Tests used in the empirical sciences are often (implicitly) assumed to be representative of a given research question in the sense that similar tests should lead to similar results. Here, we show that this assumption is not always valid. We illustrate our argument with the example of resting-state electroencephalogram (EEG). We used multiple analysis methods, contrary to typical EEG studies where one analysis method is used. We found, first, that many EEG features correlated significantly with cognitive tasks. However, these EEG features correlated weakly with each other. Similarly, in a second analysis, we found that many EEG features were significantly different in older compared to younger participants. When we compared these EEG features pairwise, we did not find strong correlations. In addition, EEG features predicted cognitive tasks poorly as shown by cross-validated regression analysis. We discuss several explanations of these results.