Evaluating the Percentage Points of a Spatial Autocorrelation Coefficient

Various statistics have been proposed in the literature to test for the presence of spatial autocorrelation on a random variable measured in each ‘county’ of a ‘country’. These measures are reviewed in Cliff and Ord [ I ] . In most empirical applications, the researcher will wish to determine the degree of significance of the calculated value of the test coefficient used. Unfortunately, very little is known about the sampling distributions of any of the spatial autocorrelation coefficients, particularly in the tail areas which are critical for significance testing, in the small and moderate sized lattices usually encountered. This is clearly a severe handicap in proposing a reliable test of significance for any of the coefficients. It is the purpose of this paper to evaluate the sampling distribution in the tail areas of the spatial autocorrelation coefficient defined below. A suitable approximation to the sampling distribution of the coefficient is suggested which provides the basis for a reliable test of significance. Monte Carlo methods are used. Consider a county system which comprises n counties. Suppose that a variate, X , has been measured in each of the n counties. Let the value of X in the ith county be xi and define x i = xi 2. The effect of county i on county j is denoted by the weight, wij . Then, the authors have proposed [ I ] , the following measure of spatial autocorrelation between the xi :