NAP (version 1.1)

implement.SBFHajnal_twoz: Implement Sequential Bayes Factor using the NAP for 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 \(H_1 : \mu_2 - \mu_1 \neq 0\). 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 \((\mu_2 - \mu_1)/\sigma_0\) under the alternative.

Usage

implement.SBFHajnal_twoz(obs1, obs2, es1 = 0.3, sigma0 = 1,
                         RejectH1.threshold = exp(-3), RejectH0.threshold = exp(3), 
                         batch1.size, batch2.size, return.plot = TRUE, 
                         until.decision.reached = TRUE)

Arguments

obs1

Numeric vector. The vector of sequentially observed data from Group-1.

obs2

Numeric vector. The vector of sequentially observed data from Group-2.

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 standard deviation in the population. Default: 1.

RejectH1.threshold

Positive numeric. \(H_0\) is accepted if \(BF \le\)RejectH1.threshold. Default: exp(-3).

RejectH0.threshold

Positive numeric. \(H_0\) is rejected if \(BF \ge\)RejectH0.threshold. Default: exp(3).

batch1.size

Integer vector. The vector of batch sizes from Group-1 at each sequential comparison. Default: rep(1, length(obs1)).

batch2.size

Integer vector. The vector of batch sizes from Group-2 at each sequential comparison. Default: rep(1, length(obs2)).

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 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.

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

# NOT RUN {
out = implement.SBFHajnal_twoz(obs1 = rnorm(100), obs2 = rnorm(100))
# }