by Jonathan Newman and Francisco Cribari-Neto

As reported in Tuesday’s Daily Egyptian, the Illinois Board of Labor Relations will hear a case brought against SIUC by the Faculty Association. The case alleges that SIU President Ted Sanders intentionally excluded Faculty Association members from the SIUC chancellor’s search committee. The facts reported in the Daily Egyptian are that the SIUC Faculty Senate (no relation to the Faculty Association) was asked by Sanders for nine names of faculty from which he would choose six. In the end, for reasons not relevant to this letter, Sanders chose five of the nine faculty. It turns out that, of the nine names put forward by the Faculty Senate, four of them were members of the Faculty Association (the four who were not chosen).

Let’s agree to make two assumptions. First, all nine of the faculty forwarded by the Faculty Senate were equally qualified to serve on the search committee. Second, Sanders did not know which faculty belonged to the Faculty Association. Then, the question becomes, What is the probability that President Sanders would choose five faculty members from the list of nine and not include any Association members, by chance alone?

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That probability is easily calculated. Following the well-known hypergeometric distribution, the probability that, by chance alone, no Association members were chosen is given by

where A is the number of faculty who did not belong to the Faculty Association (A=5), B is the number of faculty who did belong to the Association (B=4), x is the number of non-Association faculty chosen to serve on the committee (x=5) and n is total number of faculty chosen to serve on the committee (n=5). With these numbers, it is a simple matter of arithmetic to see that

(5) ( 5 – 5)

In other words, there is a 0.8-percent probability that Sanders excluded the Faculty Association members by chance alone.

We don’t wish to make any judgment on the matter. Rare events do happen, and maybe this is one of them. We are not familiar with each side’s arguments in this case. Our interest is purely academic, as a matter of applied probability theory.

Jonathan Newman, assistant professor, zoology

Francisco Cribari-Neto, assistant professor, economics

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