Have you ever heard someone say:
I’ve experienced a couple of incidences like that now.
The word wanted there is incidents, not incidences.
Incidence is one of those words, like disinterested and percentile, that tends to crop up where it doesn’t belong.
Both incident and incidence derive from a medieval Latin word with the sense of to fall into, to fall upon, or happen to. Look up both words in the OED and you will find numerous meanings.
All that need concern us here is the most common use of each word in modern English.
The title of the movie, by the way, is The Ox-Bow Incident.
As a noun incident means an occurrence or an event. It can be something trivial.
That reminds me of an incident that occurred while I was walking the dog.
Foreign travelers are warned against behavior that might provoke an “incident.” Here the meaning is an event that could lead to political difficulties between two governments.
Incidence has a mathematical meaning. In geometry it means
The situation of one locus with respect to another when they have a common point or points, but do not completely coincide; e.g. of a point to a line on which it lies, of a point or a line to a plane in which it lies, or of two intersecting lines to each other.
It’s a term used by airplane pilots:
The pilot is able to increase or decrease the lift by altering the angle of incidence. Ibid., As the angle of incidence increases, the lift also increases and the aircraft is able to climb, but if the tilt is made too large the flow on the upper surface separates and eddies are formed.
The most usual non-specialized meaning is
Manner of falling upon or affecting in any way; the range or scope of a thing, the extent of its influence or effects.
We can speak of the incidence of poverty in depressed areas of the country, or the incidence of disease in a given population.
Best advice: Don’t say incidence if all you mean is event, happening, or occurrence. That’s an incident.