HajnalBF_twoz {NAP}

Hajnal's ratio 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 Hajnal's ratio in favor of H_1 when the prior assumed under the alternative on the difference between standardized effect sizes (\mu_2 - \mu_1)/\sigma_0 places equal probability at +\delta and -\delta (\delta>0 prefixed).

Usage

HajnalBF_twoz(obs1, obs2, n1Obs, n2Obs, mean.obs1, mean.obs2, 
              test.statistic, es1 = 0.3, 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 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).

es1

Positive numeric. \delta as above. Default: 0.3. For this, the prior on (\mu_2 - \mu_1)/\sigma_0 takes values 0.3 and -0.3 each with equal probability 1/2.

sigma0

Positive numeric. Known common standard deviation of the populations. Default: 1.

Details

• 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.

Value

Positive numeric or numeric vector. The Hajnal's ratio(s).

Author(s)

Sandipan Pramanik and Valen E. Johnson

References

Hajnal, J. (1961). A two-sample sequential t-test.Biometrika, 48:65-75, [Article].

Schnuerch, M. and Erdfelder, E. (2020). A two-sample sequential t-test.Biometrika, 48:65-75, [Article].

Examples

HajnalBF_twoz(obs1 = rnorm(100), obs2 = rnorm(100))