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I have the total number of calls received each week and have plotted them on a chart, going back nearly 3 years.

By eye it seems that there was a massive drop over Christmas, that doesn't seem to have recovered, it seems that there has been a step change in requests.

Is there a test I can do that can quantify this difference?

Cheers

Ben

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    $\begingroup$ Exploring the change-point tag might give you some ideas. $\endgroup$
    – whuber ♦
    Apr 14, 2011 at 14:59

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A very similar example is used in the tutorial of PyMC. If you assume that the daily amount of requests was constant until some point in time (maybe exactly Christmas) and after that it was constant again, all you need to do is substitute the numbers in the example: http://pymc.googlecode.com/svn/doc/tutorial.html

As this is the Bayesian approach you won't (easily) get p values. However, the size of the step down and its credible interval (this is a Bayesian interval, similar to a confidence interval) may be equally useful.

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  • $\begingroup$ Question for all: does the idea of doing a simple T-test, before vs. after, get compromised by the fact that the researcher had the benefit of seeing the entire series before choosing that Christmas split point? Beyond that, are there methods simpler than GaBorgulya's that you would recommend? And I'm not sure that fitting 2 ARIMA models would be much simpler. $\endgroup$
    – rolando2
    Apr 17, 2011 at 2:46

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