Thursday, September 1, 2011

Still Searching for the Number of Weeks in a Year

When I put up a post titled "How Many Weeks Are There in a Year" back in April, little did I know how many hits it would get. For a while I was intrigued to see that visitors kept arriving. They still do - every day, without fail.

Then I realized the reason why. It wasn't because the readers of this post were in search of econometric enlightenment. Oh no! There was a much more obvious reason. They genuinely want to know the answer to the question posed in the title of that post!

A quick look at the blog "stats" revealed that there are some popular web search strings that lead these poor souls, no doubt kicking and screaming, to this site.

These include:
  • how many weeks in a year
  • are there 52 or 56 weeks in a year
  • how many weeks there are in a year [sic]
  • how many weeks in a year 2011
  • how many weeks are there in august
Intriguing! But where do these people come from?

Readers of this blog come from all over the globe, but I thought that before I jumped to conclusions maybe I should dig a bit deeper. The earlier post (based on a true story, I swear!) was in part a lament over the decline and fall of educational standards. In other words, implicit in my thinking was the notion that there's been a downward trend in learning "the basics".

With that in mind, I cranked up Google Trends again - see an earlier post on it here - and analyzed web searches using the phrase "how many weeks in a year". This is what came back for the world at large:

Looks like an upwards trend to me!

BTW, the vertical scale measures searches using this phrase relative to all searches. Keep this in mind when interpreting the following graphs, and see here for more information on this from Google Trends.

I downloaded all of the weekly data for the full period available (16 October 2005 to 21 August 2011, and on the Data page for this blog), and went one step further than eyeballing the trend.

I've called the series in the above chart "SEARCHES". The series is trend-stationary. The ADF p-value for the null of a unit root against the trend-stationary alternative is 0.000. The corresponding p-value when testing the logarithm of SEARCHES is 0.035.

The EViews code that produced the following OLS results is available on the Code page.

You'll see that I ended up fitting a quadratic trend-line, all coefficients for which are highly significant. Here's the fit, with the residuals:

O.K. - hopefully you're convinced that the trend in the data is more than a figment of my eyesight.

These results suggest that there's been a growth, since 2005, in the proportion of all web searches devoted to finding out how many weeks there are in a year! If that's not disturbing, I don't know what is!

So who, exactly, is responsible for this? I mean - where are these folk located? Here's the information for three sets of culprits - those in the U.S., in Canada, and in the U.K. (Google Trends is careful not to give you information when there are not enough data for reliable results.)




Even more interesting! Canadians apparently started wondering about the number of weeks only quite recently. I hope I wasn't inadvertently responsible for that jump in mid 2011! There's an upwards trend in the U.K. and U.S. data - or, if you wish, a downward trend in general knowledge!

Now, looking at the vertical scale on the chart for the world as a whole, the relative "number of weeks" searches went from 0.85 (that's 15% below average for searches on all phrases) in October 2005, to 2.4 in August 2011. For a fixed overall search intensity, people have been getting more and more curious about the number of weeks in a year!

You can interpret the information for the three separate countries yourself. Just keep in mind that everything is in relative terms, and also that Google Trends normalizes the data so that population effects don't have an impact.

If you look at the data I've supplied, you'll see that standard errors are given for each data-point. Even if you take these into account, the changes over time are statistically significant.

And just in case you're wondering about the precise location of these curious people, the Canadian hot-spots are (in order of curiosity):
  1. Etobicoke (ON)
  2. Mississauga (ON)
  3. London (ON)
  4. Burlington (ON)
  5. Waterloo (ON)
While for the U.S., we have:
  1. Salt Lake City (UT)
  2. San Antonio (TX)
  3. Las Vegas (NV)
  4. Irvine (CA)
  5. Houston (TX)
Somehow, I don't think this one's going to go away!

© 2011, David E. Giles


  1. Might the time confound be that dumber and younger people are online now?

  2. You could always turn this into a class project and have your students estimate the number of complete weeks (Mo-Sun) in a year. You could use Statcan time periods corresponding to historical GDP, say 1961, 1981, 1997. See what your students come up with.

  3. @Anonymous: great suggestion. :-)