# Visual Means Test

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The set of vectors in -space of norm 1 forms a sphere. Any particular vector , when rotated about the vector of means , defines a cone that intersects the sphere to form two spherical caps. The surface area of the caps divided by the surface area of the sphere equals the significance probability of the -test. Choose , the degrees of freedom; is then a vector in ()-space that has the -value corresponding to the other control. Although the sample vector lives in dimensions, a three-dimensional graphic is used to illustrate the cap-area phenomenon, with the cone angle determined by .

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Contributed by: Karl W. Heiner and Stan Wagon (August 2011)

(SUNY New Paltz and Macalester College)

Open content licensed under CC BY-NC-SA

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Reference

[1] G. E. P. Box, W. G. Hunter, and J. S. Hunter, *Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building*, 2nd ed., New York: Wiley–Interscience, 2005.

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