons with baseline and follow-up: analysis of change scores or ANCOVA? Doesn't matter? Well it does... https://errorstatistics.com/2019/08/02/s-senn-red-herrings-and-the-art-of-cause-fishing-lords-paradox-revisited-guest-post/
5. Simpson’s paradox
Perhaps one of the most famous paradoxes in statistics. Reversal of the direction of effect by simply combining two groups is something that may keep awake at night https://academic.oup.com/ije/article/40/3/780/746837
Perhaps one of the most famous paradoxes in statistics. Reversal of the direction of effect by simply combining two groups is something that may keep awake at night https://academic.oup.com/ije/article/40/3/780/746837
6. Berkson’s paradox
Also known as collider bias, something we have seen plenty in the COVID-19 literature https://www.nature.com/articles/s41467-020-19478-2
Also known as collider bias, something we have seen plenty in the COVID-19 literature https://www.nature.com/articles/s41467-020-19478-2
7. Prosecutor's fallacy
Pr(B|A) is not Pr(A|B). Confusing sensitivity/specificity for predictive values, p-values for probabilities about the hypothesis,.... the prosecutor's fallacy list is long https://academic.oup.com/aje/article/179/9/1125/103523
Pr(B|A) is not Pr(A|B). Confusing sensitivity/specificity for predictive values, p-values for probabilities about the hypothesis,.... the prosecutor's fallacy list is long https://academic.oup.com/aje/article/179/9/1125/103523
8. Gambler’s fallacy
Arguably the odd one in the list, but cognitive biases about probabilities of recurrent events are very real and relevant https://en.wikipedia.org/wiki/Gambler%27s_fallacy
Arguably the odd one in the list, but cognitive biases about probabilities of recurrent events are very real and relevant https://en.wikipedia.org/wiki/Gambler%27s_fallacy
9. Lindley’s paradox (not Lindsey's...)
If you are interested in the Bayesian vs frequentist statistics wars, make sure you study the paradox https://link.springer.com/article/10.1007/s11229-014-0525-z
If you are interested in the Bayesian vs frequentist statistics wars, make sure you study the paradox https://link.springer.com/article/10.1007/s11229-014-0525-z
10. The low birth weight paradox
To adjust or not to adjust for birth weight in the analysis of infant mortality? https://academic.oup.com/aje/article/164/11/1115/61454?login=true
To adjust or not to adjust for birth weight in the analysis of infant mortality? https://academic.oup.com/aje/article/164/11/1115/61454?login=true
