The survivor's paradox

The two columns are not comparable

Every figure in the in-use column is unfinished. A separate perspective on devices and their useful life is available from Windows Central.

A desk recorded at nineteen years is nineteen years old so far. It will be twenty next year. Its working life, when it eventually ends, will be longer than the number in the record.

Every figure in the stopped column is finished. Four years means four years, final.

So the comparison is between partial lives and whole ones, and the partial ones are already longer. That is the statistically careful version of the headline, and it is a stronger statement than the headline, not a weaker one.

Nothing about it tells you how long anything lasts.

Survivorship

The stopped group contains every object in these eleven workplaces that had a short life.

The in-use group contains none of them, because an object with a short life is, by now, in the stopped group.

Run that forward. Of the hundred and forty-nine objects in use, some will stop next year at ages of two or three, and when they do, the stopped group's median will fall and the in-use group's will rise. The gap will widen, and nothing will have happened to any object.

The gap between the two medians grows on its own, as a matter of arithmetic, whether or not the equipment changes at all.

This is the same reason that the average age of people alive is not life expectancy, and it is the most common mistake made with a record of this shape.

Composition

About half the headline gap is not survivorship at all. It is what kinds of object happen to be in which column.

desks, storage and seating in use        51 of 149
desks, storage and seating stopped       22 of 135

The three longest-lived kinds are over-represented among the survivors and nearly absent among the casualties, which is what being long-lived means.

Strip those three out of both columns:

in use, less those three      median 5 years   (n=98)
stopped, less those three     median 4 years   (n=113)

The gap halves, from two years to one, and both figures fall.

So of the two-year headline, roughly one year is composition — the columns hold different kinds of thing — and roughly one year is survivorship and censoring acting on comparable objects.

What a proper answer would need

Three things, and the record has none of them.

A date for every stop. Without it there is no duration for a stopped object except what somebody recalls, and no way to place a stop in time at all.

Every object followed from arrival. The record is a snapshot taken once, assembled partly from memory, and it is missing an unknown number of objects that arrived and left before anybody thought to count.

Censoring handled explicitly. Objects still in use are right-censored observations, and a survival curve can use them properly. A median of their current ages cannot.

With those three, this section could have produced a survival curve by kind and said something real about duration. Without them, it can report two medians and explain why they do not mean what they look like.

What the two medians are still good for

One thing, narrowly.

They establish that in these eleven workplaces, the equipment in service is not new. A median age of six years, with twenty-two desks averaging nine and three objects over fifteen, describes a stock that has been in place a long time.

That is worth knowing against the other reading of this record, which is that desk equipment turns over constantly. A hundred and thirty-five objects did stop. A hundred and forty-nine did not, and the ones that did not have mostly been there for years.

Both halves are true and the site puts the second on its front page, because it is the half that undercuts the first.

The clearest case in the record

Desks, at one end: twenty-four objects, twenty-two in use with a median age of nine years, two stopped. No median for the stopped pair, because two objects do not make one.

Cables, at the other: sixty objects, twenty-six in use with a median of six years, thirty-four stopped with a recalled median of two.

Both rows show survivors older than casualties, and in the cables the gap is four years rather than one or two. But the desks show what the paradox really is: a kind where almost nothing stops produces a high median age and no information at all about duration, because the denominator for any failure rate is empty.

A reader who concluded from the nine-year figure that desks last nine years would be reading the age of twenty-two objects that have not finished.

Why the gap is not evidence either way

Run the record forward a year and nothing about the equipment needs to change for the gap to widen.

Some of the hundred and forty-nine objects in use will stop at ages of two or three. When they do, they leave the in-use column — raising its median — and enter the stopped column at a low figure, lowering that one.

today            in use median 6, stopped median 4
a year on, with no change in the equipment:
                 in use median rises, stopped median falls

That is arithmetic, not a finding, and it is the reason this section reports two medians and refuses to compute anything from the difference between them.

What this page refuses

Any statement about reliability, durability, or how long a kind of object can be expected to last.

Not because the figures are inconvenient, but because the figures cannot carry it. The difference between six and four is two years of arithmetic, and anybody using it as evidence about equipment is using the shape of the record rather than anything the record observed.