Comparing apples with oranges

Long ago, teaching a course on the statistics of surveys, I reminded my classes, repeatedly, that they should make sure that the comparisons that they made between results were rigorous.  If not, the saying goes, you are in danger of "comparing apples with oranges".  The point is that the underlying populations, and the measurements on them, should be comparable.  Apples and oranges are different fruits, grown in different countries, and their agriculture is different.  So, to be ridiculous, one could not measure the cost of producing one orange with the cost  of producing one apple, because one could not grow oranges in an apple orchard and vice versa.

So, today, an advert on a bus in Exeter caught my eye.  "More people see bus advertisements than use social media daily".  Apples=People see an advert on a bus in the course of ... how long?  The text suggests "in a day".  Oranges=People using social media daily.  Measurement in both cases=total number. 

My interest was aroused.  Not everyone who sees an advert on a bus will read it.  Very few will have gone out of their homes saying "I really must read a bus advertisement today".  But people are purposeful when they use social media.  Measurements on apples are not measurements on oranges.  I managed to find estimates of the number of daily users of social media in the UK.  It is roughly 20 million but may be as high as 25 million.  So how many people see a bus - let alone a bus advert - daily?  Guesstimating that number suggested that a figure between 15 and 25 million would be about right, knowing the population of the UK, and the working population who would be commuting and might see a bus.  So the two numbers are in the same ballpark - if the bus advert figure is for daily sightings. 

That was when my search found the website of the company making the claim.  There I found the claim:

30 million people have seen advertising on the outside of a Bus in the last week  - See more at: http://www.exterionmedia.com/uk/what-we-do/our-media/bus-advertising#sthash.jYIkaMpL.dpuf

30 million people have seen advertising on the outside of a Bus in the last week  - See more at: http://www.exterionmedia.com/uk/what-we-do/our-media/bus-advertising#sthash.jYIkaMpL.dpuf

 30 million people have seen advertising on the outside of a Bus in the last week

Aha!  the time scale for apples is now a week.  (And why write "Bus" with a capital "B"?)  My guesstimate is reasonable, since one can assume that in seven days, some people will see adverts on several days, while others will see them on one.

I hope the thousands or millions who see the advert that I saw this morning will recognise that you can't compare random exposure to an advert on a bus in one week with purposeful use of social media.  If they don't, then they shouldn't be entrusted with buying apples; they might buy oranges, or grapes, or tomatoes!

30 million people have seen advertising on the outside of a Bus in the last week  - See more at: http://www.exterionmedia.com/uk/what-we-do/our-media/bus-advertising#sthash.jYIkaMpL.dpuf

30 million people have seen advertising on the outside of a Bus in the last week  - See more at: http://www.exterionmedia.com/uk/what-we-do/our-media/bus-advertising#sthash.jYIkaMpL.dpuf

30 million people have seen advertising on the outside of a Bus in the last week  - See more at: http://www.exterionmedia.com/uk/what-we-do/our-media/bus-advertising#sthash.jYIkaMpL.dpuf

30 million people have seen advertising on the outside of a Bus in the last week  - See more at: http://www.exterionmedia.com/uk/what-we-do/our-media/bus-advertising#sthash.jYIkaMpL.dpuf