# implement.SBFNAP_twoz: Implement Sequential Bayes Factor using the NAP for... In NAP: Non-Local Alternative Priors in Psychology

## Description

In case of two independent populations N(μ_1,σ_0^2) and N(μ_2,σ_0^2) with known common variance σ_0^2, consider the two-sample z-test for testing the point null hypothesis of difference in their means H_0 : μ_2 - μ_1 = 0 against H_1 : μ_2 - μ_1 \neq 0. For a sequentially observed data, this function implements the Sequential Bayes Factor design when a normal moment prior is assumed on the difference between standardized effect sizes (μ_2 - μ_1)/σ_0 under the alternative.

## Usage

 ```1 2 3 4``` ```implement.SBFNAP_twoz(obs1, obs2, sigma0 = 1, tau.NAP = 0.3/sqrt(2), RejectH1.threshold = exp(-3), RejectH0.threshold = exp(3), batch1.size, batch2.size, return.plot = TRUE, until.decision.reached = TRUE) ```

## Arguments

 `obs1` Numeric vector. The vector of sequentially observed data from Group-1. `obs2` Numeric vector. The vector of sequentially observed data from Group-2. `tau.NAP` Positive numeric. Parameter in the moment prior. Default: 0.3/√2. This places the prior modes of the difference between standardized effect sizes (μ_2 - μ_1)/σ_0 at 0.3 and -0.3. `sigma0` Positive numeric. Known standard deviation in the population. Default: 1. `RejectH1.threshold` Positive numeric. H_0 is accepted if BF ≤`RejectH1.threshold`. Default: `exp(-3)`. `RejectH0.threshold` Positive numeric. H_0 is rejected if BF ≥`RejectH0.threshold`. Default: `exp(3)`. `batch1.size` Integer vector. The vector of batch sizes from Group-1 at each sequential comparison. Default: `rep(1, length(obs1))`. `batch2.size` Integer vector. The vector of batch sizes from Group-2 at each sequential comparison. Default: `rep(1, length(obs2))`. `return.plot` Logical. Whether a sequential comparison plot to be returned. Default: `TRUE`. `until.decision.reached` Logical. Whether the sequential comparison is performed until a decision is reached or until the data is observed. Default: `TRUE`. This means the comparison is performed until a decision is reached.

## Value

A list with three components named `N1`, `N2`, `BF`, and `decision`.

`\$N1` and `\$N2` contains the number of sample size used from Group-1 and 2.

`\$BF` contains the Bayes factor values at each sequential comparison.

`\$decision` contains the decision reached. `'A'` indicates acceptance of H_0, `'R'` indicates rejection of H_0, and `'I'` indicates inconclusive.

## Author(s)

Sandipan Pramanik and Valen E. Johnson

## References

Pramanik, S. and Johnson, V. (2022). Efficient Alternatives for Bayesian Hypothesis Tests in Psychology. Psychological Methods. Just accepted.

Johnson, V. and Rossell, R. (2010). On the use of non-local prior densities in Bayesian hypothesis tests. Journal of the Royal Statistical Society: Series B, 72:143-170. [Article]

## Examples

 `1` ```out = implement.SBFNAP_twoz(obs1 = rnorm(100), obs2 = rnorm(100)) ```

NAP documentation built on Jan. 6, 2022, 5:07 p.m.