My current work assignment requires a lot of statistical reasoning. It is my job to establish quality goals for our organization and to measure and report on the attainment of those goals. When we miss a quality target, it is my responsibility to establish a process to address the short coming. We call those things “Action Plans.”
Now my greatest fear is that we will focus these extra efforts on the wrong thing. One fact a mathematician is very experienced with and a statistician must live and breathe is “variation.” It is easy for management to get worried when one month you are above or below an established target. My goal is to observe and define trends that go beyond simple random variation and not go off chasing wild ducks. So I use all my skill and training in setting reasonable and significant targets and in interpreting actual results against those targets and reporting to executives and the board of directors.
It was never my intent to become a statistician. Sounds as boring as being a bookkeeper to me, but sadly it is exactly what I’ve become. I originally studied math to go along with my other interests such as electronic engineering. However, after completing my BSEE and entering graduate school, I decided to branch out into broader topic areas and ended up getting a Master’s degree in Mathematics with a minor in Physics. (It could have easily gone the other way but for the happenstance of course schedule and class availability.) But my focus was not on statistics, but rather on analysis which is a fancy math word for “calculus.”
However, back at the workplace, we needed to determine the reliability of magnetic recording heads and diskette wear, and Mickey got the job of designing the experiment to measure reliability since his boss told everyone, “this guy just got a degree in math, and he must know how to calculate what we need.” So off I went, designing an experiment with 60 PCs running disk drives around the clock for two months to determine “mean time to failure.”
Along the way I employed tools such as Gaussian and Rayleigh modeling and Weibull analysis; plus I had to respond almost daily to a worried vice president who wanted me to affirm our products would meet specification before we released them. I kept telling him it would be 60 days before I had an answer because I had to wait until drives actually failed, and enough had to fail that I could test the distribution. He was sweating bullets as the G.A. date approached, but eventually I calculated that the head wear mean time was within stated specifications and we could proudly ship the drives without concern of warranty cost and upset customers. It turned out, as usual with IBM specs, we easily met all published values and customers never complained — at least about early life failures.
I guess I never lived that down, and IBM kept calling on me to act as a statistics expert, a role I never felt fully qualified in. Later, during my work in IBM Technical Education, I did statistical analysis as part of course validation. For one thing, statistics is hard, and it is quite counter intuitive to me. This week someone asked me what the odds of flipping a coin six times and getting heads every time. I told her what they were, 0.015625, or 1 in 64, or two to the sixth power. Then she said, “What are the odds that, on the seventh flip, you’ll get heads.” “Fifty percent, same as always,” I replied. It is hard to understand, but easy to calculate.
Now I’m a teacher and an educator by heart and experience, so I have always tried to explain to lay people how statistics really works. Everyone wants to know the “average,” or as it is precisely called, the “mean” (of which there are several). This measure of central tendency is key to most people’s use of stats. I have a saying that I use to try to explain how averages don’t contain all that much information as you might wish. I say, “Feet in the freezer and head in the oven. On average, you should be at a comfortable temperature.” When you use an average and try to apply it to an individual, watch out!
Someday I’ll write about Gaussian (or normal) distributions, six sigma, and black swans, but for now let’s keep it simple. A few weeks ago a relative in Alaska posted an article about Social Security — a topic that is of great interest to me since I will soon be receiving checks from that wonderful (and did I say “wonderful”) institution. Of course, I will have paid a lot more into SSN than I will likely ever get out, especially if I could have invested the money myself, but that doesn’t mean I don’t think it is a valuable social institution.
This article basically said that SSN is financially sound and said that growth of longevity would not “break the bank,” and was primarily due to better survival of small children rather than an increase in old age survival. Now that didn’t sound right to me knowing how the modern use of PSA often leads to a cure of the most common cancer in men — something that didn't happen a few years ago. (Plus my concern that the baby boomers, myself included, would “break the bank” just by our numbers, never mind how long we may live.)
Inquiring minds wanted to know, and who better to look at the stats than a trained statistician? And here is what I have discovered. Using the Department of Labor statistics, I found that the SSN article was wrong on the surface. There has been a significant increase in life expectancy for people who are currently 60 years of age. Look at the last three decades, the life expectancy of someone who is 60 today has increased by nearly ten years. That means people 60+ today, will live about 10 years (actually less than 10, but it is fun to round) longer than their fathers and grandfathers did.
But, again, that is one of those averages. Let’s look deeper. As we all know, there are three kinds of lies: “lies,” “damn lies,” and “statistics.” So here is what I found in that same Department of Labor data: If you take everyone alive today who is 60 years old, then their life expectancy is several years more than it would have been for someone 60 years old in 1980. But here is the interesting part. If you divide this group up by income, based on IRS data, you will find that the highest earning third will live 7 years longer, but the lowest earning third will only live a little over a year longer.
Hmmm. As one person put it, Lawyers will live longer to collect SSN, but Janitors won’t. So, in general, the article on SSN and retirement age is partially correct, especially if you realize SSN is very important for lower wage people. In other words, people that will likely have good personal or company provided retirement benefits are the ones who will statistically live longer, while those that most need SSN won’t.
Now that may not be important if the issue is funding of SSN, but it is quite important for the recipients. Whether SSN is financially stable for the next 20 or 30 years is still an open question, but the impact of increased longevity is better understood when you look into the details of the statistics rather than raw averages. That should be a learning experience for all. I was troubled by the article's conclusions, and my analysis showed they were a bit simplistic, but I found something important as I dug in deeper.
Now think about that at a time that the SSN full retirement age has increased from 65 to 66 for baby boomers, and will ultimately increase to 67 under current law. Many discussions of how to manage and reduce the deficit and debt use the statistic of longer life to justify further increase in retirement age, and to suggest raising the current retirement age to 69 or even 70. Think about that. In addition, there is talk of raising early retirement age from 62. After all, we all live longer, don’t we? Or do we? Again, think about that!
Now this is a complicated discussion and there are other ideas on the tables such as eliminating the cap on annual SSN contribution and privatization of the fund. The question is, do you understand statistics well enough to participate in that debate or and are you fooled by averages without digging deeper into the numbers for demographics and other details? Stats are the great simplifier of data, but as Albert Einstein wisely said (on the subject of physics theories, but what the heck), “Everything should be made as simple as possible, but not simpler."