Spearman Rank Order Correlation

In an effort to better understand how the strength of the CME's magnetic field, in both the magnetic cloud and solar photosphere, is related to CME propagation, we determined the Spearman rank order correlation between the strength of the magnetic field in clouds arriving at 1 AU and their corresponding transit speeds, LASCO speeds and LASCO accelerations.

Our first test examined the correlation between field strength and actual transit speeds of the cloud. We determined the actual transit speed by dividing the distance traveled by the time it took the cloud to propagate from its first LASCO sighting to 1 AU.

Our second test examined the correlation between field strength and the last observed lateral speed of the cloud before it left LASCO's field of view.

The final test examined the correlation between field strength and measured LASCO acceleration values. Initially we examined the relationship using all acceleration values, regardless of sign. Having noted in the previous relationship tests between LASCO accelerations and transit times, that negative accelerations tended to be less reliable than non-negative ones, we ran two more correlation tests, one using only positive accelerations and the other only negative ones.

The following table presents our results:

Correlation Tested	Spearman Correlation Coefficient	Degrees of Freedom	Spearman Chance Probability	Linear Correlation Coefficient
Actual transit speed	-0.55392	20	0.37%	-0.555
LASCO speed	-0.25965	17	14.15%	0.249
LASCO acceleration	-0.03860	17	43.77%	-0.554
Positive, non-zero LASCO accelerations	-0.34965	10	13.26%	-0.502
Negative, non-zero LASCO accelerations	0.08571	4	43.59%	-0.656

Click here to see plots of the correlations.

The bigger the correlation coefficient is, the more significant it is. With bigger corellation coefficients, we have more confidence in saything that two things are related to each other. The chance probability is one way of quantifying that. If we subtract the chance probability from 100%, we essentially have a confidence level. For example, these results are telling us that if you take 22 random numbers, compare them to the actual transit speeds and do this 1000 times, then you'd get a correlation as high as 0.55 something like 4 times. In other words, it is highly unlikely that the actual transit speeds randomly correlate to the magnetic field strength, thus they must be related. The negative sign on the correlation coefficient tells us that as the field strength increases, the transit speed decreases.