Description Usage Arguments 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*. 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.

1 2 3 4 |

`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. |

`sigma0` |
Positive numeric. Known standard deviation in the population. |

`RejectH1.threshold` |
Positive numeric. |

`RejectH0.threshold` |
Positive numeric. |

`batch1.size` |
Integer vector. The vector of batch sizes from Group-1 at each sequential comparison. |

`batch2.size` |
Integer vector. The vector of batch sizes from Group-2 at each sequential comparison. |

`return.plot` |
Logical. Whether a sequential comparison plot to be returned. |

`until.decision.reached` |
Logical. Whether the sequential comparison is performed until a decision is reached or until the data is observed. |

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.

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]

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

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