Comprehensive Randomness Battery — run

Runs a suite of nonparametric randomness tests from the randtests package.

run_randtests(x, alter = "two.sided", na_rm = TRUE, alpha = 0.05)

Arguments

x: A numeric vector containing the sequence to test for randomness.
alter: Alternative hypothesis. One of "two.sided", "less", "greater", "left.sided", or "right.sided". The values "less" and "greater" are mapped internally to "left.sided" and "right.sided", respectively.
na_rm: Logical. If TRUE, missing values are removed before testing. If FALSE, the function throws an error when x contains missing values.
alpha: Significance level used to determine the Reject_H0 column. Default is 0.05.

Value

A data.frame with one row per randomness test and the following columns:

Test: Short name of the randomness test.
Method: Method name returned by the underlying randtests function.
Alternative: Alternative hypothesis used in the test.
N: Number of non-missing observations tested.
Statistic: Observed test statistic.
Statistic_Name: Name of the test statistic, when available.
Expected_Mu: Expected value of the statistic under the null hypothesis, when available.
Variance: Variance of the statistic under the null hypothesis, when available.
P_Value: Raw p-value returned by the test.
Error: Error message if the test failed; otherwise NA.
Reject_H0: Logical value indicating whether the null hypothesis is rejected at level alpha using the raw p-value.

Details

The overall null hypothesis is that the input sequence is randomly ordered, independent, and has no systematic trend or non-random structure. Each test evaluates this null hypothesis from a different perspective, such as runs, ranks, signs of differences, turning points, or monotonic trend.

The null hypothesis for the full battery is:

$$H_0: the sequence is randomly ordered, independent, and contains no systematic pattern.$$

The tests included are:

Bartels Rank Test: Tests whether the observations are randomly ordered, with no serial dependence or trend.
Cox Stuart Test: Tests whether there is no monotonic trend in the sequence.
Difference Sign Test: Tests whether successive differences show no systematic upward or downward tendency.
Runs Test: Tests whether the sequence is randomly ordered around a reference point, typically the median.
Turning Point Test: Tests whether the number of local peaks and valleys is consistent with randomness.
Rank Test: Tests whether the ordering of the observations is random, with no trend.

The Reject_H0 column indicates whether each test rejects its null hypothesis at the chosen alpha level using the raw p-value returned by that test.

Examples

library(randngen)
n <- 10000
seed <- 12345
lcg_digits <- lcg(n=n, seed=seed)
run_randtests(lcg_digits)
#>              Test                 Method Alternative     N    Statistic
#> 1    Bartels Rank     Bartels Ratio Test   two.sided 10000   -0.9519354
#> 2      Cox Stuart        Cox Stuart test   two.sided 10000 2491.0000000
#> 3 Difference Sign   Difference Sign Test   two.sided 10000    0.3290732
#> 4       Runs Test              Runs Test   two.sided 10000    1.0600530
#> 5   Turning Point     Turning Point Test   two.sided 10000   -1.9291642
#> 6       Rank Test Mann-Kendall Rank Test   two.sided 10000    0.2980996
#>   Statistic_Name Expected_Mu     Variance    P_Value Error Reject_H0
#> 1      statistic         2.0 3.999440e-04 0.34112974  <NA>     FALSE
#> 2      statistic          NA           NA 0.81001047  <NA>     FALSE
#> 3      statistic      4999.5 8.334167e+02 0.74210036  <NA>     FALSE
#> 4      statistic      5001.0 2.499750e+03 0.28912048  <NA>     FALSE
#> 5      statistic          NA           NA 0.05371048  <NA>     FALSE
#> 6      statistic  24997500.0 2.778194e+10 0.76562711  <NA>     FALSE