Description Usage Arguments Details Value Author(s) References See Also Examples

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

1 2 3 4 5 |

`rho.sim` |
simulated population correlation coefficient, |

`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, |

`alternative` |
a character string specifying the alternative hypothesis, |

`delta` |
minimum difference to be detected, |

`alpha` |
type-I-risk, |

`beta` |
an integer or a numerical vector indicating the type-II-risk, |

`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 |

`plot` |
logical: if |

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.

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) |

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

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

`seqtest.cor`

, `plot.sim.seqtest.cor`

, `print.sim.seqtest.cor`

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)
``` |

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