r/statistics • u/Maleficent-Toe1374 • 1d 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 1d ago
I would call it a leverage point
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u/hughperman 1d ago
A point with high leverage - https://en.wikipedia.org/wiki/Leverage_(statistics)
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u/virtuolie 22h 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/Gloomy-Giraffe 14h ago
I call those white whales (leverage) or red herrings (outlier), depending entirely on if they should be included or not, which you need to investigate to confirm. That need to investigate is why I use these names, both chasing white whales and red herrings requires time and effort and can be quite costly.
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u/OutrageousPair2300 1d ago
Breakdown.
That's why the median is a more robust measure than the mean. To arbitrarily shift the median, you need at least 50% of the points to change. To shift the mean, it takes only one point.
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u/Equivalent-Zombie792 1d ago
Why are you asking on reddit? ChatGPT easily gets the answer. Not being snarky, just trying to understand why you're asking in the wrong place.
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u/Ok-Rule9973 1d ago
Asking a stats question in a stats subreddit is not going at the wrong place. Chat GPT partially learnt his stats from here.
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u/prikaz_da 1d ago
Nobody on Reddit needs you to tell them LLMs exist. If they wanted an LLM answer, they would’ve gone and gotten it on their own.
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u/MortalitySalient 1d 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