Meta Analysis: A Guide to Calibrating and Combining by Elena Kulinskaya

By Elena Kulinskaya

Meta research: A consultant to Calibrating and mixing Statistical Evidence acts as a resource of easy equipment for scientists desirous to mix proof from diverse experiments. The authors target to advertise a deeper figuring out of the idea of statistical evidence.

The booklet is constituted of components – The Handbook, and The Theory. The Handbook is a advisor for combining and examining experimental proof to unravel normal statistical difficulties. This part permits anyone with a rudimentary wisdom as a rule data to use the tools. The Theory presents the incentive, idea and result of simulation experiments to justify the methodology.

it is a coherent creation to the statistical ideas required to appreciate the authors’ thesis that proof in a try statistic can usually be calibrated whilst reworked to the precise scale.

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E. the overall reduction in length of stay. 5 Comparing K treatments In this chapter we consider the simplest case of treatment comparisons. Based on K samples taken under K different conditions we want to know whether the conditions lead to notable changes in the sample means. 1 Methodology Data and model • We are given K sequences of measurements of some outcome variable Y : y11 , . . , y1n1 through yK1 , . . , yKnK . The measurements are taken under varying conditions, either by applying different treatments or by modifying in some other way the circumstances of the measurements.

Xn on a variable X obtained by an instrument of unknown precision. • The measurements are considered independent observations from a normal population with unknown parameters µ, σ. Questions • What is the evidence for a positive effect µ − µ0 > 0; or, equivalently, for a positive standardized effect δ > 0? • What is a confidence interval for µ or for δ? Meta Analysis: A Guide to Calibrating and Combining Statistical Evidence E. Kulinskaya, S. Morgenthaler, and Robert G. Staudte © 2008 John Wiley & Sons, Ltd.

1), for sample sizes n ≥ 5 and δ encountered in applications. 2. 8). The corrected evidence Tunbiased is preferable to T . 85, but nominal 95 % confidence intervals for δ have coverage nearer 97 %. 0, and nominal 95 % confidence intervals for δ are reliable for |δ| < 2. This interval includes most δ encountered in applications. 0, and nominal 95 % confidence intervals are reliable for |δ| < 10. 1) where ln(x) = loge (x) is the natural logarithm. 1. 1. 1 K(δ) plotted as a function of δ. The graph is typical of many key functions K(·) which determine the expected evidence in different contexts, in that for small values δ the function K(δ) ≈ δ, but larger values are√diminished in magnitude, in this case logarithmically.

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