{{ message }}

The one sample non parametric test of location tests the hypothesis that

\[ H_0: \theta=0 \text{ versus } H_a: \theta \neq 0. \]This hypothesis is commonly tested with the Wilcoxan signed rank test.

To set up the power calculation for this hypothesis, we need three values: \(p_2\), \(p_3\), and \(p_4\). These values are generally estimated from pilot studies.

Let \(z_i\) be defined by the model:

\[ z_i = \theta + \epsilon_i \]where \(\theta\) is location parameter of interest and \(\epsilon_i\) is the error term whose mean is 0. We can estimate the parameters needed by:

\[ \hat{p}_2 = \frac{1}{n(n - 1)} \sum_{i \ne j} I\{|z_i| \ge |z_j|, z_i > 0 \} \] \[ \hat{p}_3 = \frac{1}{n(n - 1)(n - 2)} \sum_{i \ne j_1 \ne j_2} I \{ |z_i| \ge |z_{j_1}|, |z_i| \ge |z_{j_2}|, z_i > 0 \} \] \[ \hat{p}_4 = \frac{1}{n(n - 1)(n - 2)} \sum_{i \ne j_1 \ne j_2} I\{|z_{j_1}| \ge |z_i| \ge |z_{j_2}|, z_i > 0 \} \]To input multiple values, seperate them by a comma.

{{ this.errors }}

- 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.
- \(p_2\)
- The value of \(p_2\) whose formula is given above.
- \(p_3\)
- The value of \(p_3\) whose formula is given above.
- \(p_4\)
- The value of \(p_4\) whose formula is given above.

No calculation has been generated yet.

N | Alpha | Power | \(p_2\) | \(p_3\) | \(p_4\) |
---|---|---|---|---|---|

{{ val }} |

There are no results to graph yet.

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