Statistics ... Disraeli was Correct

Many Americans attribute the quote to Mark Twain. Twain, on the other hand, attributed it to former British Prime Minister, Benjamin Disraeli. Disraeli was purported to have written (or spoken): "There are three kinds of lies: lies, damned lies, and statistics."

Let's not worry about who actually coined the phrase. Even so, what does it have to do with our usual subject matter here? In the benefits and compensation arena (and many others), people love statistical data. They seem to love to create it, to cite it, to reference it, and to make decisions from it.

I beg them not to. Consider such data, but consider it as a point of reference. Use it intelligently.

I saw a survey last week or the week before that asked three questions of its respondents. Roughly recalling the questions, respondents were asked whether they were going to have enough money in retirement to make it to ages 75, 85, and 95 respectively. Less than half said they would have enough to live happily until age 85. The article reporting on the survey then told its readers that most Americans won't have enough money for their life expectancies.

Excuse me! Where did that come from? What made age 85 the life expectancy of any, let alone all, of the survey respondents. Were the respondents all the same age? Were they all the same gender? How many of them even know how much money they will need?

Just this morning, this summary of an article appeared in my inbox:

Fidelity Investments reported the average 401(k) balance in 401(k) plans it administers rose to $74,600 at the end of the first quarter, an increase of 8% from the end of the fourth quarter 2011. The first quarter balance also represents a 62% increase since the end of the first quarter 2009, often considered the low of the 2008-2009 market downturn, when the average balance was $46,200.

This is not to be construed as a condemnation of Fidelity. In fact, I feel quite certain that what they have said is correct. What concerns me is how others will use the data. Who will cite this information and how will they use it?

Let's consider what has happened between the end of the first quarter of 2009 and the end of the first quarter in 2012. I'm not looking for just investment performance and deferral behaviors, but how about external factors.

• After the severe market losses from 4th quarter 2007 through 1st quarter 2009, many people who had been considering retirement were forced to defer it. These would be almost exclusively in the older group of workers. As a group, we would suspect that these would be people with higher account balances who were not withdrawing their 401(k) money from Fidelity. Does this not skew the data point upward?
• As more companies freeze defined benefit plans, many of them have increased their 401(k) match. The way I see it, this makes it more likely that participants will take full advantage of the match. So, their deferrals will increase and the matching money will increase. Does this not move the data point upward?
• Does Fidelity administer the same plans that it did three years ago? I'm sure that many are the same, but not all of them. Vendors gain new clients and lose existing ones. They don't all have the same participant profiles. I don't know which way this moved Fidelity's data, but it certainly moved it.

Let's go back to life expectancy. Let me ask you some questions. What is your life expectancy? Do you know? If you think you do, on what do you base it? Life expectancy from birth? From now? Is it based on IRS tables? Is it based on some other mortality tables? Newspaper articles? A guess? Does it consider your health? Does it consider the life spans of your ancestors? Does it consider your gender?

I am going to tell you something. Your life expectancy is a nice number, whatever it is. It may be the best estimate (at a point in time) of the age you will be when you die. That said, unless we are using a lot of rounding, you will not die at your life expectancy. That's right, if we are precise, you will not die at your life expectancy. 

If we were to choose a mortality table and calculate your life expectancy (or mine), it might tell you that your life expectancy is another 20 years (rounded). Or, if you are more precise, it might tell you that your life expectancy is another 20.3 years. Or 20.27 years. Or, 20.26637185943 years. 

Another table might generally increase those numbers by several months, or even years. Another one might shorten your life expectancy. In any event, given a table, your life expectancy would have your life ending on a particular day at a particular time. 

It's not going to happen.

But, people using statistical date cite life expectancy as if it were the most relevant point in time. 

Statistics are very useful. They are especially useful when they are not misused.