Circular statistics - define period?
Hi all,
I have a very silly question, but am unable to find documentation or other forum posts about it.
When running hypothesis testing in the JASP circular statistics module, there is an option to define the period of the signal as pi or 2pi (or custom in degrees). I am a little confused by this, because isn't a complete wave period is always 2pi long?
Anyway, the phase angles in my data are given as being between -pi and +pi. Do I set my period as 2pi, because that is the total period length between -pi and pi? Or as pi, because there are no values larger than abs(pi) in the dataset?
Comments
I will ask the team, good question.
Dear @SusanL82,
this is not a silly question at all!
The complete wave period is indeed always 2pi long, and JASP treats it as such. However, the variables used for the analysis may come in different units and that's why there is the "period" option (note that the third option need not be degrees necessarily, the 360 is just a default. You could change it to 12 for months, 24 for hours, 60 for minutes, etc). The period value is used internally as a divisor in a modulo operation; the remainder is then normalized back to the 2pi interval for the rest of the analysis.
If your variable is already between -pi and +pi, you can just set your period to 2pi and everything should be fine.
Regarding the period=pi: It does not come up very often but sometimes people might want to analyze their data disregarding directions. For instance, in a 2pi coding, a vertical line might be coded as pi/2 or 3pi/2 depending on whether it's thought to be "going up" or "going down". Using a period of pi instead represents this line with a single value, essentially "wrapping" the exact opposite directions together.