r/statistics • u/Maleficent-Toe1374 • 4d ago
Question [Question] What is it called when one plot point shifts an entire study?
Is there a name for the concept of one point being such an outlier that it actually shifts the average above any other known point.
For example let’s say there’s 10 people in a study, 9 of them generally average let’s say 150 lbs weight wise with normal distribution, but then one person who weighs upwards of 600 lbs and they actually shift the entire graph to the average weight now being 210 lbs.
What would this concept be called?
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u/Silviaso3536 4d ago
I would call it a leverage point
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u/hughperman 4d ago
A point with high leverage - https://en.wikipedia.org/wiki/Leverage_(statistics)
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u/virtuolie 3d ago
Since others have given you the correct answer already, I'll add a note about analysis, which may be more subtle than what you hear in a classroom. Namely, how you interpret the data point can depend on whether the study is descriptive vs causal. If you're describing some extant characteristic in the population, being an extreme outlier may be evidence of membership in a separate population or at least of sampling from a low-probability region of the same distribution. There's a strong rationale for interpreting the data without the data point. (Although you should report the outlier and its omission from the analysis.) If you're measuring an effect, conditioning the analysis on post-causal outcomes can invalidate your causal interpretation completely. I mean, people still do it (because what else are you going to do?) but it likely breaks the "causal" part of your causal analysis. On the other hand, if it's a pre-causal measure, you may be required to omit the associated post-causal data point, or at least to reweight it appropriately.
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u/MortalitySalient 4d ago
That would be an influential case. One with high leverage and high influence. Could be an outlier, could also be part of the population of interest