the most clear and concise explanation of illusory correlation that i've found comes from wikipedia: "the phenomenon of seeing the relationship one expects in a set of data even when no such relationship exists." data here can be taken as traditional data (statistics, reports, etc.), and can also be applied to a broader scope in understanding it as events, experiences, perceptions, and so on.
this is a common phenomenon and examples of it can be found in most any context. stereotypes are an extremely common example, studies claiming correlation between environmental factors and personal effects can readily fall victim to it, and people simply seeking explanations will typically find them, though they may be completely irrelevant and utterly incorrect (conveniently animating this principle). this is why someone may think that people named trace are not as handsome as neils or rogers(after people meet me, neil, and roger), that pot roasts cure colds (after an ill child pips up after a bit of beef), or that a pair of trousers dictates his or her academic fate (after a success or failure in a pair of 501s).
i've not failed any tests as of recent, but illusory correlations have certainly seemed to have played a role in many of my recent actions. both in the way i make decisions and in the way i explain the reasons of their successes or failures, retrospect and further experience seems to be showing where various correlations were indeed illusory.
illusory: based on or producing illusion.
correlation: the state or relation of correlated. specifically : a relationship existing between phenomena or things.