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Non Parametric Test of Independance

The non parameteric test for independance tests the hypothesis that the Kendall coefficient, \(\tau\) is equal to 0. To test this hypothesis, two values must be estimated: \(p_1\) and \(p_2\) where

\[ \hat{p}_1 = \frac{1}{n (n-1)} \sum_{i \ne j} I\{ (x_i - x_j)(y_i - y_j) > 0 \} \] \[ \hat{p}_2 = \frac{1}{n(n-1)(n-2)} \sum_{i \ne j_1 \ne j_2 } I \{ (x_i - x_{j_{1}})(y_i - y_{j_{1}})(x_i - x_{j_{2}})(y_i - y_{j_{2}}) > 0 \} \]

Power Calculation Parameters

To input multiple values, seperate them by a comma.

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Power Calculation Explanation

Solve For
The unknown you are interested in solving for.
N
The sample size used to test the hypothesis.
Alpha
The \(\alpha\) (Type I error rate) level of the hypothesis test.
Power
The power (1 - Type II error rate) of the hypothesis test.
\(p_1\)
The value of \(p_1\) whose formula is given above.
\(p_2\)
The value of \(p_2\) whose formula is given above.

Calculation Results

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N Alpha Power \(p_1\) \(p_2\)
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Power Graph

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References

  • Chow, S., Shao, J., & Wang, H. (2003), Sample size calculations in clinical research, New York: Marcel Dekker.