How can omitted variables create confusion in correlation and causation?

Omitted variables create confusion in correlation and causation primarily because they indicate that a third factor influences both variables being studied. When a relevant variable is left out of the analysis, it can lead to misleading conclusions about the relationship between the two variables under consideration. For instance, if researchers are examining the correlation between ice cream sales and drowning incidents, they might mistakenly conclude that one causes the other. However, if they omit the variable of temperature, they can understand that hot weather influences both higher ice cream consumption and increased recreational swimming, which in turn impacts drowning rates. This illustrates how omitted variables can obscure the true nature of relationships, leading to incorrect interpretations of causation.

In contrast, the other options do not accurately describe the role of omitted variables. The establishment of clear cause-effect relationships typically requires all relevant factors to be included in the analysis. Showing direct links between two variables also depends on a full accounting of all influential factors. Lastly, while redundancies can highlight issues in data, they do not specifically address how omitted variables complicate the understanding of correlation and causation.