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. This function calculates the operating characteristics (OC) and average sample number (ASN) of 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 5 6 | SBFNAP_twoz(es = c(0, 0.2, 0.3, 0.5), n1min = 1, n2min = 1,
n1max = 5000, n2max = 5000,
tau.NAP = 0.3/sqrt(2), sigma0 = 1,
RejectH1.threshold = exp(-3), RejectH0.threshold = exp(3),
batch1.size.increment, batch2.size.increment,
nReplicate = 50000, nCore)
|
es |
Numeric vector. Standardized effect size differences (μ_2 - μ_1)/σ_0 where OC and ASN are desired. Default: |
n1min |
Positive integer. Minimum sample size from Group-1 in the sequential comparison. Default: 1. |
n2min |
Positive integer. Minimum sample size from Group-2 in the sequential comparison. Default: 1. |
n1max |
Positive integer. Maximum sample size from Group-1 in the sequential comparison. Default: 1. |
n2max |
Positive integer. Maximum sample size from Group-2 in the sequential comparison. Default: 1. |
tau.NAP |
Positive numeric. Parameter in the moment prior. Default: 0.3/√{2}. This places the prior modes of (μ_2 - μ_1)/σ_0 at 0.3 and -0.3. |
sigma0 |
Positive numeric. Known common standard deviation of the populations. Default: 1. |
RejectH1.threshold |
Positive numeric. H_0 is accepted if BF ≤ |
RejectH0.threshold |
Positive numeric. H_0 is rejected if BF ≥ |
batch1.size.increment |
function. Increment in sample size from Group-1 at each sequential step. Default: |
batch2.size.increment |
function. Increment in sample size from Group-2 at each sequential step. Default: |
nReplicate |
Positve integer. Number of replicated studies based on which the OC and ASN are calculated. Default: 50,000. |
nCore |
Positive integer. Default: One less than the total number of available cores. |
A list with three components named summary
, BF
, and N
.
$summary
is a data frame with columns effect.size
containing the values in es
. At those values, acceptH0
contains the proportion of times H_0
is accepted, rejectH0
contains the proportion of times H_0
is rejected, inconclusive
contains the proportion of times the test is inconclusive, ASN
contains the ASN, and avg.logBF
contains the expected weight of evidence values.
$BF
is a matrix of dimension length(es)
by nReplicate
. Each row contains the Bayes factor values at the corresponding standardized effec size in nReplicate
replicated studies.
$N
is a matrix of the same dimension as $BF
. Each row contains the sample size required to reach a decision at the corresponding standardized effec size in nReplicate
replicated studies.
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 = SBFNAP_twoz(n1max = 100, n2max = 100, es = c(0, 0.3), nCore = 1)
|
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