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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

No calculation has been generated yet.

N Alpha Power $$p_1$$ $$p_2$$
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