Answer me this: what happened to waiting times in A&Es in England last week? To help you answer, here are some tweets published by reputable news organisations today:

A&E waiting times in England improve to their best level since November, figures show http://t.co/N2ib5ttFyO pic.twitter.com/YVALTkJ9qW

— BBC News (UK) (@BBCNews) January 23, 2015

A&E waiting times in England improve http://t.co/mQtiuk12yc

— The Guardian (@guardian) January 23, 2015

NHS England pays tribute to staff after figures show slight reduction in A&E waiting times http://t.co/PNOq2Yyv9Y pic.twitter.com/mvQfNX3eHS

— ITV News (@itvnews) January 23, 2015

A&E waiting times improve but fail to hit target http://t.co/cC7NO055aB

— PoliticsHome (@politicshome) January 23, 2015

A&E crisis: Waiting times improve for second week running http://t.co/tNTEYstIx6 pic.twitter.com/jWk9FKELmH

— Telegraph News (@TelegraphNews) January 23, 2015

You would be forgiven for thinking that waiting times had reduced. You would be… possibly right, possibly wrong. The correct answer is that we don’t know. Performance against the weekly A&E waiting time targets—which is what all of the above are actually reporting—tells us nothing about the waiting time in A&E.

As an aside, before we get into this properly, I should clarify that “waiting time” doesn’t mean what most people think it means. The “waiting time” referred to in these statistics is the total time a patient spends in A&E, from the moment they walk in the door, to the moment they walk out again (whether that is to go home, to go to a ward, to go to the pub, or wherever). That’s not what we think of as “waiting” in common parlance: while you’re with the doctor, you are—in statistical terms—still “waiting”.

The NHS doesn’t report on waiting times, only on the proportion of patients seen in less than four hours. When the reporters wrongly say that A&E waiting times have improved, what they actually mean is that a greater proportion of people entering A&E are leaving again in less than four hours. This tells nothing about the amount of time people wait on average.

Imagine an A&E department that sees only five patients: A and B have minor injuries, and are seen and treated within 30 minutes. C and D need a more complex set of investigations, so end up being in the A&E department for 3 hours. E needs a very full assessment and ultimately admission; as a result, E ends up being in the department for a total of 5 hours before a bed can be found. The average time these patients spend in A&E is 2 hours and 24 minutes; 80% of them were discharged in 4 hours.

Now let’s say that someone puts a laser-focus on that 80% and says it’s unacceptable: whatever the cost, it must be brought down. So the department tells the nurse that used to do the “see and treat” job (which served patients A and B so well) that she must help with only the most complex patients, because they are breaching the target.

The same five people with the same five injuries now come into the revamped A&E. A and B have minor injuries, but now must wait alongside everyone else. They hang around for 3 hours. C and D need complex investigations, but these are slower to start because of people with minor injuries clogging up the queue. They are discharged after 4 hours. The new complex patient team deals with patient E slightly faster, getting her up to the ward with seconds to spare before the four-hour deadline.

100% of patients were seen within 4 hours. The hospital’s management is overjoyed! The BBC tweets that A&E waiting times have decreased: 100% of patients are seen within four hours instead of 80%. Politicians become a little self-congratulatory.

Yet… what has actually happened? The average waiting time has increased from 2 hours and 24 minutes to 3 hours and 36 minutes. 80% of patients are waiting longer than they did before.

And that is why—whatever the news tells you—we have no idea what happened to A&E waiting times last week. The average time could have doubled; it could have halved; it could have stayed precisely the same. We simply do not know.