Can a Statistician Say that Age Is Just a Number?

Minitab Blog Editor 08 January, 2015

Last fall I had a birthday. It wasn’t one of those tougher birthdays where the number ends in a zero. Still, the birthday got me thinking. In response, I told myself, age is just a number. Then I did a mental double-take. Can a statistician say that? After all, numbers are how I understand the world and the way it works.

birthday cake

Can age just be a number? After some musing, I concluded that age is just a number!

How did I reach my conclusion? I’m pretty sure that I’m not just deluding myself to feel better. In statistics, you need to be able to trust your data. Whether you’re performing an ANOVA, regression analysis, or a designed experiment, if you can’t trust your data, you can’t trust the results of your analysis.

I can hear some of you protesting, "But certainly your age is accurate!" Yes, it’s a straightforward matter to count the number of revolutions the Earth has made around the Sun since the day I was born. There is absolutely no doubt that number is correct. Trust me, I've tried counting it different ways.

However, there are other ways that numbers can deceive you. In statistics and experimental design, we are concerned with both reliability and validity. These issues require us to question whether the measurements we use are consistent and whether we are really studying what we think we are studying.

Reliability relates to the repeatability of the measurements and the experiment as a whole. If you measure the same thing multiple times, do you get the same measurements? Do similar studies produce the same results? We’re good here. Or, rather, I should say that it’s at least consistent if not “good”. Every time I check the calendar, I’m undoubtedly no younger!

Validity relates to how well a conclusion reflects the requirements of the scientific method. There are various types of validity such as internal, external, and construct. Here we’ll focus mainly on internal validity, which deals with how confident we can be in the cause-and-effect relationships in a study.

A Hypothetical Study: Does Age Cause Bad Things?

Which study, you ask? That’s where we’ll have to get a bit hypothetical. Presumably, we have some basis behind our dislike of higher ages. Perhaps we’re imagining a study that relates older ages to negative outcomes. But, which outcomes? That’s a bit foggy. We also need to be sure that age causes these undefined outcomes rather than just being correlated with them.

These issues are good indications that our hypothetical study doesn’t have good internal validity. We can’t be sure of the cause and effect. In fact, we’re not even sure which effects we’re talking about! At this point, we can’t trust the conclusion that higher ages cause negative outcomes.

In a quick, preliminary assessment, it seems to me that there are two general categories of life outcomes for this study area.

Biological changes: It’s a fact that over time biological processes occur and that we change. We develop and go through puberty. As we get older, mental and physical abilities decline, etc. While these changes are unavoidable, they occur at different rates for different people. We can influence some of the underlying factors for these changes. For example, we can make decisions about eating a healthy diet, exercising, and reducing UV exposure. Unfortunately, some of the underlying factors are out of our control and depend on luck.

However, an important question is, which way does the causal arrow point? Do the annual changes in our calendar age cause these biological changes? Or, do these biological changes define our concept of age? I’d argue that the causal arrows are thus: Underlying factors -> Biological changes -> Concept of age.

Important life matters: These are not so biology- or time-dependent, and are more under our control. This category includes things such as happiness, having strong relationships, maximizing your potential, performing rewarding activities, making a positive contribution to your community, etc.

So, we have one category where the casual connection is unclear and perhaps in the opposite direction of what our study is designed to show. The other category doesn’t seem age-dependent at all. None of this supports what our thought experiment is attempting to show, that age causes bad things. This study is already questionable...and I haven't even mentioned the fact that it’s impossible to randomly assign people to different age groups.

Based on all of these issues, my professional opinion is that age is just a number!

This conclusion should free you from worrying about that constant increase in age every year. Don't sweat that number. However, it places responsibility on you to make smart choices in your life. After all, your choices have more impact on your life than some meaningless number. And, the rest you can't control.