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38 – Encouraging a Critical Mindset on Social Statistics
Statistical Literacy: Scanlan's Paradox
Milo Schield
Augsburg University
When dealing with binary outcomes, two groups and two situations or times, a counter-intuitive phenomena emerges. As the percentages of one outcome decrease, the associated risk ratio and relative difference tend to increase when using the larger as the numerator. As the percentages of the complimentary outcome increase, the associated risk ratio and relative difference tend to decrease when using the larger as the numerator. Scanlan first identified this situation in 1987. Since then he has written numerous articles trying to increase awareness of these confusing effects. Others have named this result Scanlan's rule. Since this result is so surprising, I call it Scanlan's Paradox. Scanlan described it this way: "The rarer an outcome, the greater tends to be the relative difference in experiencing it and the smaller tends to be the relative difference in avoiding it." This paper presents and analyzes examples of the Scanlan Paradox. When some things improve, other things tend to worsen. This paper reviews Scanlan's 'tendency' and identifies the conditions under which Scanlan's Paradox will occur. Scanlan's call to find a better measure of disparity is strongly endorsed.