Advanced lesson on cognitive biases that distort statistical reasoning and probability judgment. Students learn to recognize the clustering illusion in random data, confirmation bias in data interpretation, anchoring effects on numerical estimates, the ludic fallacy of over-relying on statistical models, and the law of small numbers where people over-generalize from small samples.
The tendency to perceive patterns, clusters, or streaks in random data when none actually exist, or to underestimate how frequently clusters appear in truly random sequences. This involves mistaking the expected irregularity of randomness for meaningful patterns requiring explanation.
The tendency to search for, interpret, emphasize, and recall statistical information in ways that confirm pre-existing beliefs or hypotheses while giving disproportionately less consideration to alternative possibilities or disconfirming evidence. In statistical contexts, this involves selectively analyzing or interpreting data to support preferred conclusions.
The cognitive bias where numerical estimates and probability judgments are overly influenced by initial values or reference points (anchors), even when those anchors are arbitrary, irrelevant, or obviously uninformative. People adjust insufficiently from anchors, leading to systematic bias in numerical reasoning and decision-making.
The erroneous belief that small samples reliably reflect the properties of the population they are drawn from, leading to over-confidence in conclusions based on limited data. This involves expecting small samples to show the same regularities and patterns as large samples, underestimating the role of chance in small sample statistics.
Attributing regression to the mean to a causal intervention when extreme measurements naturally tend to be followed by more moderate ones due to random variation. This fallacy mistakes statistical regression for genuine causal effects.