- #1
stephenx_86
- 15
- 0
Hi,
I've got a distribution of points in two dimensions and would like to demonstrate if these are randomly distributed. The points have been measured using single particle tracking, so likely have some degree of error in their position. What I'd like to show is whether, as time progresses (I have 10 distributions at different time points), the distribution remains random.
So far I've been using the nearest neighbour index (NNI) and seem to have this working correctly (I've compared the results I get to those obtained using CrimeStat III; http://www.icpsr.umich.edu/CrimeStat/). Similarly, I've calculated the Z-score and also got the same results as with CrimeStat III.
What I'd like to be able to do is specify some confidence or precision in each measurement of NNI. However, my problem is that for a relatively small variation in the nearest neighbour index (NNI ranges from 0.985 to 1.03) I get a large variation in Z-score (Z ranges from 0.31 to 2.58). There is also no apparent trend (i.e. NNI and Z-score getting larger over time). To test this, I generated a similar sized sample of random points in MATLAB and see the same massive fluctuations in Z. I'm surprised by these large values of Z, since the NNI values are very close to the expected value of 1 for complete spatial randomness.
I was wondering if there is a better way to demonstrate if I have complete spatial randomness? For example, can I take the precision of measurements into account, since it seems my large number of measurements (n ~2500) is influencing Z, while the accuracy of each measure is ignored.
From what I've seen on-line; people are generally assuming complete spatial randomness if Z<1.65 (or greater, depending on how confident they need to be), since this corresponds to a confidence of 90%. However, when I'm trying to show if there IS, rather than ISN'T, randomness do I need to have Z<0.13, so I have a 10% confidence of a non-random process (i.e. 90% of randomness)?
What I'd like is a value I can plot along with the measures of NNI, such as "x% likelihood of complete spatial randomness".
Sorry if this is written confusingly; I'm still trying to get my head round the problem! Please let me know if more information is required.
Any help would be greatly appreciated
Stephen
I've got a distribution of points in two dimensions and would like to demonstrate if these are randomly distributed. The points have been measured using single particle tracking, so likely have some degree of error in their position. What I'd like to show is whether, as time progresses (I have 10 distributions at different time points), the distribution remains random.
So far I've been using the nearest neighbour index (NNI) and seem to have this working correctly (I've compared the results I get to those obtained using CrimeStat III; http://www.icpsr.umich.edu/CrimeStat/). Similarly, I've calculated the Z-score and also got the same results as with CrimeStat III.
What I'd like to be able to do is specify some confidence or precision in each measurement of NNI. However, my problem is that for a relatively small variation in the nearest neighbour index (NNI ranges from 0.985 to 1.03) I get a large variation in Z-score (Z ranges from 0.31 to 2.58). There is also no apparent trend (i.e. NNI and Z-score getting larger over time). To test this, I generated a similar sized sample of random points in MATLAB and see the same massive fluctuations in Z. I'm surprised by these large values of Z, since the NNI values are very close to the expected value of 1 for complete spatial randomness.
I was wondering if there is a better way to demonstrate if I have complete spatial randomness? For example, can I take the precision of measurements into account, since it seems my large number of measurements (n ~2500) is influencing Z, while the accuracy of each measure is ignored.
From what I've seen on-line; people are generally assuming complete spatial randomness if Z<1.65 (or greater, depending on how confident they need to be), since this corresponds to a confidence of 90%. However, when I'm trying to show if there IS, rather than ISN'T, randomness do I need to have Z<0.13, so I have a 10% confidence of a non-random process (i.e. 90% of randomness)?
What I'd like is a value I can plot along with the measures of NNI, such as "x% likelihood of complete spatial randomness".
Sorry if this is written confusingly; I'm still trying to get my head round the problem! Please let me know if more information is required.
Any help would be greatly appreciated
Stephen