Salvation and Statistical Error

In the Church statistical error rates are a problem.  To understand what I mean, some introductory statistics are in order:

In probability theory and statistics, the binomial distribution is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p.  Say what?

Let's use a baseball analogy to illustrate:  a certain percentage of the fans who come to a Cardinals game have tickets and are admitted.  Those that don't have valid tickets don't get in. If 90 out of 100 fans have tickets then the probability of any one of them getting in (without knowing whether than person had a ticket in advance) is 90%. But what if the ballpark uses those newfangled bar code reader thingys to determine whether a ticket is good or not? Some times when the bar code is smudged a good ticket will be rejected - statisticians describe that as a 'false negative' or 'Type Two Error'. Likewise someone who mistakenly bought a fake ticket might be accepted - which is called a 'false positive' or "Type One Error". Knowing the likelihood of these errors helps us understand how effective our testing process is. If in our example of 100 ticket holders the probability of a false negative was 10% that means in all likelihood that 9 of the 90 legitimate ticket holders will be turned away. The same probability for a false positive would mean that one fake ticket holder would get in. Usually increasing the level of accuracy against one type of error means that the other type of error becomes more common. The phrase 'it is better that ten guilty men go free than one innocent man hang' neatly captures the trade off inherent in binomial statistical errors.

In certain respects God's act of salvation is a binomial equation: just like at the game there are only two  mutually exclusive outcomes for each soul: saved or not saved. Of course God does not make errors but we, the Church, do. A false positive in salvation terms is a soul that is not saved but believes that it is. Likewise a false negative is a soul that believes it is not saved but in fact is. Or rather both the Church and the soul come to imperfect conclusions about the spiritual state of themselves and the people around them.

This is an interesting question because the distribution of people in and outside the Church is not random. In particular, more women are members, attend services and participate in Church activities than do men. Indeed in terms of actual hours spent working on Church or spiritual activities a well run Church will have a significant disproportion of women's time represented. Likewise, men tend to be far more heavily represented in 'sinful' activities be they crime, prison, addictive behaviors or simply living isolated from Christian fellowship. Taken literally, this imbalanced distribution of women and men would imply that more women will be saved than men. After all, the best indicator of a saving faith must be active involvement in the life of the Church and on this measure women win hands down.

Yet I can conceive of no reason why God should a priori choose to save more women than men. Indeed reading the Bible one could conclude that the Faith is largely a male affair (which at one time was used to justify the argument that women had no souls (!)). So if (as I suspect with absolutely no evidence) that half of those saved will be men and the other half women then we have a 'statistically significant spiritual conundrum'. One that has three possible explanations:

1. Mostly False Negative (Type 2) Errors: There are large numbers of mostly men who do not participate in the life of the Church who nevertheless God will save.

2. Mostly False Positive (Type 1) Errors: There are large numbers of mostly women who actively participate in the life of the Church who are not saved.

3. Both False Positives and Negatives evenly balanced: There are many unchurched men and churched women whose spiritual status is inconsistent with their Church status.

I suppose there are two other alternative hypotheses:  One, that I call the "Jehovah's Witness" Hypothesis, is that God will save very few of us so therefore substantially everyone who will be saved is already in Church (or more accurately Kingdom Hall) but the proportion of people in Church who will be saved is very, very small.  The second, my "Mormon"  Hypothesis is that substantially everyone will be saved and that we just need to pull our sacred underwear (and socks) up and 'giterdone'.  Not being a Jehovite or Mormon I shall ignore these alternatives.

So what does this have to do with the price of dingos in Dallas?

If we believe that explanation 1 is the most true then the Church's goal should be to structure itself to attract more men who have or will come to Christ so that they can be integrated into the Body of Christ and be sanctified. If we believe 2 is the more likely explanation, then we need to undertake programs that help this surfeit of unsaved but active women recognize the truth of their condition. If we believe that three is true we need to do both.

And this is the rub: regardless of the 'dominant' hypothesis that you choose, the differential challenge of the Church must be to attract men and convict women. Of course there are many women who need attraction and many men who need conviction but statistically speaking (if you buy my a priori argument) men are more likely to be under-served by the Church relative to their salvation and women more likely to be over-served. Yet I would argue that the Church today (and I am generalizing wildly here) does precisely the opposite: it repels men and caters to women. I could spend a lot of time describing the details of this phenomenon but I don't think I would get much push back from most informed observers when I point out that the Church is a fairly feminized institution.

And my question is: is this OK? If so, why? And if not, what do we do about it?

Statistically speaking, I mean.