174,001 research outputs found
The power of A/B testing under interference
In this paper, we address the fundamental statistical question: how can you
assess the power of an A/B test when the units in the study are exposed to
interference? This question is germane to many scientific and industrial
practitioners that rely on A/B testing in environments where control over
interference is limited. We begin by proving that interference has a measurable
effect on its sensitivity, or power. We quantify the power of an A/B test of
equality of means as a function of the number of exposed individuals under any
interference mechanism. We further derive a central limit theorem for the
number of exposed individuals under a simple Bernoulli switching interference
mechanism. Based on these results, we develop a strategy to estimate the power
of an A/B test when actors experience interference according to an observed
network model. We demonstrate how to leverage this theory to estimate the power
of an A/B test on units sharing any network relationship, and highlight the
utility of our method on two applications - a Facebook friendship network as
well as a large Twitter follower network. These results yield, for the first
time, the capacity to understand how to design an A/B test to detect, with a
specified confidence, a fixed measurable treatment effect when the A/B test is
conducted under interference driven by networks.Comment: 14 page
Are autistic traits measured equivalently in individuals with and without an Autism Spectrum Disorder?:An invariance analysis of the Autism Spectrum Quotient Short Form
It is common to administer measures of autistic traits to those without autism spectrum disorders (ASDs) with, for example, the aim of understanding autistic personality characteristics in non-autistic individuals. Little research has examined the extent to which measures of autistic traits actually measure the same traits in the same way across those with and without an ASD. We addressed this question using a multi-group confirmatory factor invariance analysis of the Autism Quotient Short Form (AQ-S: Hoekstra et al. in J Autism Dev Disord 41(5):589-596, 2011) across those with (n = 148) and without (n = 168) ASD. Metric variance (equality of factor loadings), but not scalar invariance (equality of thresholds), held suggesting that the AQ-S measures the same latent traits in both groups, but with a bias in the manner in which trait levels are estimated. We, therefore, argue that the AQ-S can be used to investigate possible causes and consequences of autistic traits in both groups separately, but caution is due when combining or comparing levels of autistic traits across the two group
Two sample tests for high-dimensional covariance matrices
We propose two tests for the equality of covariance matrices between two
high-dimensional populations. One test is on the whole variance--covariance
matrices, and the other is on off-diagonal sub-matrices, which define the
covariance between two nonoverlapping segments of the high-dimensional random
vectors. The tests are applicable (i) when the data dimension is much larger
than the sample sizes, namely the "large , small " situations and (ii)
without assuming parametric distributions for the two populations. These two
aspects surpass the capability of the conventional likelihood ratio test. The
proposed tests can be used to test on covariances associated with gene ontology
terms.Comment: Published in at http://dx.doi.org/10.1214/12-AOS993 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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