# sim.seqtest.cor: Simulation of the sequential triangular test for the... In miscor: Miscellaneous Functions for the Correlation Coefficient

## Description

This function performs a statistical simulation for the sequential triangular test for the product-moment correlation coefficient

## Usage

 ```1 2 3 4 5``` ```sim.seqtest.cor(rho.sim, k, rho, alternative = c("two.sided", "less", "greater"), delta, alpha = 0.05, beta = 0.1, runs = 1000, m.x = 0, sd.x = 1, m.y = 0, sd.y = 1, digits = 3, output = TRUE, plot = FALSE) ```

## Arguments

 `rho.sim` simulated population correlation coefficient, ρ. `k` an integer or a numerical vector indicating the number of observations in each sub-sample. `rho` a number indicating the correlation under the null hypothesis, ρ0. `alternative` a character string specifying the alternative hypothesis, `delta` minimum difference to be detected, δ. `alpha` type-I-risk, α. `beta` an integer or a numerical vector indicating the type-II-risk, β. `runs` numer of simulation runs. `m.x` population mean of simulated vector x. `sd.x` population standard deviation of simulated vector x. `m.y` population mean of simulated vector y. `sd.y` population standard deviation of simulated vector y. `digits` integer indicating the number of decimal places to be displayed. `output` logical: if `TRUE`, output is shown. `plot` logical: if `TRUE`, plot is shown.

## Details

In order to determine the optimal k, simulation is conducted under the H0 condition, i.e., `rho.sim` = `rho`. Simulation is carried out for a sequence of k values to seek for the optimal k where the empirical alpha is as close as possible to the nominal alpha. In order to determine optimal beta (with fixed k), simulation is conudcted under the H1 condition, i.e., `rho.sim` = `rho` + `delta` or `rho.sim` = `rho` - `delta`. Simulation is carried out for a sequencen of beta values to seek for the optimal beta where the empirical beta is as close as possible to the nominal beta.

In order to specify a one-sided test, argument `alternative` has to be used (i.e., two-sided tests are conducted by default). Specifying argument `alternative = "less"` conducts the simulation for the null hypothesis, H0: ρ >= ρ.0 with the alternative hypothesis, H1: ρ < ρ.0; specifying argument `alternative = "greater"` conducts the simluation for the null hypothesis, H0: ρ <= ρ.0 with the alternative hypothesis, H1: ρ > ρ.0.

## Value

Returns an object of class `sim.seqtest.cor` with following entries:

 `call` function call `spec` specification of function arguments `simres` list with results (for each k or beta) for each run `res` data.frame with results, i.e., k, alpha.nom (nominal alpha), alpha.emp (estimated empirical alpha), beta.nom (nominal beta), beta.emp (empirica beta), p.H0 (proportion decision = H0), p.H1 (proportion decision = H1), AVN (average number of V), ASN (average number of sample pairs)

## Author(s)

Takuya Yanagida takuya.yanagida@univie.ac.at,

## References

Schneider, B., Rasch, D., Kubinger, K. D., & Yanagida, T. (2015). A Sequential triangular test of a correlation coefficient's null-hypothesis: 0 < ρ ≤ ρ0. Statistical Papers, 56, 689-699.

## See Also

`seqtest.cor`, `plot.sim.seqtest.cor`, `print.sim.seqtest.cor`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ```## Not run: #--------------------------------------------- # Determine optimal k and nominal type-II-risk # H0: rho <= 0.3, H1: rho > 0.3 # alpha = 0.01, beta = 0.05, delta = 0.25 # Step 1: Determine the optimal size of subsamples (k) sim.seqtest.cor(rho.sim = 0.3, k = seq(4, 16, by = 1), rho = 0.3, alternative = "greater", delta = 0.25, alpha = 0.05, beta = 0.05, runs = 10000, plot = TRUE) # Step 2: Determine the optimal nominal type-II-risk based on # the optimal size of subsamples (k) from step 1 sim.seqtest.cor(rho.sim = 0.55, k = 16, rho = 0.3, alternative = "greater", delta = 0.25, alpha = 0.05, beta = seq(0.05, 0.15, by = 0.01), runs = 10000, plot = TRUE) ## End(Not run) ```

miscor documentation built on May 1, 2019, 10:14 p.m.