OneSampleCTest {FuzzyResampling}

Calculate p-value of the one-sample test for the mean

Description

OneSampleCTest returns the p-value of the one-sample test for the mean using the resampling method.

Usage

OneSampleCTest(
  initialSample,
  mu_0,
  numberOfSamples = 100,
  theta = 1/3,
  resamplingMethod = "ClassicalBootstrap",
  increases = FALSE
)

Arguments

initialSample

The initial sample which consists of triangular or trapezoidal fuzzy numbers. More than one value can be given in the form of matrix.

mu_0

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

numberOfSamples

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

theta

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

resamplingMethod

Name of the resampling method, which is used to generate the bootstrapped samples. For the possible names check the values of resamplingMethods vector.

increases

If TRUE is used, then the fuzzy numbers should be given in the form: left increment of the support, left end of the core, right end of the core, right increment of the support. Otherwise, the default value FALSE is used and the fuzzy numbers should be given in the form: left end of the support, left end of the core, right end of the core, right end of the support.

Details

The input fuzzy values should be triangular or trapezoidal fuzzy numbers, given as a single vector or a whole matrix. In each row, there should be a single fuzzy number in one of the forms:

1. left end of the support, left end of the core, right end of the core, right end of the support, or

2. left increment of the support, left end of the core, right end of the core, right increment of the support.

In this second case, the parameter increases=TRUE has to be used.

The procedure uses the resampling method given in the resamplingMethod parameter to estimate the p-value of the one-sample test for the mean (denoted further as the one-sample C-test, see Lubiano et al. (2016)). This test checks the null hypothesis that the Aumann-type mean of the fuzzy numbers is equal to a given fuzzy number mu_0.

Value

This function returns double value which is equal to the p-value of the one-sample C-test.

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

TwoSampleCTest for the two-sample C-test

Other bootstrapped version of test: TwoSampleCTest()

Examples

# prepare some fuzzy numbers (first type of the initial sample)

fuzzyValues <- matrix(c(0.25,0.5,1,1.25,0.75,1,1.5,2.2,-1,0,0,2),ncol = 4,byrow = TRUE)

# seed PRNG

set.seed(1234)

# calculate the p-value using the classical (i.e. Efron's) bootstrap

OneSampleCTest(fuzzyValues, mu_0 = c(0,0.5,1,1.5))

# calculate the p-value using the VA resampling method

OneSampleCTest(fuzzyValues, mu_0 = c(0,0.5,1,1.5),resamplingMethod = "VAMethod")