I am not totally satisfied with Ludwik Kowalski's explanation of the
"paradox" concerning airlines.
I agree that the Seattle data somewhat dominate Airline-1's record and
the Phoenix data really dominate Airline-2's record. And I agree that
when analyzing data like these we can get different results by
averaging percentages as opposed to averaging data (then calculating a
new percentage).
My disagreement comes from the certainty with which Ludwik attributes
this to the weather. The weather explanation makes good sense, and it
could be the true explanation, but the data don't prove this. To get a
better idea of the cause we ought to truly examine what caused the
delays rather than making guesses as to what caused the delays.
Let's just compare Seattle and Phoenix because we get the same
"paradox" if we simplify the data by excluding the other cities.
Perhaps Seattle just has too much traffic for the size of airport.
That is, maybe it doesn't have enough runways with different
orientations; or maybe there aren't enough gates.
Maybe there are restricted areas of the city where planes cannot fly,
or where high altitudes must be obtained (noise abatement). For
example, I am aware of an airport where there are a whole host of
departures scheduled at 10:30 PM because the surrounding community does
not allow departures/arrivals between 11:00 PM and 7:00 AM. I suppose
they could schedule departures at 10:30, 10:35, 10:40, 10:45, etc., but
they just schedule them all at 10:30. (I think that allows them to cue
on the runway ramp according to what order they actually got away from
the gate.) But of course all planes can't truly depart at the same
time, so some of them are technically going to be "delayed." The point
here is that airport management and scheduling can make a difference in
the "on-time" record.
America West is a larger airline than Alaska Airline and Phoenix is a
hub for America West. At hub airports, the airline using that airport
as a hub often gets preferred departure times and gates. Although
Seattle is a hub for Alaska Air, the fact that Alaska is smaller might
mean that it has less advantage in its hub city than America West has
in its hub city.
Not convinced? Let's just compare the data for Phoenix and Los
Angeles. The "paradox" comes out the same (Alaska wins if we average
percentages, America West wins if we look at total flights). It might
be easy to assume that bad Seattle weather is the cause when Seattle
and Phoenix are compared. But is bad southern California weather the
problem when we compare Phoenix to LA? That's not as easy to swallow.
Let's just leave the solution to this "paradox" in its most simple
form. The number of data points (flight departures) for each entity
being compared (airlines) under different circumstances (cities) are
not the same. Whenever this type of situation occurs, the results
(expressed as fractions or percentages) come out differently if we c
alculate percentages first then average, as opposed to performing data
totals then finding the percentage. That much is clear. All the rest
(weather) is speculation.
Michael D. Edmiston, Ph.D. Phone/voice-mail:
419-358-3270
Professor of Chemistry & Physics FAX:
419-358-3323
Chairman, Science Department E-Mail
edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817