User:Brian P. Josey/Notebook/Junior Lab/2010/10/25: Difference between revisions
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In this code, '''A''' is simply a vector that contains the data from the "Counts". These values were then put into the second sheet on each of the tables above. From the min and max value, I was then able to find a range over which I could create bins for a histogram. In Google Spreadsheets, I then used the "count" function on the whole range of data to find the number of times a specific number of radiations occurred. I then put this into MATLAB as a vector, and then using the plot function I created | In this code, '''A''' is simply a vector that contains the data from the "Counts". These values were then put into the second sheet on each of the tables above. From the min and max value, I was then able to find a range over which I could create bins for a histogram. In Google Spreadsheets, I then used the "count" function on the whole range of data to find the number of times a specific number of radiations occurred. I then put this into MATLAB as a vector, and then using the plot function I created plots of the data, with the number of windows as a function of the number of radiations. Here are all the plots for my data: | ||
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Because I was unable to label these graphs in the wiki code, they represent all of the data sets starting at the smallest window size, 10 ms, and increasing up to the largest window size, 1s. So going left to right, the graphs are: 10, 20, 40, 80, 100, 200, 400, 800 ms and 1 s. While I realize that it is not clear in the above graphs, it is important to note that there is a general trend in the graphs. As the window size increases, the peaks move to ever increasing values. Also they become more flattened, and spread out at increasing window size. This is an important feature of a Poisson distribution, and indicates that our measurements of the radiation does in fact fit the model. To better illustrate this, here is a graph of several different | |||
==Conclusion== | ==Conclusion== | ||
Revision as of 18:07, 7 November 2010
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Poisson DistributionThis week, my lab partner, Kirstin, and I did the Poisson distribution experiment. This is a fairly straight forward experiment that is used to demonstrate the Poisson distribution. The Poisson distribution is used to describe when an event that occurs at random times independent of the last occurrence, but with an overall average rate. Examples of when this can be useful is counting the radiation off of a sample, or the number of births per day in a maternity ward. For this experiment, we counted the number of background radiation events in the lab. We used a combined scintillator-PMT to detect the events, and counted them using the UCS 30 software on the computer. From this, we were able to generate a series of data sets that contained the number of events in a given window of time, and then analyze them. Equipment  Because most of this experiment was performed on the computer, there was very little equipment needed for the experiment. The first piece of equipment was the combined scintillator-PMT. We used this to detect the background radiation in the lab. When the scintillator absorbs radiation, it would fire a beam of ultraviolet light down the tube to the PMT. The PMT, then creates a signal voltage that is picked up by a card in the computer. The card then sends this information to the UCS 30 software, that then counts the number of radiation events in a given window of time. We also used a Spectech Universal Computer Spectrometer power supply to give a bias voltage to the detector. This voltage determines the sensitivity of the detector. Set-Up and ProcedureThe set-up was exceptionally simple:
Like the set up, the procedure is pretty basic, the only issue is that the user interface on the computer doesn't make much sense. To set up the data collection, you want to set the cut off voltage fairly high before collecting the data. So the step by step process for collecting data is as follows:
From this point, the procedure is actually in the data analysis. We did every single dwell time between 10 ms and 1 second. The values for these are then, 10, 20, 40, 80, 100, 200, 400, 800 ms and 1 s. Data and ResultsHere is the data that I collected. Each spreadsheet contains all the individual data points per window on the first page, then the maximum and minimum values, number of windows with a given number of events, averages, and errors on the second page of each table. How I calculated this is described below in the data analysis section, but I included it on these tables for simplicity. The tables are arranged in increasing window size, starting at 10 ms, and concluding with 1 s at the bottom. {{#widget:Google Spreadsheet |
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}} Because she was sick the first week and I was sick the second, Kirstin and I will actually work from different data sets even though we worked together on the lab. So our individual data points will not be the same, but our end results should be very similar. Data AnalysisOur primary goal is to show how our data illustrates a Poisson distribution. To do this, I need to create histograms for the data and illustrate that they move as the window size increases. To do this, I loaded the results from the data into MATLAB, found their maximums and minimums, averages, and standard deviations. When I knew what the maximum and minimum values were, I was then able to create a new string of data that was the number of times that a specific number of events occurred in a window. In my tables, this is marked as "Number of Radiation" and "Number of Windows". For example, if I had six windows that contained eight number of radiation events, they would be included in this table as "Number of Radiation: 8" and "Number of Windows: 6". With this new table, I was then able to create histograms of the data. Here is a sample of my code from MATLAB: wsize=0.01 % size of window in seconds Amin=min(A) % minimum number of counts Amax=max(A) % maximum number of counts Aave=sum(A)/length(A) % Average count per window stdc=std(A) % Calculated standard deviation stdt=(Aave)^.5 % Thoretical standard deviation (square root of average) perr=abs((stdt-stdc)/(stdt)*100) % percent error in calculated over theoretical Asec=Aave/wsize % Average count per second stdcs=stdc/wsize % calculated standard deviation per second stdts=stdt/wsize % theoretical standard deviation per second In this code, A is simply a vector that contains the data from the "Counts". These values were then put into the second sheet on each of the tables above. From the min and max value, I was then able to find a range over which I could create bins for a histogram. In Google Spreadsheets, I then used the "count" function on the whole range of data to find the number of times a specific number of radiations occurred. I then put this into MATLAB as a vector, and then using the plot function I created plots of the data, with the number of windows as a function of the number of radiations. Here are all the plots for my data: Because I was unable to label these graphs in the wiki code, they represent all of the data sets starting at the smallest window size, 10 ms, and increasing up to the largest window size, 1s. So going left to right, the graphs are: 10, 20, 40, 80, 100, 200, 400, 800 ms and 1 s. While I realize that it is not clear in the above graphs, it is important to note that there is a general trend in the graphs. As the window size increases, the peaks move to ever increasing values. Also they become more flattened, and spread out at increasing window size. This is an important feature of a Poisson distribution, and indicates that our measurements of the radiation does in fact fit the model. To better illustrate this, here is a graph of several different ConclusionAcknowledgments and ReferencesNOTE TO SELFBrian P. Josey 17:41, 25 October 2010 (EDT) Koch suggested that you could set up a random Poisson distribution on your computer to compare to the official data, as a way to compare with what we've done so far. It might be a good way to really learn the Poisson for your own good.
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