It's a Math, Math World

Here is a blog that I found. It belongs to Michael O'Brien. I have not had a chance to really read through any of his posts, but it is on my to-do list as soon as I have a little tiny bit of time. Based on my quick cursory view of it, he seems to be writing quite a bit about statistics. And not the crazy insane look how whippety smart I am statistics writing that makes my eyes hurt and my brain feel small. I'm not a stat wizard! I'm just a programmer!

I just glanced through some of his posts, and while there was math, it didn't seem impenetrable. In fact, a quick scan of this post actually made my brain feel a little bigger.

Kudos to Michael of It's a Math, Math World

A Great Blog From A SAS User

I just checked out Ann Maria's Blog from the Julia Group and was so impressed with her writing that I had to share it.

I particulary liked The Dangers and Wonders of Statistics Using SAS post.

Go check it out.

Now.

Bootstrap Resampling

First of all, I should mention here and now at the beginning of this post that I am not a statistician. But I am married to one (Happy Bithday Orla!), and I dounderstand normal distributions and confidence intervals and standard deviations and such. Suffice it to say, I generally get the concepts but my eyes invariably glaze over once the equations are presented.

Now that I've gotten that out of the way, I will attempt to make this post about... statistics! Hopefully everything I write will make sense, but if anything is outrageously stupid, feel free to forgive me and correct me in the comments.

On one of my travels through the internet I came across something I had never heard of before: bootstrap resampling. I will attempt to describe my understandingof it, but please do check out the links at the bottom because I am sure to over-simplify or exaggerate some parts.

In traditional parametric statistics the data is generally assumed to follow a particular pattern or distribution with the "normal" bell curve distribution being the ideal. Statisticians use various tests to determine if the sample data is normally distributed (a very surprising amount of data is) and then proceed to make statistically sound inferences about the population the data was drawn from (confidence intervals, standard deviation, etc). If it is true for the randomly drawn sample then it is true for any randomly drawn sample from the population. Assuming the sample fits the normal distribution.

Now If I understand bootstrap resampling correctly there is no need to assume the data follows a normal distribution; or any particular statistical distribution. You take a sample from your data and record the mean, then you put your sample back and get another sample of data and record the mean. You repeat that many, many, many times and then use the resulting means to pick your intervals. Here is the original description I read from a wonderful site called the World Question Center. It is an excerpt from the response of Bart Kosko. If you scroll about halfway down the page you will find it. He is way smarter than I am so his explaination will surely make more sense than mine:

"The hero of data-based reasoning is the bootstrap resample. The bootstrap has produced a revolution of sorts in statistics since statistician Bradley Efron introduced it in 1979 when personal computers were becoming more available. The bootstrap in effect puts the data set in a bingo hopper and lets the user sample from the data set over and over again just so long as the user puts the data back in the hopper after drawing and recording it. Computers easily let one turn an initial set of 100 data points into tens of thousands of resampled sets of 100 points each. Efron and many others showed that these virtual samples contain further information about the original data set. This gives a statistical free lunch except for the extensive computation involved—but that grows a little less expensive each day. A glance at most multi-edition textbook on statistics will show the growing influence of the bootstrap and related resampling techniques in the later editions.
Consider the model-based baggage that goes into the standard 95% confidence interval for a population mean. Such confidence intervals appear expressly in most medical studies and reports and appear implicitly in media poll results as well as appearing throughout science and engineering. The big assumption is that the data come reasonably close to a bell curve even if it has thick tails. A similar assumption occurs when instructors grade on a "curve" even the student grades often deviate substantially from a bell curve (such as clusters of good and poor grades). Sometimes one or more statistical tests will justify the bell-curve assumption to varying degrees — and some of the tests themselves make assumptions about the data. The simplest bootstrap confidence interval makes no such assumption. The user computes a sample mean for each of the thousands of virtual data sets. Then the user rank-orders these thousands of computed sample means from smallest to largest and picks the appropriate percentile estimates. Suppose there were a 1000 virtual sample sets and thus 1000 computed sample means. The bootstrap interval picks the 25th — largest sample mean for the lower bound of the 95% confidence interval and picks the 975th — largest sample mean for the upper bound. Done.
Bootstrap intervals tend to give similar results as model-based intervals for test cases where the user generates the original data from a normal bell curve or the like. The same holds for bootstrap hypothesis tests. But in the real world we do not know the "true" distribution that generated the observed data. So why not avoid the clear potential for modeler bias and just use the bootstrap estimate in the first place?"

So my questions to the statisticians: do you use bootstrap resampling? Is this something you do in SAS? Do you feel it helps to simplify statistics and open it up to us non-statisticians?

Really good explaination of bootstrap resampling:
http://www.uvm.edu/~dhowell/StatPages/Resampling/Bootstrapping.html

Bootstraping in SAS:
http://support.sas.com/ctx/samples/index.jsp?sid=479

Summer Reading

Currently I am reading a book that is so good, I thought I would give it a quick recommendation. Against The Gods: The Remarkable Story of Risk is one of those books that I know-- before even finishing it, I will read again, and again. And I will gain deeper insights into history, humanity, stock markets, statistics and even the decisions that I make in my everyday life.

So if you get the chance, pick up a copy. And if you have any other good reads that you think I or others might be interested in, please share them here.