table.pvalues {BANOVA} | R Documentation |

## Function to print the table of p-values

### Description

Computes the Baysian p-values for the test concerning all coefficients/parameters:

For `p = 1,...,P`

`H_0:\theta_{j,k}^{p,q}=0`

`H_1:\theta_{j,k}^{p,q} \neq 0`

The two-sided P-value for the sample outcome is obtained by first finding the one sided P-value, `min(P(\theta_{j,k}^{p,q}<0),P(\theta_{j,k}^{p,q}>0 ))`

which can be estimated from posterior samples. For example, `P(\theta_{j,k}^{p,q}>0) = \frac{n_+}{n}`

, where `n_+`

is the number of posterior samples that are greater than 0, `n`

is the target sample size. The two sided P-value is `P_\theta(\theta_{j,k}^{p,q}) = 2*min(P(\theta_{j,k}^{p,q}<0),P(\theta_{j,k}^{p,q}>0 ))`

.

If there are `\theta_{j,k_1}^{p,q},\theta_{j,k_2}^{p,q},...,\theta_{j,k_J}^{p,q}`

representing J levels of a multi-level variable, we use a single P-value to represent the significance of all levels. The two alternatives are:

`H_0:\theta_{j,k_1}^{p,q} = \theta_{j,k_2}^{p,q} = \cdots = \theta_{j,k_J}^{p,q}=0`

`H_1`

: some `\theta_{j,k_j}^{p,q} \neq 0`

Let `\theta_{j,k_{min}}^{p,q}`

and `\theta_{j,k_{max}}^{p,q}`

denote the coefficients with the smallest and largest posterior mean. Then the overall P-value is defined as

`min(P_\theta (\theta_{j,k_{min}}^{p,q}), P_\theta(\theta_{j,k_{max}}^{p,q}))`

.

### Usage

```
table.pvalues(x)
```

### Arguments

`x` |
the object from BANOVA.* |

### Source

It borrows the idea of Sheffe F-test for multiple testing: the F-stat for testing the contrast with maximal difference from zero. Thank Dr. P. Lenk of the University of Michigan for this suggestion.

### Examples

```
data(goalstudy)
library(rstan)
# or use BANOVA.run
res1 <- BANOVA.run(bid~progress*prodvar, model_name = "Normal",
data = goalstudy, id = 'id', iter = 1000, thin = 1, chains = 2)
table.pvalues(res1)
```

*BANOVA*version 1.2.1 Index]