implement.SBFHajnal_onez {NAP}

Implement Sequential Bayes Factor using the Hajnal's ratio for one-sample z-tests

Description

In a N(\mu,\sigma_0^2) population with known variance \sigma_0^2, consider the two-sided one-sample z-test for testing the point null hypothesis H_0 : \mu = 0 against H_1 : \mu \neq 0. For a sequentially observed data, this function implements the Sequential Bayes Factor design when the prior assumed on the standardized effect size \mu/\sigma_0 under the alternative places equal probability at +\delta and -\delta (\delta>0 prefixed).

Usage

implement.SBFHajnal_onez(obs, es1 = 0.3, sigma0 = 1, 
                         RejectH1.threshold = exp(-3), RejectH0.threshold = exp(3), 
                         batch.size, return.plot = TRUE, until.decision.reached = TRUE)

Arguments

obs

Numeric vector. The vector of sequentially observed data.

es1

Positive numeric. \delta as above. Default: 0.3. For this, the prior on the standardized effect size \mu/\sigma_0 takes values 0.3 and -0.3 each with equal probability 1/2.

sigma0

Positive numeric. Known standard deviation in the population. Default: 1.

RejectH1.threshold

Positive numeric. H_0 is accepted if BF \leRejectH1.threshold. Default: exp(-3).

RejectH0.threshold

Positive numeric. H_0 is rejected if BF \geRejectH0.threshold. Default: exp(3).

batch.size

Integer vector. The vector of batch sizes at each sequential comparison. Default: rep(1, length(obs)).

return.plot

Logical. Whether a sequential comparison plot to be returned. Default: TRUE.

until.decision.reached

Logical. Whether the sequential comparison is performed until a decision is reached or until the data is observed. Default: TRUE. This means the comparison is performed until a decision is reached.

Value

A list with three components named N, BF, and decision.

$N contains the number of sample size used.

$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.

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

out = implement.SBFHajnal_onez(obs = rnorm(100))