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In other words, the difference could easily be due to what statisticians call sampling error.
Let’s look a little more closely at these surprising results.
The second group was told that the solution required the lines to be drawn outside the imaginary box bordering the dot array.
In other words, the “trick” was revealed in advance.
Only 20 percent managed to break out of the illusory confinement and continue their lines in the white space surrounding the dots.
The symmetry, the beautiful simplicity of the solution, and the fact that 80 percent of the participants were effectively blinded by the boundaries of the square led Guilford and the readers of his books to leap to the sweeping conclusion that creativity requires you to go outside the box.
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Most people assume that 60 percent to 90 percent of the group given the clue would solve the puzzle easily. What’s more, in statistical terms, this 5 percent improvement over the subjects of Guilford’s original study is insignificant.
At the first stages, all the participants in Guilford’s original study censored their own thinking by limiting the possible solutions to those within the imaginary square (even those who eventually solved the puzzle).
Even though they weren’t instructed to restrain themselves from considering such a solution, they were unable to “see” the white space beyond the square’s boundaries.
Because they hadn’t, they were obviously not as creative or smart as they had previously thought, and needed to call in creative experts. The nine-dot puzzle and the phrase “thinking outside the box” became metaphors for creativity and spread like wildfire in marketing, management, psychology, the creative arts, engineering, and personal improvement circles.
There seemed to be no end to the insights that could be offered under the banner of thinking outside the box.
Today many people are familiar with this puzzle and its solution.