# HajnalBF_onet: Hajnal's ratio in one-sample t tests In NAP: Non-Local Alternative Priors in Psychology

## Description

In a N(μ,σ^2) population with unknown variance σ^2, consider the two-sided one-sample z-test for testing the point null hypothesis H_0 : μ = 0 against H_1 : μ \neq 0. Based on an observed data, this function calculates the Hajnal's ratio in favor of H_1 when the prior assumed on the standardized effect size μ/σ under the alternative places equal probability at and (δ>0 prefixed).

## Usage

 `1` ```HajnalBF_onet(obs, nObs, mean.obs, sd.obs, test.statistic, es1 = 0.3) ```

## Arguments

 `obs` Numeric vector. Observed vector of data. `nObs` Numeric or numeric vector. Sample size(s). Same as `length(obs)` when numeric. `mean.obs` Numeric or numeric vector. Sample mean(s). Same as `mean(obs)` when numeric. `sd.obs` Positive numeric or numeric vector. Sample standard deviation(s). Same as `sd(obs)` when numeric. `test.statistic` Numeric or numeric vector. Test-statistic value(s). `es1` Positive numeric. δ as above. Default: 0.3. For this, the prior on the standardized effect size μ/σ takes values 0.3 and -0.3 each with equal probability 1/2.

## Details

• Users can either specify `obs`, or `nObs`, `mean.obs` and `sd.obs`, or `nObs` and `test.statistic`.

• If `obs` is provided, it returns the corresponding Bayes factor value.

• If `nObs`, `mean.obs` and `sd.obs` are provided, the function is vectorized over the arguments. Bayes factor values corresponding to the values therein are returned.

• If `nObs` and `test.statistic` are provided, the function is vectorized over 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

 `1` ```HajnalBF_onet(obs = rnorm(100)) ```

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