KNOWLEDGEBASE - ARTICLE #1645

The arcsin function.

The arcsin function is an obscure trigonometric function that also can play a role in statistics.

Prism offers an arcsin function in its list of built-in functions, and the asin()  function you can use to build user-defined equations or transforms.  The answer is the angle whose sine equals the input value. 

Note that the input value (the argument of the function) must be a fraction, not a percentage, and that the result is an  angle in radians, not degrees.

The function in Prism does is exactly what it name says. It computes the arcsine of a fraction. It is a mathematical, not a statistical, function.

When performing t tests or ANOVA on results that are proportions, statisticians used to recommend transforming the data to equalize variances. The transform is often called "the arcsine" transform. But, when used in this way, the required function really is the arcsine of the square root of the proportion. Prism cannot calculate this with a builtin function. You'd need to write a user defined transform:

 Y = arcsin(sqrt(Y)) {result in radians}

      or

Y = 57.296*(arcsin(sqrt(Y)) {result in degrees}

 The statistical use of arcsin is explained well here and here

The use of this transform is a bit old-fashioned, replaced by logistic regression. The use of the arcsin transform is criticized in these articles:

 

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