Taking Credit for Chance Occurences

According to the Cancer Information Center of the National Cancer Institute "A disease cluster is the occurrence of a greater than expected number of cases of a particular disease within a group of people, a geographic area, or a period of time." (see http://www.cancer.gov/cancertopics/factsheet/Risk/clusters) Disease clusters can signify the occurrence of an epidemic, a biohazard, or some other threat to public health. Therefore they must be taken very seriously. But before panic sets in, one must always ask if the "greater than expected number of cases" could merely have happened by chance.

Consider some horrible non-contagious disease (SHND) that occurs in only 1% of the population. In a particular office building with 250 workers, 4 cases of SHND are reported. Should this raise an alarm concerning the building, or could it have happened by chance?

Open the Building.xls model and press the F9 key a few times to make sure the model is working.

The building, with 25 floors and ten workers per floor, is modeled as follows. For each of the 250 workers, we generate a random between 0 and 1 with RAND(). If the number is less than the population probability of having SHND (in cell R13), the worker is represented by a 1. Otherwise the worker is represented as a Blank. Note that by making the columns narrow and adding decimal palces to the 1s, # signs appear on the screen to represent the cases of the disease. Since R13 is set at 1%, we would expect one worker in 100 to have the disease, or 2.5 cases on average for a building of this size. Press the calculate key (F9) a few times to see the range of outcomes. The indicator in cell R19 is equal to 1 if the total cases in the building equals or exceeds the value in cell Q19 (4 in this case).