Pokemon Go Researcher jFarr hatched a total of 169 eggs

EXAMPLE:

Researcher jFarr hatched a total of 169 eggs (not including 10km eggs). The expected counts are 169 x 669 / 1715 = 65.925 2km eggs and 169 x 1046 / 1715 = 103.075 5km eggs. Next we take the square of the difference between the expected and observed count and divide it by the expected count. In our example, jFarr got 67 2km eggs and 102 5km eggs, so we get values (67 - 65.925)^2/65.925 = 0.0175 and (102 - 103.075)^2/103.075 = 0.0112. These values give a measure of how much the expected and observed counts differ from each other.

We add up the values for all trainers, and come up to a total of 43.905. If the egg distribution were independent of PokeStop, this total would follow a chi-squared distribution with 25 degrees of freedom. The number of degrees of freedom is calculated as:

(#researchers - 1) x (#egg types - 1) = 25 x 1 = 25

We can now calculate the p-value, this is the probability that a random variable following a chi-squared distribution with 25 degrees of freedom is 43.905 or larger. The result is:

p = 0.0111

This is lower than the 0.05 threshold for significance, so we have concluded that the hypothesis that distance distribution is independent of PokeStop has been refuted (See Note 2).

FURTHER TESTING (SPECIES DISTRIBUTION, ETC.):

We continued by looking at the individual species hatched. It is believed that the contents of an egg are already determined upon receiving it at a PokeStop (largely due to the fact that Pokemon with legacy movesets were hatched after global moveset changes, among other compelling reasons). Under the assumption that this is true (most importantly: hatching location is not important) we can research the contents of the eggs. The counts for individual species are too low to do any meaningful testing, so we had to group different species together. One way to do this is to compare the distribution between Water and non-Water Pokemon from 5km eggs. It's important that we look at 5km eggs only; if we looked at all eggs, a difference in species distribution could be caused by the difference in distance distribution we just discovered.

We ran a chi-squared test similar as before to the counts of Water and non-Water Pokemon from 5km eggs. This test gave a p-value of p=0.1728, which means we did not find a significant difference in the contents of 5km eggs of the different researchers. Other ways of grouping up species have also been tried, but none gave a significant result.

Despite not getting a result here, we are still very interested in the distribution of individual species from eggs and we will be running further, more specific, experiments in the future.

NOTES

Note 1:

The chi-squared test requires that no more than 20% of the expected counts are lower than 5. If we included 10km eggs, this would not be the case.

Note 2:

Strictly speaking, we can only conclude that the researchers obtained egg distances from different distributions. It could theoretically be the case that this is caused by something other than PokeStop location (such as time of day, level, etc.). More research is planned to help confirm/isolate factors affecting egg drop distributions.

Source: http://www.pokeaccountbuy.com/news/112--pokemon-go-study-pokestops-and-egg-distances