Individuals tend to select again alternatives about which they have positive impressions and to avoid alternatives about which they have negative impressions. Here we show how this sequential sampling feature of the information acquisition process leads to the emergence of an illusory correlation between estimates of the attributes of multi-attribute alternatives. The sign of the illusory correlation depends on how the decision maker combines estimates in making her sampling decisions. A positive illusory correlation emerges when evaluations are compensatory or disjunctive and a negative illusory correlation can emerge when evaluations are conjunctive. Our theory provides an alternative explanation for illusory correlations that does not rely on biased information processing nor selective attention to different pieces of information. It provides a new perspective on several well-established empirical phenomena such as the "Halo" effect in personality perception, the relation between proximity and attitudes, and the in-group out-group bias in stereotype formation.