ComparisonOneSampleCTest {FuzzyResampling}

Comparison of the resampling approaches based on the power for the one-sample test for the mean.

Description

ComparisonOneSampleCTest returns the percentage of rejections for the one-sample C-test when different resampling methods are used.

Usage

ComparisonOneSampleCTest(
  generator,
  mu_0,
  shift = 0,
  sampleSize = 10,
  numberOfSamples = 10,
  initialSamples = 100,
  theta = 1/3,
  significance = 0.05,
  ...
)

Arguments

generator

Name of the generator for sampling initial samples. For the possible names check the values of samplingGenerators vector.

mu_0

Triangular or trapezoidal fuzzy number which is used for the null hypothesis of the C-test.

shift

Deterministic shift added to all initial samples.

sampleSize

Size of the single initial sample.

numberOfSamples

Number of the bootstrapped samples used to estimate the p-value.

initialSamples

Number of the generated initial samples. More than one value can be given in the form of matrix.

theta

The weighting parameter for the mid/spread distance applied in the C-test.

significance

The significance value used to accept/reject the hypothesis for the one-sample C-test.

...

Parameters which are passed to OneSampleCTest or the respective generator

Details

The function generates a sequence of initial samples (their number is given in initialSamples, the size is determined by sampleSize) for fuzzy numbers of the type specified by generator. Then some deterministic shift of the size shift is added to each fuzzy observation in these samples. Next, function OneSampleCTest is executed to calculate the p-value for each combination of the initial sample and resampling method. Then, by comparing the p-value with the assumed significance level significance we make a decision whether to reject the null hypothesis for the one-sample C-test for the mean (see Lubiano et al. (2016)) or not. The output of this procedure is the percentage of rejections in the sequence of experiments.

Value

This function returns a vector of percentage of rejections for the one-sample C-test for the mean.

References

Lubiano, M.A., Montenegro M., Sinova, B., de Saa, S.R., Gil, M.A. (2016) Hypothesis testing for means in connection with fuzzy rating scale-based data: algorithms and applications European Journal of Operational Research, 251, pp. 918-929

See Also

ComparisonSEMean for the comparison of resampling methods based on SE/MSE for the mean, ComparePowerOneSampleCTest for the comparison of resampling methods based on power for the one-sample C-test for the mean.

Other comparison of resampling methods: ComparePowerOneSampleCTest(), ComparisonSEMean()

Examples

## Not run: 

# seed PRNG

set.seed(1234)

# compare the resampling methods for the synthetic data generated using GeneratorNU function

ComparisonOneSampleCTest(generator="GeneratorNU",mu_0 = c(-0.4,-0.1,0.1,0.4),
 sampleSize = 10,numberOfSamples = 100, initialSamples = 100,mu = 0, sigma = 1,a = 0.2,b = 0.6)
## End(Not run)