More Evidence of Experimental Errors

We can further see the errors in our experiment when we examine the mean versus variance of our data as we receive an increasing number of photon counts. Figure 3 reveals a deviation of the variance from the mean as we increase the mean⁵. We know that the Poisson distribution should fit well with our data because the number of atoms within our LED is much greater than the number of photons that we are receiving. We also know that for Poisson statistics, $\mu = \sigma^{2}$. Figure 3 shows that experimentally this relationship slowly falls apart as we increase the mean. We also saw from above in my discussion in section 4.1 that at lower rates (i.e. high number of counts) we got more experimental errors from dropped counts and other kinds of erroneous data. These errors serve to increase the variance of our data, so that would be the most likely explanation of the deviation of the variance from the mean. Another explanation could be that the variance is actually statistically deviating from the mean and that the Poisson distribution is actually becoming a worse approximation for the sample distribution. However, this is unlikely because even if we are getting photon counts on the order of a million, the photon counts are still much smaller than the number of atoms in the semiconductor diode of the LED that is emitting the light⁶.

Figure 3: The plotted points are the mean vs. variance of a specific rate. The solid line is the mean vs. mean line so we can visualize the deviation of the variance from the mean as the mean increases.