NAPBF_twoz: Bayes factor in favor of the NAP in two-sample z tests
In NAP: Non-Local Alternative Priors in Psychology

Description Usage Arguments Details Value Author(s) References Examples

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. Based on an observed data, this function calculates the Bayes factor in favor of H_1 when a normal moment prior is assumed on the difference between standardized effect sizes (μ_2 - μ_1)/σ_0 under the alternative.

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NAPBF_twoz(obs1, obs2, n1Obs, n2Obs, 
           mean.obs1, mean.obs2, test.statistic, 
           tau.NAP = 0.3/sqrt(2), sigma0 = 1)

`obs1`	Numeric vector. Observed vector of data from Group-1.
`obs2`	Numeric vector. Observed vector of data from Group-2.
`n1Obs`	Numeric or numeric vector. Sample size(s) from Group-1. Same as `length(obs1)` when numeric.
`n2Obs`	Numeric or numeric vector. Sample size(s) from Group-2. Same as `length(obs2)` when numeric.
`mean.obs1`	Numeric or numeric vector. Sample mean(s) from Group-1. Same as `mean(obs1)` when numeric.
`mean.obs2`	Numeric or numeric vector. Sample mean(s) from Group-2. Same as `mean(obs2)` when numeric.
`test.statistic`	Numeric or numeric vector. Test-statistic value(s).
`tau.NAP`	Positive numeric. Parameter in the moment prior. Default: 0.3/√{2}. This places the prior modes of (μ_2 - μ_1)/σ_0 at 0.3 and -0.3.
`sigma0`	Positive numeric. Known common standard deviation of the populations. Default: 1.

A user can either specify obs1 and obs2, or n1Obs, n2Obs, mean.obs1 and mean.obs2, or n1Obs, n2Obs, and test.statistic.
If obs1 and obs2 are provided, it returns the corresponding Bayes factor value.
If n1Obs, n2Obs, mean.obs1 and mean.obs2 are provided, the function is vectorized over the arguments. Bayes factor values corresponding to the values therein are returned.
If n1Obs, n2Obs, and test.statistic are provided, the function is vectorized over each of the arguments. Bayes factor values corresponding to the values therein are returned.

Positive numeric or numeric vector. The Bayes factor value(s).

Sandipan Pramanik and Valen E. Johnson

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]