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

This function tests the product-moment correlation coefficient for H0: *ρ = ρ*0,
so that any value for *ρ*0 can be specified.

1 2 3 |

`x` |
a numeric vector. |

`y` |
a numeric vector. |

`r` |
alternative specification, product-moment correlation coefficient. |

`n` |
alternative specification, number of observations. |

`rho0` |
a number indicating |

`alternative` |
a character string describing the alternative hypothesis,
must be one of |

`reduced` |
logical: if |

`conf.level` |
confidence level of the interval. |

`digits` |
integer indicating the number of decimal places to be displayed. |

`output` |
logical: if |

Computation is based on Fisher's z transformation *\textbf{z} = 0.5 /cdot ln(\frac{1 + r}{1 - r})*. The
difference between the full formula (i.e., `reduced = FALSE`

) and the reduced formula (i.e., `reduced = TRUE`

)
is that the full formula includes the term *\frac{ρ}{n - 1}* in the formula of the exectation *E*, i.e.,

*\emph{E}(\textbf{z}) = 0.5 /cdot ln(\frac{1 + ρ}{1 - ρ}) + \frac{ρ}{n - 1}*

whereas the reduced formula does not include this term, i.e.,

*\emph{E}(\textbf{z}) = 0.5 /cdot ln(\frac{1 + ρ}{1 - ρ})*

It is recommended to always use the full formula, especially in small samples.

Returns an object of class `test.cor`

with following entries:

`call` | function call |

`dat` | data.frame with x and y (if available) |

`spec` | specification of function arguments |

`res` | list with results, i.e., t or z (test statistic), df (degree of feedom), pval (significance value), r (correlation coefficient), n (sample size), lower (lower limit of CI), upper (upper limit of CI) |

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

Cramer, H. (1946). *Mathematical methods of statistics*. Princeton: Princeton Press.

Rasch, D., Kubinger, K. D., & Yanagida, T. (2011). *Statistics in psychology - Using R and SPSS*.
New York: John Wiley & Sons.

Kubinger, K. D., Rasch, D., & Simeckova, M. (2007). Testing a correlation coefficient's significance:
Using H0: 0 *< ρ ≤ λ* is preferable to H0: *ρ = *0. *Psychology Science, 49*, 74-87.

`size.cor`

, `comptest.cor`

, `seqtest.cor`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | ```
#--------------------------------------
# Two-sided test
# H0: rho == 0, H1: rho != 0
# r = 0.23, n = 60
test.cor(r = 0.23, n = 120)
#--------------------------------------
# Two-sided test
# H0: rho == 0.4, H1: rho != 0.4
# r = 0.55, n = 120
test.cor(r = 0.55, n = 120, rho0 = 0.4)
#--------------------------------------
# One-sided test
# H0: rho <= 0.4, H1: rho > 0.4
# Generate random data
dat <- sim.cor(100, rho = 0.4)
test.cor(dat$x, dat$y, rho0 = 0.4)
``` |

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