Archive for the ‘Statistics’ category

Making Decisions

20 August, 2007 EUTC

The following is related to my dissertation, but should be easily understood without any statistical background. I wrote it for a job interview, no success yet…

Many decisions we make involve uncertainty, such as whether to buy flood insurance, whether to hold an event outside, or which candidate to offer the job to. A common way of modelling such decisions is utility theory. According to this theory, for any person facing a decision, each possible outcome has a number called its utility. Together with the probabilities involved in the decision, these utilities determine which choice they make.

So how do we determine these utilities? Well, suppose a person indicates that she is equally happy to receive 4,000 pounds for certain or to take a gamble where there is a 50 percent chance she receives 10,000 pounds and a 50 percent chance she receives nothing. Then utility theory gives us the equation that the utility of 4000 pounds is equal to half the utility of 10,000 pounds. With more information about her preferences, involving different sums of money and probabilities, we will get more equations which we should be able to solve to find her utilities.

Unfortunately there is a problem. Often we can’t solve the equations because the preferences are inconsistent. This is often dealt with by fiddling the figures to arrive at estimates for the utilities. This is a very unsatisfactory approach because there is no proper justification for the results.

However, I have developed a more justifiable method for dealing with this problem. It is based on a model of how a person’s preferences depend randomly on his/her utilities. This model depends on the unknown utilities and another number which represents how well the person discriminates between choices.

My approach involves 4 components:

  1. The person’s view of his/her utilities, i.e. how cautious he/she is.
  2. The person’s view of how well he/she discriminates, i.e. how strongly he/she responds to changes in the choices,
  3. The person’s specific preferences, i.e. the pairs of choices that he/she finds equally desirable and
  4. The model itself.

By combining these 4 components the estimates of the unknown utilities can be calculated. This can easily be done on a computer.

We don’t have to calculate estimates for every utility. In my report I have used these 4 components to find an equation for the utilities. I’ve used a mathematical computer program to calculate the exact form of my chosen utility function.

This method provides a simple, but justifiable way of calculating the utilities required for making decisions, based on utility theory, and which takes into account the inconsistent nature of preferences.

Modesty Survey Results

28 June, 2007 EUTC The Modesty Survey
Back on St Valentine’s day the folks at The Rebulution posted the results to their modesty survey, which they describe as ‘a resource to help Christian girls (and guys), not a list of legalistic rules… which encourage young women to focus on the heart, not the hemline, to honor their parents, etc.’. I didn’t find the presentation conducive to examining the results, so I have now made up a spreadsheet based on their data. Their website includes a lot of other resources on this topic.

I switched some of the questions around so that agreeing with the statements always represented a more conservative position (so in particular agreement with questions regarding clothing implies the clothing is immodest). If the reversed questions had been asked then the results would likely have been slightly different, but not by much. Then I ordered the percentage agreement (including agree and strongly agree) for each category of questions. The questions are not consistent in form, eg. they vary between asking whether something is a stumbling block, immodest etc., but hopefully this doesn’t make too much difference so that the percentages can still be seen as a consistent measure of the extent to which guys struggle with these various things. That said it clearly illustrates that guys vary in their attitudes/struggles with lust. So for example, 6.9% don’t agree that miniskirts as immodest while 9.1% find sparkly, shiny skirts a stumbling block, regardless of length.

Here are some more examples with the % who agree or agree strongly that these things are immodest/stumble-inducing etc. in parentheses: showing any cleavage (70.3), exposing the stomach when wearing a swimsuit (57.5), the lines of undergarments being visible under clothing (71.6), reaching into the shirt to adjust a bra strap (65.4), spaghetti-strap shirts and dresses (60.8), skirts that fall above the knee (58.4), the way a girl walks can be immodest (74.9).

Dawkins On The Improbability Of God

5 June, 2007 EUTC

In The God Delusion Dawkins responds to claims that certain entities are too complex to have formed by chance by arguing that since such a designer must be even more complex, he must also be less likely. He turns this into his argument for why there is almost certainly no God: since a creator God (particularly one like the Christian God) is extremely complex, He is also extremely improbable.

The problem with this argument is that Dawkins gives no reason why the probability of an uncreated spiritual entity is thus dependent on its complexity. It might make sense for biological entities where there is some mechanism for chance formation in mind, but why should the probability of God existing depend thus on His complexity? Dawkins’ main argument for atheism turns out to be fundamentally flawed.

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Quick Stat: Above Average

19 February, 2007 EUTC

According to a Washington Post poll cited here,

94 percent of Americans said they are “above average” in honesty,
89 percent “above average” in common sense, 86 percent “above
average” in intelligence, and 79 percent “above average” in looks.

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Statistical and Scientific Basics

22 January, 2007 EUTC

Over at Scienceblogs, a number of contributors have started producing posts that explain basic concepts within their fields.

Mark Chu-Carroll at Good Math, Bad Math has been producing posts on concepts within statistics. So far he has written on the topics: mean, median and mode; normal distributions; standard deviation; margin of error. Others are covering topics in Physics, Biology and Mathematics. An up-to-date list is being held here.

Trusting God More Than Statistics

17 August, 2006 EUTC

Candice Watters has written an article that looks at a Barna poll that shows that there are more unmarried men than unmarried women who are identified as born again Christians. She conlcudes from this that “Never-married Christian women don’t outnumber never-married Christian men.” However as I said in a previous post, those who identify as born again Christians are not the same as those who actually are Christians. There is a general impression that there are more single women than men in churches and I have much greater confidence in that than the Barna statistic.

Fortunately as Watters says in her post, it doesn’t matter anyway if her conclusion is false. The way I wish to put it is that God is not bound by probability and if he desires for somebody to be married, then they will be married (and he will continue to be faithful in the meantime). This is a good illustration of one danger regarding statistics, that we might believe them more than we believe God. The probability of Gideon’s small army being sucessful against the Midianites was small, but Gideon believed God and God clearly brought about their defeat through him.

As Prov 16:33 says, The lot is cast into the lap, but its every decision is from the LORD. If our odds look bad, whether those odds relate to our chances of marriage, or the probability of avoiding divorce, or the likelihood of illness or something else, remember that the outcome is from our good God and trust in Him.

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Doubting Christian Statistics

1 August, 2006 EUTC

You’ve probably heard various statistics about Christians, such as Christians having slightly higher divorce rates than non-Christians. Such statistics should be treated with a certain level of skepticism. If the data were based on a random sample of regenerate Christians and accurately reflected the reality of those polled, then it would be reasonable to accept the results (in accordance with the margin for error), but reality is not like that. There are at least 3 reasons why we should be careful about our conclusions based on such data:

1. Misidentification

First, in polls (as in real life) it is simply not possible to determine who is a regenerate Christian. (more…)