The statistical problem of multiplicity in teleconnection studies was recognized early in this century by Sir Gilbert T. Walker. This problem arises when several sample correlation coefficients between climatic/oceanic time series are computed, but only the largest ones in magnitude are selected as significant. Testing a large number of hypotheses leads to a rapid increase in the probability of erroneously rejecting at least one hypothesis if the significance level of each test is kept fixed. Walker developed methods to counteract the effects of multiplicity, but this problem is still ignored in most modern studies. The effects of multiplicity are compounded for time series with autocorrelation, as is the case for most climatic variables. Monte Carlo simulations of sets of climatic time series indicate that multiplicity can be counteracted by using a modernized version of Walker's approach that includes a correction of the test statistics for the effects of autocorrelation. Overall significance levels obtained by applying other testing approaches that fail to account for either multiplicity or autocorrelation are generally much larger than the desired value.
