2,906 research outputs found

    Interim analyses of data as they accumulate in laboratory experimentation

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    BACKGROUND: Techniques for interim analysis, the statistical analysis of results while they are still accumulating, are highly-developed in the setting of clinical trials. But in the setting of laboratory experiments such analyses are usually conducted secretly and with no provisions for the necessary adjustments of the Type I error-rate. DISCUSSION: Laboratory researchers, from ignorance or by design, often analyse their results before the final number of experimental units (humans, animals, tissues or cells) has been reached. If this is done in an uncontrolled fashion, the pejorative term 'peeking' has been applied. A statistical penalty must be exacted. This is because if enough interim analyses are conducted, and if the outcome of the trial is on the borderline between 'significant' and 'not significant', ultimately one of the analyses will result in the magical P = 0.05. I suggest that Armitage's technique of matched-pairs sequential analysis should be considered. The conditions for using this technique are ideal: almost unlimited opportunity for matched pairing, and a short time between commencement of a study and its completion. Both the Type I and Type II error-rates are controlled. And the maximum number of pairs necessary to achieve an outcome, whether P = 0.05 or P > 0.05, can be estimated in advance. SUMMARY: Laboratory investigators, if they are to be honest, must adjust the critical value of P if they analyse their data repeatedly. I suggest they should consider employing matched-pairs sequential analysis in designing their experiments

    Constraints on the χ_(c1) versus χ_(c2) polarizations in proton-proton collisions at √s = 8 TeV

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    The polarizations of promptly produced χ_(c1) and χ_(c2) mesons are studied using data collected by the CMS experiment at the LHC, in proton-proton collisions at √s=8  TeV. The χ_c states are reconstructed via their radiative decays χ_c → J/ψγ, with the photons being measured through conversions to e⁺e⁻, which allows the two states to be well resolved. The polarizations are measured in the helicity frame, through the analysis of the χ_(c2) to χ_(c1) yield ratio as a function of the polar or azimuthal angle of the positive muon emitted in the J/ψ → μ⁺μ⁻ decay, in three bins of J/ψ transverse momentum. While no differences are seen between the two states in terms of azimuthal decay angle distributions, they are observed to have significantly different polar anisotropies. The measurement favors a scenario where at least one of the two states is strongly polarized along the helicity quantization axis, in agreement with nonrelativistic quantum chromodynamics predictions. This is the first measurement of significantly polarized quarkonia produced at high transverse momentum
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