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Assessment of reliability of linear relationship between spatially distributed autocorrelated variables

The paper deals with the problem of the assessment of the reliability of the relationship between variables when these variables show a level of spatial autocorrelation (similarity of values between near locations). Relationships between characteristics are being characterized by two different, while similar properties: the strength and the reliability. The commonly used correlation coefficient measures the relationship’s strength and cannot determine by its own whether the relationship is statistically significant. In return, statistical significance is measured with p-level, which shows the probability that the relationship revealed in the sample is non-existent in population. Significance level depends not only on the strength of the relationship but also on the degrees of freedom. Its calculation is based on the assumption of the independent samples. Yet it is often not the case when spatial data are being analyzed. These data are usually characterized by spatial autocorrelation, which leads to highly inflated degrees of freedom and overestimated significance levels. The method to deal with this problem is proposed, based on (Clifford, Richardson, Hemon, 1989). It has been implemented with R function that takes as an input raster layers and by analyzing their autocorrelation structure calculates the effective sample size. On the basis of the latter the variance of correlation coefficient r, its p-level and confidence intervals are calculated as outputs of the function. The created function has been tested by analyzing relationships between terrain parameters (elevation and slope) and land cover characteristic (NDVI index) with data gathered for a test area in the Ukrainian Carpathians and three its subareas. Key words: autocorrelation, statistical significance, R, spatial relationships.