# rao.spacing.test: Rao's Spacing Test of Uniformity In circular: Circular Statistics

## Description

Performs Rao's spacing test of uniformity.

## Usage

 ```1 2 3``` ```rao.spacing.test(x, alpha=0) ## S3 method for class 'rao.spacing.test' print(x, digits = 4, ...) ```

## Arguments

 `x` a vector. The object is coerced to class `circular`. `alpha` numeric value specifying the significance level of the test. The default value is 0, in which case, a range for the p-value will be returned. Valid significance levels are 0.10, 0.05, 0.01 and 0.001. `digits` integer indicating the precision to be used. `...` further arguments passed to or from other methods.

## Details

If alpha is specified, critical values are determined (using the `print` function) from a table of simulated critical points (see reference below); in this case the `print` function return a further value `accepted` which is `TRUE` if the null hypothesis is accepted and `FALSE` otherwise. If alpha is not specified, a range for the p-value is determined using the table of simulated critical points in the `print` function but not reported.

## Value

a list with the statistic, alpha and the number of observations.

## Author(s)

Claudio Agostinelli and Ulric Lund

## References

Jammalamadaka, S. Rao and SenGupta, A. (2001). Topics in Circular Statistics, Section 7.4, World Scientific Press, Singapore.

Rao, J.S. (1976). Some tests based on arc-lengths for the circle. Sankhya, The Indian Journal of Statistics, Serial B(4), 38, 329-338.

Russell, G.S. and Levitin, D.J. (1995). An expanded table of probability values for Rao's Spacing Test. Communications in Statistics - Simulation and Computation, 24, 4, 879-888.

`range.circular`, `kuiper.test`, `rayleigh.test` and `watson.test`

## Examples

 ```1 2 3 4 5 6 7 8``` ```x <- circular(runif(200, 0, 2*pi)) rao.spacing.test(x) res <- print(rao.spacing.test(x, alpha=0.1)) res\$accepted x <- rvonmises(100, circular(0), 20) rao.spacing.test(x) ```

### Example output

```Attaching package: 'circular'

The following objects are masked from 'package:stats':

sd, var

Rao's Spacing Test of Uniformity

Test Statistic = 130.3379
P-value > 0.10

Rao's Spacing Test of Uniformity

Test Statistic = 130.3379
Level 0.1 critical value = 140.06
Do not reject null hypothesis of uniformity

 TRUE

Rao's Spacing Test of Uniformity

Test Statistic = 297.8676
P-value < 0.001

```

circular documentation built on May 1, 2019, 7:57 p.m.