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Law, Probability and Risk Advance Access originally published online on March 27, 2009
Law, Probability and Risk 2009 8(1):25-38; doi:10.1093/lpr/mgp008
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© The Author [2009]. Published by Oxford University Press. All rights reserved.

The effect of dependence between observations on the proper interpretation of statistical evidence

Yulia R. Gel{dagger}

Department of Statistics and Actuarial Science, University of Waterloo, 200 University Ave. W, Waterloo, ON, N2L 3G1 Canada

Weiwen Miao{ddagger}

Haverford College, Haverford, PA 19041, USA

Joseph L. Gastwirth§

Department of Statistics, George Washington University, Pennsylvania Ave. 2140, Washington, DC 20052, USA

{dagger} Corresponding author. Email: ygl{at}math.uwaterloo.ca

{ddagger} Email: wmiao{at}haverford.edu

§ Email: jlgast{at}gwu.edu

Received on 25 June 2008. Revised on 5 February 2009. Accepted on 11 February 2009.


  Abstract

In a recent securities law case, the statistical methods used by the regulator in analysing data on daily commissions and hypothetical profits from initial public offerings (IPOs) assumed that the data on consecutive days were independent. Consecutive observations in most business and economic data, however, are positively correlated. While statistical articles demonstrate that this type of dependence affects the distribution of virtually all statistics, including non-parametric and goodness-of-fit tests, the magnitude of the effect may not be fully appreciated. For example, in one comparison of commissions one broker received on days with an IPO to the days when no IPO was issued yielded a statistically significant p-value of 0.02, under the independence assumption. Accounting for serial correlation, the test actually had a non-significant p-value close to 0.09. Other examples of the effect of dependence include jury discrimination cases in locales where grand jurors can serve two consecutive terms as well as cases concerned with environmental pollution where measurements are spatially and temporally correlated. This paper describes the noticeable effect violations of the independence assumption can have on statistical inferences. The methods for correcting some standard non-parametric tests for serial correlation are also discussed.

Keywords: serial correlation; dependence; non-parametric tests


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