Collection 7.8

Numerical Misrepresentation

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).

What to Notice

  • Identify misleading presentations of statistical information
  • Distinguish between percentage changes and absolute changes in risk or outcome
  • Recognize when base rates are essential for interpreting numerical claims
  • Detect Simpson's Paradox where aggregate trends reverse in subgroups
  • Evaluate numerical claims for potential misrepresentation or manipulation

Concepts in This Collection

F097

Misleading Statistics

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.

1 of 5
F098

Percentage Fallacy

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.

2 of 5
F099

Absolute vs Relative Risk

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.

3 of 5
F100

Base Rate Neglect

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.

4 of 5
F101

Simpson's Paradox

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.

5 of 5