dfba_sign_test {DFBA} | R Documentation |

## Bayesian Sign Test

### Description

Given two paired continuous variates `Y1`

and `Y2`

, provides a
Bayesian sign test to assess the positivity rate for the difference
`Y1 - Y2`

.

### Usage

```
dfba_sign_test(Y1, Y2, a0 = 1, b0 = 1, prob_interval = 0.95)
```

### Arguments

`Y1` |
Vector of the continuous measurements for one group |

`Y2` |
Vector of the continuous values paired with the |

`a0` |
The first shape parameter for the prior beta distribution for the positive-sign rate parameter (default is 1). Must be positive and finite. |

`b0` |
The second shape parameter for the prior beta distribution for the positive-sign rate parameter (default is 1). Must be positive and finite. |

`prob_interval` |
Desired probability within interval limits for interval estimates of the positivity rate parameter (default is .95) |

### Details

Given two paired continuous variates `Y_1`

and `Y_2`

for two
repeated measures, statistical tests for differences examine the difference
measure `d = Y_1 - Y_2`

. The `t`

-test is a conventional frequentist
parametric procedure to assess values of `d`

. There are also two common
frequentist nonparametric tests for assessing condition differences: the sign
test and the Wilcoxon signed-rank test. The sign test is less powerful than
the Wilcoxon signed-rank test (Siegel & Castellan, 1988). The appeal of the
sign test, for some researchers, is that it is simple and - in some cases -
sufficient for demonstrating strong differences.

The `dfba_sign_test()`

function provides a Bayesian version of the sign
test (the function `dfba_wilcoxon()`

provides the Bayesian signed-rank
test). While the Wilcoxon procedure uses both rank and sign information, the
sign test uses only sign information. The `dfba_sign_test()`

function
finds the number of positive and negative `d`

values, which appear in the
output as `n_pos`

and `n_neg`

, respectively. Note that it is
standard both in the frequentist sign test and in the frequentist Wilcoxon
signed-rank procedure to remove the `d`

values that are zero. Consequently,
the signs for the nonzero `d`

values are binary, so the posterior is a
beta distribution with shape parameters `a`

- denoted in the output as
`a_post`

and `b`

- denoted in the output as `b_post`

- where
`a_post = a0 + n_pos`

and `b_post = b0 + n_neg`

and `a0`

and `b0`

are the respective first and second beta shape parameters for the prior
distribution. The default prior is a uniform distribution `a0 = b0 = 1`

.

The function estimates the population rate for positive signs by calling
`dfba_beta_descriptive()`

using the computed `a_post`

and `b_post`

as arguments. Since interest in the sign test is focused on the null
hypothesis that the positivity rate is less than or equal to .5,
`dfba_sign_test()`

calls `dfba_beta_bayes_factor()`

to calculate the
prior and posterior probabilities for the alternative hypothesis that the
positivity rate is greater than .5. The output also includes the Bayes
factors `BF10`

and `BF01`

, where `BF01 = 1/BF10`

. Large values
of `BF01`

indicate support for the null hypothesis; large values of `BF10`

indicate support for the alternative hypothesis.

### Value

A list containing the following components:

`Y1` |
Vector of continuous values for the first within-block group |

`Y2` |
Vector of continuous values for the second within-block group |

`a0` |
First shape parameter for the prior beta distribution for the population parameter for the positivity rate |

`b0` |
Second shape parameter for the prior beta distribution for the population positivity rate |

`prob_interval` |
The probability within the interval limits for the interval estimate of population positivity rate |

`n_pos` |
Sample number of positive differences |

`n_neg` |
Sample number of negative differences |

`a_post` |
First shape parameter for the posterior beta distribution for the population positivity rate |

`b_post` |
Second shape parameter for the posterior beta distribution for the population positivity rate for differences |

`phimean` |
Mean of the posterior distribution for the positivity rate parameter |

`phimedian` |
Median of the posterior distribution for the positivity rate parameter |

`phimode` |
Mode of the posterior distribution for the positivity rate parameter |

`eti_lower` |
Lower limit of the equal-tail interval estimate of the positivity rate parameter |

`eti_upper` |
Upper limt of the equal-tail interval estimate of the positivity rate parameter |

`hdi_lower` |
Lower limit for the highest-density interval estimate of the positivity rate parameter |

`hdi_upper` |
Upper limit for the highest-density interval estimate of the positivity rate parameter |

`post_H1` |
Posterior probability that the positivity rate is greater than .5 |

`prior_H1` |
Prior probability that the positivity rate is greater than .5 |

`BF10` |
Bayes factor in favor of the alternative hypothesis that the positivity rate is greater than .5 |

`BF01` |
Bayes factor in favor of the null hypothesis that the positivity rate is equal to or less than .5 |

### References

Chechile, R. A. (2020). Bayesian Statistics for Experimental Scientists: A General Introduction Using Distribution_Free Methods. Cambridge, MIT Press.

Siegel, S., & Castellan, N. J. (1988). Nonparametric Statistics for the Behavioral Sciences. New York: McGraw Hill.

### See Also

`dfba_beta_descriptive`

for details on the descriptive statistics
in the output

`dfba_beta_bayes_factor`

for details on Bayes Factors calculated
on the basis of beta distributions

`dfba_wilcoxon`

for an alternative, more powerful Bayesian
nonparametric test for evaluting repeated-measures data.

### Examples

```
measure_1 <- c(1.49, 0.64, 0.96, 2.34, 0.78, 1.29, 0.72, 1.52,
0.62, 1.67, 1.19, 0.860)
measure_2 <- c(0.53, 0.55, 0.58, 0.97, 0.60, 0.22, 0.05, 13.14,
0.63, 0.33, 0.91, 0.37)
dfba_sign_test(Y1 = measure_1,
Y2 = measure_2)
dfba_sign_test(measure_1,
measure_2,
a0 = .5,
b0 = .5,
prob_interval = .99)
```

*DFBA*version 0.1.0 Index]