Advanced lesson on fallacies involving misleading use of statistics and numerical information. Students learn to recognize misleading statistical presentations, distinguish between absolute and relative risk, understand base rate neglect in numerical contexts, and identify situations where aggregated data reverses in subgroups (Simpson's Paradox).
Presenting technically accurate statistics in ways that create false or misleading impressions through selective framing, inappropriate comparisons, omitted context, or exploiting statistical illiteracy. The numbers themselves are correct but their presentation is designed to deceive or mislead rather than inform.
Misinterpreting or being misled by percentage changes without considering the base numbers, or treating percentage changes as symmetric when they are not. This includes failing to recognize that a 50% decrease cannot be reversed by a 50% increase, and that identical percentage changes can represent vastly different absolute changes depending on the base.
Confusing or selectively presenting relative risk (the ratio of risks between groups) versus absolute risk (the actual probability of an event), often presenting relative risk increases while hiding small absolute risks to make effects appear more dramatic or consequential than they actually are.
Ignoring or underweighting the base rate (prior probability or prevalence) of an outcome when evaluating numerical evidence, particularly in contexts involving diagnostic tests, risk assessment, or prediction. This leads to systematic overestimation or underestimation of probabilities when base rates differ significantly from intuition.
A phenomenon where a trend or relationship appears in several subgroups of data but disappears or reverses when the subgroups are combined into aggregate data, or vice versa. This occurs due to confounding variables that affect both group membership and the outcome, creating misleading conclusions when data is examined at the wrong level of aggregation.