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I'm now reading a note on Biostatistics written by PMT Education, and notice the following sentences in Section 2.7:

A baby born at the 50th percentile for mass is heavier than 50% of babies.
A baby born at the 25th percentile for mass is heavier than 75% of babies.
A baby born at the 75th percentile for mass is heavier than 25% of babies.

But as I know, a baby born at the 25th percentile for mass should be heavier than 25% of babies. Is there a special definition of "percentile" in this field, or I misunderstand the sentences as a non-native speaker?

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    $\begingroup$ Your understanding is correct. Especially in Biomedicine percentile descriptors are following the basic idea of left to right. I worked with people from WHO in the past, saying: "A baby born at the 75th percentile for mass is heavier than 25% of babies." would probably make them think I am statistically illiterate. $\endgroup$ – usεr11852 Jul 10 at 17:43
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While the definition of percentiles given by Stephen Kolassa is technically correct in statistical theory (the best kind of correct?), this is an issue where there is a lot of variation in practice --- some people refer to percentiles with the highest percentile as the maximum, but others flip it over so that the highest percentile is the minimum. In the latter case people will sometimes talk about someone being in the 5th percentile when they are in the top five percent, rather than the bottom five percent. Sometimes they will say this explicitly (e.g., John Smith is in the top 5th percentile for shot-put distance), but sometimes they won't specify this clearly. For this reason, it is always important to clarify with the reader/speaker which way around they are defining the percentiles. (In the absence of any specification to the contrary, they should really use the standard statistical definition.)

Also, I disagree with Stephen on one point. I doubt this is a typographical error. More likely, the writer of the document is simply speaking of percentiles in the second sense I have described, which while not technically correct, is nonetheless quite common. I don't really regard this as an "error" so much as a non-standard use of the term, which is excusable if it is explained. Here is an example of the reversed use of "percentiles" in an article on income levels in the Wall Street Journal. (Most instances of reversal of the percentages occur in the context of discussions of wealth/income levels. Though it is much less common than the technically correct usage, it occurs commonly enough that you need to be careful to check the meaning.) Here is a follow-up question where I seek examples of this reversed practice.

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    $\begingroup$ This is interesting but implausible: growth charts are standard stuff. I haven't ever seen the definition of percentiles reversed there. See cdc.gov/growthcharts/who/boys_weight_head_circumference.htm for a WHO chart, for instance. Thus, I would find your explanation more credible if you could exhibit some instances of the reversed percentiles in actual use (preferably by some recognizable authority and not just, say, a school teacher or Web blogger). $\endgroup$ – whuber Jul 10 at 12:21
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    $\begingroup$ I agree with @whuber. I have never seen the practice you refer to. "Top five percent" to refer to someone at or above the 95th percentile, yes, but "at the 5th percentile" to refer to the same someone, no. Do you have any examples of this use? $\endgroup$ – Stephan Kolassa Jul 10 at 13:34
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    $\begingroup$ @Stephen: Well you've both seen it at least once, in the quoted section in the question. So that is one data point of evidence in favour of this practice existing. I don't think it is the kind of thing you are likely to see in authoritative sources, precisely because those sources tend to check the technical meaning. However, I have seen this reversing done informally (arguably by mistake, but still sufficiently common that it is important to check). $\endgroup$ – Ben Jul 10 at 13:41
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    $\begingroup$ In discussions of wealth/income, it is not unusual for sources to refer to the top X% of wealth/income, and in such cases, it is also not uncommon for them to drop the reference to the top and just say "the 1%" or "the 10%". Here is an example of an article about "the global 1%" where you have to read three paragraphs in before they specify that they are talking about the top 1%. This reversal of percentile reference is fairly common in discussions of wealth/income. $\endgroup$ – Ben Jul 10 at 14:02
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    $\begingroup$ @Ben: thank you. (Incidentally, if you use "@Stephan", not "@Stephen", I'll be notified.) I concede your point. However, I'd like to point out that this usage typically involves "the 1%", rarely "the 1% percentile". $\endgroup$ – Stephan Kolassa Jul 10 at 14:56
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This is just a typo in the document. Your understanding of percentiles is correct.

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    $\begingroup$ For a broad definition of "typo". $\endgroup$ – Acccumulation Jul 10 at 18:10
  • $\begingroup$ The text goes on to say: Being in a high percentile (e.g 90th percentile or higher) can indicate a health problem. It's not a typo - the author is either mistaken or for some reason uses growth charts that are backwards. $\endgroup$ – JPhi1618 Jul 11 at 14:51
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    $\begingroup$ Or, while admittedly very confusing, the surrounding context of the snippet ranks weight on an inverse scale. For example, the 90th percentile of 100m runners take less time to run 100m than 90% of runners. The surrounding context might make such an interpretation clearer, e.g. when focusing on the severity of being underweight: severity goes up as weight goes down. If the severity is the main focus, it makes sense to sort it by severity (and thus inversely by weight); similar to how you sort track runners by performance (and inversely by time taken to complete the run). $\endgroup$ – Flater Jul 11 at 16:05

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