Nothing like asking a question to get you thinking about how to answer it. Ward & Gleditsch show a calculation provided by Cressie which relates spatial correlation to overstating the sample size (Ward & Gleditsch 2008). Of course the sample size is also overestimated when calculating Level 2 effects in a multilevel model, and this can be computed with the design effect, at least when groups are the same size.
A t value for regression coefficient b is the ratio of b to its standard error, which can be expressed as SQRT ( (1-r^2) * ( Σ(y-[y-bar])/(N-2) ) ). That's the variance of Y (multiplied by the unexplained variance). So one way of unifying the explanation of uncontrolled spatial autocorrelation and uncontrolled intraclass-correlation on the results of a method like ordinary least squares, at least for sigificance testing of regression coefficients) is to talk about in terms of overstated sample size.A t value for regression coefficient b is the ratio of b to its standard error, which can be expressed as SQRT ( (1-r^2) * ( Σ(y-[y-bar])/(N-2) ) ). That's the variance of Y (multiplied by the unexplained variance). So one way of unifying the explanation of uncontrolled spatial autocorrelation and uncontrolled intraclass-correlation on the results of a method like ordinary least squares, at least for sigificance testing of regression coefficients) is to talk about in terms of overstated sample size.
Is this reasonable?