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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

\[ \hat{p}_1 = \frac{1}{n (n-1)} \sum_{i \ne j} I\{ (x_i - x_j)(y_i - y_j) > 0 \} \] \[ \hat{p}_2 = \frac{1}{n(n-1)(n-2)} \sum_{i \ne j_1 \ne j_2 } I \{ (x_i - x_{j_{1}})(y_i - y_{j_{1}})(x_i - x_{j_{2}})(y_i - y_{j_{2}}) > 0 \} \]To input multiple values, seperate them by a comma.

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- 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.

No calculation has been generated yet.

N | Alpha | Power | \(p_1\) | \(p_2\) |
---|---|---|---|---|

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