Visualizing Correlations

For dimension two, we have either the bivariate normal with unit variances, mean zero, and correlation parameter , or, in the contaminated case (with a 10% probability), the observation is replaced with one from the same distribution but multiplied by 3. The contaminated distribution is sometimes used to describe non-normal data with a higher proportion of outliers than the normal. The estimated correlation is shown and reflects the pattern seen in the data, but it may not be an accurate estimator of for small even in the normal case. Increasing increases the accuracy of the estimator . If is kept fixed, the variability of the estimator decreases as the absolute magnitude of is increased. This is seen by varying the seed and then experimenting with different . As we zoom out, our perception may spuriously suggest that the association between the variables increases. Using the contaminated normal distribution increases the variability in our estimate and the likelihood of an apparent spurious association when .

For dimension three, the symmetrically correlated trivariate normal distribution is used. Once again the effect of the contaminated normal is to increase variability in .