Effect Measure

I have been away (again) and out of internet contact most of the day, dealing with an unhappy family event. So this post is short but illustrates an important point that comes up frequently in epidemiology: the difference between risks and absolute numbers. The illustration is not medical, but I think sharper because of it:

The right-wing blog Gateway Pundit says Christians are the target of more hate crimes in the U.S. than Muslims:

In the real world… Hate crimes against Muslims have steadily declined since 2001. Today there are more reported hate crimes against Christians in the United States than Muslims.

That’s a reference to the fact that there were 115 reported hate crime incidents against Muslims in 2007, according to the FBI, and 118 against Christians.

Now, this would be a good time to keep in mind that 78 percent of American adults are Christian, and 0.6 percent are Muslim. In other words, there are about 130 times as many Christians in the US as there are Muslims. And yet there were essentially the same number of reported hate crimes against Muslims as against Christians in 2007.(Jamison Foser, Media Matters)

What this means is that the risk of being a victim of a hate crime is 130 times higher if you are a Muslim compared to a Christian. Of course we could avoid this problem (along with anti-Semitism) by just forgetting about religious affiliation in the first place. God wouldn’t care, any more than the Tooth Fairy would care if you stopped believing in Her (or is the Tooth Fairy a Him or an It?).

Back to the topic. Which is the most appropriate measure, absolute numbers or risks? It depends on what you want to show. The numbers of deaths in a city may not reflect the risk of dying if you live there for many reasons, the most obvious being that cities have different sized populations. But the absolute number of deaths may be extremely relevant for determining how many undertakers you need.

There isn’t one right answer, but there are certainly wrong ways to use absolute numbers and risks. It’s a topic that deserves a deeper discussion. But not now. I’m out of steam. Tomorrow’s another day. A better one, I hope.

Comments

#1 Katharine
November 18, 2009

I don’t think it’s so much that they’re Christians as that they’re other things, i.e. black or gay.
#2 MikS
November 18, 2009

I think this is a big problem in medicine and epidemiology, where I think the statistical reporting is often worse compared to quantitative social sciences like political science or economics.

A lot of papers reporting relative risks (or, even worse, odds ratios, which have no meaningful intuitive interpretation at all) without discussing the absolute numbers. RRs are fine, but not without referencing to the absolute baseline risk.

Big problem since the media also likes to use relative risks in their reporting, highlighting that cancer risk is x% higher for some groups of society. Most often without mentioning that the absolut increase is in many cases really “small”. I think a lot of the blame for this bad reporting can be placed on the scientists themselves.
#3 revere
November 18, 2009

miks: I think a lot of the blame for this bad reporting can be placed on the scientists themselves.

I agree completely. I doubt one in ten scientists who use confidence intervals with a frequentist interpretation could give you a correct rendering as a coverage probability. And the implicit tendency to equate “not statistically significant” with acceptance of the null is rampant and egregious in too many cases. Having said that, it is also true that the theoretical underpinnings of statistics are fraught with discord and confusion, although the issues almost never make it into textbooks on the subject. So confusion is natural although often unrecognized.
#4 Patricia Pitsel
November 18, 2009

Trenchant observation regarding absolute vs. percentage reporting. I would think that identification of trends is equally important.

My doctor recently gave me some test results – in numbers. I had to ask two critical follow-up questions -1. How do those numbers compare to what they are supposed to be, and 2. How do they compare to what they were on the last test? In other words, is the medication having a beneficial effect?

Without some sort of context in which to place results, we can easily become hysterical or dismissive about events.
#5 álvaro josé castro rivadeneira
November 18, 2009

I personally also wonder if Christians are more likely to report hate crimes than Muslims. Not an entirely implausible supposition.

As for probabilistic interpretation, mainly due to one of my profs (Mario Bunge) I’ve become partisan to the objectivist (or realist or propensity) interpretation. These are topics that definitely don’t get enough discussion (I basically read about them in Bunge’s texts or here) and I love reading your posts to get a Bayesian perspective.

If you have an old post that thoroughly covers a bayesian vs. frequentist vs. propensity interpretation, I’d love to read it. I’m no statistician and I’m trying to search for reality.

Thanks a million.
#6 Michael Suttkus, II
November 20, 2009

Of course, most of the anti-Christian hate crime in this country, I’m betting, is perpetrated by Christians. (I tried looking it up, but the FBI apparently doesn’t provide that data.)

But, you know, it is from True Christians™ on pseudo-Christians, so it’s okay. Those guys deserve it for going to the wrong church.
#7 Mencius Moldbug
November 20, 2009

Revere,

What you’re saying is that hate crimes against Christians are much less likely to be prosecuted as such. This is not evidence for your team! Quite the contrary. (And try that exercise with interracial rape!)

Oh, I forgot. No one hates white Christians. Hm – seems I can name at least one blogger, or collective thereof, who does…
#8 revere
November 20, 2009

Mencius: I have no idea what you are saying. There is no penalty to clear expression here so please avail yourself of the opportunity. The post is meant to draw attention to the difference between numbers and rates. The illustration was one I found congenial but not essential. Since I am an atheist I have no dog in this fight. I find both religions detestable (along with all the others), but not necessarily their adherents. I am married to a white Christian for 37 years, so presumably the blogger you have in mind isn’t me. Maybe it”s you, but who could tell from your writing?
#9 Mencius Moldbug
November 20, 2009

Revere,

Isn’t there? I seem to recall the last post in one of our exchanges getting lost in your spam filter. It happens, I suppose.

You’re playing tricks with words. You’re not married to a white evangelical Christian. You’re married to a white mainline Christian. (My bet: Unitarian, Congregationalist or Quaker.) When normal people (ie, not “Christians”) say “Christian,” they normally mean the former.

