NAPBF_twoz {NAP} | R Documentation |
Bayes factor in favor of the NAP in two-sample z
tests
Description
In case of two independent populations N(\mu_1,\sigma_0^2)
and N(\mu_2,\sigma_0^2)
with known common variance \sigma_0^2
, consider the two-sample z
-test for testing the point null hypothesis of difference in their means H_0 : \mu_2 - \mu_1 = 0
against H_1 : \mu_2 - \mu_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 (\mu_2 - \mu_1)/\sigma_0
under the alternative.
Usage
NAPBF_twoz(obs1, obs2, n1Obs, n2Obs,
mean.obs1, mean.obs2, test.statistic,
tau.NAP = 0.3/sqrt(2), sigma0 = 1)
Arguments
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 |
n2Obs |
Numeric or numeric vector. Sample size(s) from Group-2. Same as |
mean.obs1 |
Numeric or numeric vector. Sample mean(s) from Group-1. Same as |
mean.obs2 |
Numeric or numeric vector. Sample mean(s) from Group-2. Same as |
test.statistic |
Numeric or numeric vector. Test-statistic value(s). |
tau.NAP |
Positive numeric. Parameter in the moment prior. Default: |
sigma0 |
Positive numeric. Known common standard deviation of the populations. Default: 1. |
Details
A user can either specify
obs1
andobs2
, orn1Obs
,n2Obs
,mean.obs1
andmean.obs2
, orn1Obs
,n2Obs
, andtest.statistic
.If
obs1
andobs2
are provided, it returns the corresponding Bayes factor value.If
n1Obs
,n2Obs
,mean.obs1
andmean.obs2
are provided, the function is vectorized over the arguments. Bayes factor values corresponding to the values therein are returned.If
n1Obs
,n2Obs
, andtest.statistic
are provided, the function is vectorized over each of the arguments. Bayes factor values corresponding to the values therein are returned.
Value
Positive numeric or numeric vector. The Bayes factor value(s).
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
NAPBF_twoz(obs1 = rnorm(100), obs2 = rnorm(100))