How to measure a spike in data For example, if I had data like the number of daily coronavirus cases for different countries and I wanted to compare the 'intensity' of the spikes (abnormally large number of cases), what statistical method should I use? Thank you!
 A: A spike in data is usually measured as a z-score. And as a kind of rule of thumb, z-scores lower than -3 or higher than +3 could be considered extreme, as 99.7% of values in a normal distribution should fall between -3 and +3.
This requires you to make the assumption that your data distribution is normal.
Because it is a number, the z-score satisfies your desire to be able to compare different spikes in the data. Of course, you could have just compared their absolute values. But with a time-series you could have a moving mean and standard deviation. So if you want to use this to discover unusual daily peaks you might using a moving window of the past 60 days, and base z-scores off the mean and s.d. in its 60 day window.
Aside: Having found the spikes, you will then want to sanity-check them. For instance, with "raw" reported deaths you will find the biggest spikes are just after weekends and public holidays. So you may choose to first smooth that raw data with a 7-day moving average, and then run your 60-day window on the smoothed data; remember though that all peaks and troughs will have been smoothed by this, not just the ones that occur every 7 days.
