Statistics and prayer

TL;DR – Statistics can only study correlations between populations and are blind to the effect on individuals.

Since I moved to the United States of America, I have met people with very strong views about religion and science. One would say: “the bible says the world was created 10,000 years ago.” Another would say: “science says God does not exists because of evolution.” Both would say: “science and religion are in direct conflict.” I must have missed the memo.

This whole idea that science and religion are at war is perplexing to me. I mean, yes there have been incidents like when Galileo wrote a book and, inadvertently, made the then Pope look like a fool. Or when Mendel, an Augustine friar, inappropriately used church resources for scientific activities. But what troubles me is something else: how can science or religion point a weapon at each other? They don’t have opposable thumbs.

I have even found that in the USA there are people who have conducted “scientific” studies on the power of prayer. For example, they took two sets of patients. They instructed one set of relatives to pray for their loved ones and the other not to. And then tried to measure whether one set got healthier than the other. And if they found no correlation… then they would conclude prayer is ineffective? And these are published in journals… of science? While this sounds absurd to me, somehow there are some people who think this is a fruitful endeavor. Just like discussing politics on social media.

Now, I am not going to discuss the theological implications here, which are numerous. I am not even going to discuss whether this constitutes science or not. I’ll overlook the most glaring problems and concentrate on a small detail: can you even conclude anything? That is, if you find no correlation can you say that prayer didn’t do anything? Let’s find out in a seriously ridiculous thought experiment.

The power of prayer

You are God. This is indeed a step up if you read the other thought experiments, where you have been a scientist, a mad statistician or a mathropologist. If you haven’t read the other thought experiments, you should! They are great stuff! And I am not above shameless self-promotion.

Anyway, you have just learned that there are these “scientists” that want to test you. They have divided a set of patients into two groups, one group will be prayed for and the scientist will check whether it will survive longer. Now, you distinctly remember saying: (Deut 6:16) “You shall not put the Lord your God to the test.” So, this kind of bugs you. And therefore, in your infinite spite, decide to intervene and fudge the data.

Now, you care about preserving free will. You don’t want to influence the result of the experiment at all, or people would be forced to conclude that you are answering the prayers and then people would pray only for utilitarian reasons. But you still want to answer the prayers. Can you do that? Can you affect the lives of those who pray without affecting the result of the experiment? Of course, you are God!

The idea is this. You know what would happen if you took no action. For the control group, the one that does not pray, you simply make it happen. For the group that prays, instead, you keep the overall outcomes the same. So, for example, if 12% died after a month, then 12% will die after a month. But, here’s the key: you can switch the outcomes between two people.

For example, without your intervention, Bob would live only 1 week while Rob would live 6 more months. The problem is that Rob would pass those 6 months in agony, while Bob would be only in mild pain and would use that time to make peace with his loved ones. So you switch. One would survive the illness, though would die anyway in a car crash 4 days after. So you switch with another guy that would have survived only 4 days. And so on.

You see: because the study is checking only the survival rate distribution, it would see no difference whatsoever in the data. It’s the same data. Just reshuffled. And here is the kicker: the bigger the study, the more people are in the group that prays, the more chances you have to find a better match for the switch. So, if the scientist sees no correlation, he will be more sure that prayer has no effect, while really the effect gets better and better!

You see all that you have done and think that it is good.

Outcomes over individuals or populations

The issue here is that statistical distributions and statistical measurements can only tell us correlations between statistical properties, which are properties of the population as a whole. They cannot tell us anything about the individuals. Two populations may be statistically identical but may be physically different and a statistical measurement cannot tell them apart.

Suppose you have a fair coin, you position it on your hand tails up and you toss it a number of times. You will get 50% chance of getting either heads or tails. Now, suppose you position it on your hand heads up and you toss it a number of times. You will still get 50% chance of getting either heads or tails. We get the same statistical distribution. So it seems switching initial orientation of the coin had no effect. Yet, it may have had the effect that it changed all the tails to heads and all the heads to tails. But this experiment will never be able to tell us. Only one that is much more controlled, that studies the tossing mechanism in a non-statistical way could tell.

Statistics only keeps track of the frequency of some attribute within some population, and not which individual has what attribute. So we have to be careful when extrapolating results to individual experience, which is ultimately what religion cares more about. Ah, and about conflict: the memo I got is that conflict is always between people, typically over some kind of power. When the fool points at the enemy, the wise looks at the finger.