# Monthly Archives: June 2017

## Simpson’s Paradox And The Positive/Negative Effect of Religious Belief

While not necessarily related to Bayes Theorem, something like this has been popping up in my mind whenever I read news stories dealing with statistics so I thought I would make a post about it.

In simplest terms, aggregate data might have different statistical properties than subsets of the aggregate data. As a matter of fact, the aggregate data might show the completely opposite effect when looked at in subsets.

An intuitive example of this is weather. You can average the temperature over the course of the year, or you could find the average of temperature over the course of six months. It might be that temperature over the course of the year has a slightly positive upward slope, yet temperature from June to December has a negative slope.

This seems obvious. But what if you’re dealing with something that’s not so obvious?

The example Wikipedia gives that I think is a non-controversial example is kidney stone treatment. Say you have Treatment A for either large or small kidney stones and Treatment B for large or small kidney stones.

Treatment A is effective on 81 out of 87 (93%) small kidney stones while Treatment B is effective on 87% (234/270) small kidney stones. For large kidney stones, Treatment A is effective 73% (192/263) of the time and Treatment B is effective 69% (55/80) of the time.

Clearly, Treatment A is what you should use for both small and large kidney stones. But what happens when we aggregate over both small and large kidney stones? Treatment A is 81/87 + 192/263 = 273/350 (78%) while Treatment B is 234/270 + 55/80 = 289/350 (83%). Now it turns out that Treatment B is better than Treatment A!

Therein lies Simpson’s Paradox. What happens when we have something controversial? Wikipedia also has the example of apparent sexism in graduate school admissions (which it still seems like no one has tried to account for this paradox when talking about modern controversies like the gender wage gap). But this is mainly a religion blog: So what about whether religion is good or bad for people or society?

Very religious Americans […] have high overall wellbeing, leading healthier lives, and are less likely to have ever been diagnosed with depression… These positive associations between religious engagement and the good life are reverse when comparing more versus less religious places rather than individuals…

Gallup World Poll data from 152 countries [show] a striking negative correlation between these countries’ population percentages declaring that religion is “important in your daily life” and their average life satisfaction score…

Across US states, religious attendance rates predict modestly lower emotional well-being…

Epidemiological studies reveal that religious engagement predicted longer life expectancy…

Across states, religious engagement predicts shorter life expectancy…

Across states religious engagement predicts higher crime rates. But across individuals, it predicts lower crime rates…

If you want to make religion look good, cite individual data. If you want to make it look bad, cite aggregate data…

Stunning individual versus aggregate paradoxes appear in other realms as well. Low-income states and high-income individuals have [recently] voted Republican…

Liberal countries and conservative individuals express greater well-being…

Highly religious states, and less religious individuals, do more Google “sex” searching…

One might wonder if the religiosity-happiness association is mediated by income — which has some association with happiness. But though richer people are happier than poor people, religiously engaged individuals tend to have lower incomes — despite which, they express greater happiness.

This is from a conference paper. I’m not actually sure if this is an example of Simpson’s Paradox, but the larger point remains. Breaking up data along different axes might yield paradoxical results. As the author says, if you want to make religion look bad, cite aggregate data. If you want to make religion look good, cite individual data.

But which statistic should one use? The aggregate data or the individual data? They’re both true, for lack of a better word, so it’s not like one is “lying”. I would tend to lean towards using the aggregate data if forced to choose. But there’s no harm in looking at both. And if both paint the same picture that just means that you have a more complete view of the phenomenon at hand.

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Posted by on June 26, 2017 in Bayes, economics/sociology, religion

## People on the left and right use different cognitive systems to make moral judgments

“When it comes to emotionally charged, morally contentious decisions, people who self-identify as conservatives tend to make these decisions based on their emotive, intuitive responses to the scenario in question (their gut feelings), whereas those who identify as liberal tend to put gut-feelings aside and make decisions based on an attempt to reason logically and consciously about the scenario,”

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Posted by on June 26, 2017 in cognitive science

## Partisan Bias in Factual Beliefs About Politics

"It is difficult to get a man to understand something, when his salary depends upon his not understanding it!"

Bullock, et al., 2013:

In both experiments, all subjects were asked factual questions, but some were given financial incentives to answer correctly. In both experiments, we find that the incentives reduce partisan divergence substantially–on average, by about 55% and 60% across all of the questions for which partisan gaps appear when subjects are not incentivized. But offering an incentive for accurate responses will not deter cheerleading among those who are unsure of the correct factual response, because such people stand to gain little by forgoing it. In our second experiment, we therefore implement a treatment in which subjects were offered incentives both for correct responses and for admitting that they did not know the correct response. We find that partisan gaps are even smaller in this condition–about 80% smaller than for unincentivized responses. This finding suggests that partisan divergence is driven by both expressive behavior and by respondents’ knowledge that they do not actually know the correct answers.

(h/t Bryan Caplan http://econlog.econlib.org/archives/2013/06/the_myth_of_the_8.html)

Posted by on June 9, 2017 in religion

## Study uncovers how brain damage increases religious fundamentalism

Research has found religious belief is associated with certain regions of the human brain, but there is still much to learn about how these areas influence religious belief. A new study in the journal Neuropsychologia found that lesions in a particular brain region tend to increase religious fundamentalism.

“Human beliefs, and in this case religious beliefs, are one of the cognitive and social knowledge stores that distinguish us from other species and are an indication of how evolution and cognitive/social processes influenced the development of the human brain,” Jordan Grafman of Northwestern University, the study’s corresponding author, told PsyPost.

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Posted by on June 8, 2017 in cognitive science, religion

## Online purchase patterns show left-wingers and right-wingers read very different science books

Liberals were far more drawn to engineering, anthropology, and purer sciences like biology, astronomy or to a lesser extent physics. Conservatives were drawn more to applied disciplines such as medicine and law, and – in the highest association for the red tribe – climate science

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Posted by on June 6, 2017 in economics/sociology

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