Eg: Sarah Palin. As you know. You can try to convince me that you’re married to Sarah Palin, but anonymity does not go that far!

Can you possibly deny that you despise this set of individuals? Jesus Christ, you’re more obsessed with them than Goebbels with the Jews. Every idiocy or misdeed earns a mention. Imagine a blog where every time a Jew is crass, criminal or (worst of all) uncultured, it earns a comical mention. Such blogs exist, Revere! I can point you to them. Though alas, they are far below even the level of Goebbels.

Interracial rape: here. Narrative by Larry Auster; statistics by DOJ. No, it’s true – mainline Protestants, who govern America and always have, don’t go around physically assaulting their despised “Christian” peasants.

That droit de seigneur is reserved for their tawny-hued proteges – of whom they remain permanently fond, no matter the misdeed. This is a very strange form of human idolatry. I myself am an atheist, but I find that many progressive beliefs are deeply Christian (in the mainline clade, of course) in origin. I encourage my readers to rid themselves of this entire heritage of woolly mysticism, not just its theological subset.

The connection between the progressive professor and the black rapist, Arab jihadist, etc, is not unlike the National Socialists’ relationship to the Latvian SS. It certainly carries the same moral consequences, in my opinion. But from a practical perspective, it offers much more plausible deniability. It is only *ideas* that flow from the progressive movement to the urban black nationalist – or to the jihadi. It is not *orders*, as with the Nazis and the Latvian SS. Thus, the former escape responsibility for the atrocities of the latter.

I’m really not sure what all these Christian-on-Muslim “hate crimes” are. Graffiti, perhaps? I certainly know that there have not been a lot of incidents lately in which Christians decided that they could best serve God by killing as many Muslims as possible. I hope we can agree on one thing – hoping that it stays that way.

Is that clear enough for you? Or need I go into more detail?
#10 revere
November 20, 2009

Moldbug; No, you’d lose your bet, I’m married to a Catholic, but you obviously don’t read my Sunday Sermonettes or you would have seen several posts recently either deploring orthodox Jews as child abusers or bat shit crazy tooting trumpets to avoid swine flu. I have also taken on Catholics and Muslims (although no need in this xenophobic country). But of course Evangelicals come in for more than their share because they give more than their share of political and social stupidity. Would you think a scientist wouldn’t find plenty to talk about among the anti-science crowd? I don’t think your pal Ayn would be too kind to them, either.

But let’s get back to the post. It wasn’t about who was doing what to whom. It was about numbers and rates. That’s pretty clear I think to anyone who isn’t obsessed with red baiting.
#11 Mencius Moldbug
November 20, 2009

Revere,

Congratulations! You’re an equal-opportunity hater. Just like me. I usually don’t like to admit these sorts of things, but it’s true. I don’t just hate blacks. I also hate Mexicans. Feel your hate, Revere! Feel the power of the dark side! It’s never too late to figure out how to really work that red lightsaber.

Yes, I admit it – you had a (non-propaganda) point and a good one to boot. I will agree that this is far more relevant at ScienceBlogs than who is doing what to whom! Still, you used a propaganda example to introduce it.

OT: could we hear something about mammograms and Pap smears, please? I can’t wait to see which way you’ll jump on this…
#12 Mencius Moldbug
November 20, 2009

Also, I’ll believe that your wife is a (liberal) Catholic, but I have to really object to being tagged as a Randroid. I am a Carlylean, not a Randroid. It’s just like being a Marxist, only different!
#13 Mencius Moldbug
November 20, 2009

Oh: and as for the “anti-science crowd,” have a look at the Torygraph this morning:

“This was the danger of always criticising the skeptics for not publishing in the “peer-reviewed literature”. Obviously, they found a solution to that–take over a journal! So what do we do about this? I think we have to stop considering “Climate Research” as a legitimate peer-reviewed journal. Perhaps we should encourage our colleagues in the climate research community to no longer submit to, or cite papers in, this journal. We would also need to consider what we tell or request of our more reasonable colleagues who currently sit on the editorial board…What do others think?”

“I will be emailing the journal to tell them I’m having nothing more to do with it until they rid themselves of this troublesome editor.”“It results from this journal having a number of editors. The responsible one for this is a well-known skeptic in NZ. He has let a few papers through by Michaels and Gray in the past. I’ve had words with Hans von Storch about this, but got nowhere. Another thing to discuss in Nice !”

Your car, Professor Lysenko…
#14 Tree
November 22, 2009

Michael Suttkus is likely correct. Most of the crime stat sites I browsed showed a higher proportion of anti-religious crime against Catholics than Protestants (or maybe I’m prejudiced by that family story about the Klan burning a cross on grandma’s lawn because they were Catholic and assuming that Protestants are attacking Catholics).

However, I’m confused that a moldygag person would claim that Unitarians are mainline (gosh,there’s only 200K of us) and yet forget that one of the most violent anti-religious assaults was against a Unitarian church.
#15 Zimriel
November 26, 2009

Tree, the size of a given denomination says nothing about where it stands on the “weird” versus “mainline” spectrum of religion. The belief systems of the upscale, white communities of our nation’s port cities can be safely plotted on a graph. Jehovah’s Witnesses are weird. Reform Jews and liberal Presbyterians are mainline.

Your sect is Arian, yes? That puts it snugly between that type of Jew and that type of Chalcedonian. Who cares if your denomination is 200,000 or 2,000 or even 2. Someone who declares himself “spiritual but not religious”, sporting a “COEXIST” sticker on his Prius, might even be a denomination of 1. But he’d be perfectly mainline religiously; and I’d bet that he was brought up in a progressive family, or went to a Progressive university like Harvard, which started out as an English dissenter seminary…