User:Garrett E. McMath/Notebook/Junior Lab/2008/11/24/Summary

From OpenWetWare

Jump to: navigation, search
SJK 17:29, 17 December 2008 (EST)
17:29, 17 December 2008 (EST)I am really glad that you guys focused in on the error as a function of dwell time & number of passes.  This was a great way to look at the problem--though I think not using the absolute value would be even  better.  I still don't understand why but it does look like you found a way to minimize it.
17:29, 17 December 2008 (EST)
I am really glad that you guys focused in on the error as a function of dwell time & number of passes. This was a great way to look at the problem--though I think not using the absolute value would be even better. I still don't understand why but it does look like you found a way to minimize it.

Summary

We first had assumed given what we knew about the expirement that the product of the dwell time and the number of passes should be all that matters. As is shown in the data and the analysis in Excell this was not the case. As is shown in the Excel sheet our percent error had a rough linear trend that went down with more passes and up with longer dwell times. I put four different trendlines on each graph; linear, logarithmic, power, and exponential, given that none of the R squared values were very high I concluded that it could not be done quite that simply. I believe that there is a perfect dwell time to get the best data and it appears to be in the 1 ms range, this hypothesis is strengthened by the lab manual which mentions this time to be used. Given that I created a third graph using only the ms time range data sets. It again has a very rough linear trend showing that the more passes done in the ms time range will give smaller margin of error which is given by the fact that a poisson distribution should have equal mean and variance. I have not been able to determine why the data is so bad as far as showing a clear linear trend. We did however on the last day set up the expirement to run in the ms time range for approx. 7 days worth of passes so we will see if this much larger data set will prove the hypothesis more definitively.

Trial Dwell Passes Mean Variance Deviation (%)
1 ? ? 4.085938 4.431801 8.46474
2 ? ? .292969 .239323 18.31111
3 ? ? 1.113281 1.355744 21.77915
4 10ms 120 4.40234375 5.01787684 13.9819406
5 400ms 1 1.421875 0.966422 32.03189
6 8ms 300 8.769531 8.374127 4.508843
7 200ms 20 13.0625 8.552941 34.52294
8 100ms 20 6.746094 5.798024 14.05361
9 1s 1 3.460938 1.637684 52.68092
10 400us 1800 2.625 3.223529 22.80112
11 1ms 600 2.226563 2.113174 5.092535
12 1ms 1200 4.519531 4.383931 3.000322
13 1ms 2400 9.023438 8.407292 6.828283
14 1ms 4800 18.20313 18.49975 1.629555
15 200ms 3 2.332031 1.791284 23.18783
Personal tools