Experimental Errors

As I examined some of the data, I noticed that there were several plots that contained one or two isolated points at a great distance away from the mean. This occurred when I got data with a high number of photon counts (i.e. low rates). Most of these points were much lower than the mean value. I turned to statistics to analyze whether these counts were feasible or not. Statistics tells us that for a normalized distribution, 99.994% of the data lies within 4 standard deviations ($\sigma$) from the mean. For a non-normalized distribution, the same percentage lies within about 7 standard deviations from the mean. I ended up choosing 7 standard deviations to be the limit for whether I should include the counts or not in my data. Therefore, anything that fell outside of this range I interpreted as dropped counts due to experimental error or error from the equipment.

Figure 1: Here is an example of one of the plots where I saw a dropped count. You can see one data point at about 2.5 seconds after the start of the experiment that is isolated from the rest of the counts.