Test if Google searches differ by week of year

Question

I'm looking into resuscitation related search queries using Google Trends. I see that the rate of resuscitation relevant searching falls dramatically each December. I'm not sure how to test for the statistical significance of this. I have experience with basic statistical testing in Excel and I'm learning SPSS now.

Does it make sense to structure my hypotheses like this?

1. Null hypothesis is that there is no difference between week of the year and relative search volume for the search term "CPR / cardiopulmonary resuscitation"

2. Alternatively, there is a difference.

By simple visual inspection for the past decade weeks 49, 50, 51, 52 all appear to have the lowest volume of searches, every year.

• Also, am I correct to believe that weeks of the year (1 thru 52) are an interval variable and the relative search volume (0 to 1) is continuous?

• So how do you recommend I go about comparing / testing for statistical differences with this data: "week of the year" and "relative search volume"?

P.S. Any textbooks, papers, website resources would be greatly appreciated.

Answer 1

One simple approach would be to assume that the search patterns are identical over time except for level shifts at particular weeks. (This is quite restrictive and may or may not not be acceptable, but it serves well for an illustration.) Then you could run a linear regression of the search volume on the left hand side on dummy variables on the right hand side, where each dummy variable would have value 1 for a particular week (say, week 49) and 0 for all the other weeks. If the coefficient on a particular dummy variable is found to be statistically significant (using a $t$-test), you may conclude that that particular week has a volume different from the volume of the benchmark level (which comprises all the weeks that do no have their dummies, e.g. weeks 1 through 48). You may also have dummies for all weeks but one (to avoid multicollinearity) and then test for their joint statistical significance using an $F$-test. That would allow you conclude whether there is weekly seasonality at all (where all weeks are important, not just weeks 49 through 52).

In practice there may (and likely will) be some complications. There may be linear or nonlinear time trends, structural changes, conditional or unconditional heteroskedasticity, etc. Neglecting these would invalidate the simple approach outlined above. Therefore, ideally you would build a comprehensive model including the weekly dummies and test them within that model.

Another complication is that a year has a fractional number of weeks (365.25/7). If you want to be precise, you may want to use, say, a set of Fourier terms with appropriate frequencies as described here and here. However, this is not completely straightforward when you want to make sense of calendar weeks rather than certain "portions" of a year.