A Barnum Statement
A Barnum statement is a description of a person that someone may feel is applicable to them directly, despite being actually vague enough to apply to a wide range of people. They (and the accompanying "Barnum Effect") were named after showman P. T. Barnum by psychologist Paul Meehl in his book "Wanted - A Good Cookbook" as he related the vague descriptions used in certain psychotests to those by given by Barnum.
There are many things that affect how well the Barnum effect - that is, how much the person believes the statement about them - actually works. These include how much the subject trusts the facilitator, how positive the traits are, and whether the test subject has been primed to think that the statements are about them, allowing them to apply their own meanings to them.
We have used Barnum statements in our astrology demonstration at our stall at The Meadows, where we invite pairs of people to read a description of themselves according to their starsign and ask the person to tell us if they think the description is applicable to them. A large proportion of people think they are, despite them being written incredibly vaguely. In fact, all of the statements are exactly the same for all starsigns!