# Chained inequality signs in opposite directions

#### Lafargue

##### New Member
Dear all,

I have no higher educational background in statistics or mathematics. I am almost embarrassed to come here ask for help, but it seems for me that either an elementary principle of inequality is wrong in a research paper or that I am lacking basic skills in Maths. I have tried to search online, but I could not find anything to address the issue.

I need to present an academic article, in which there is this table I am having trouble with. The problem is that the signs in the chained inequalities seem wrong for me. I am attaching a screenshot to this post with the said table (in the table "HC" stands for head circumference).

For example, how can "-2 < HC > -3" be possible? Is it possible that in any given circumstances the signs in a chained inequality point to opposite directions? In my interpretation it is clear that what the authors mean is that HC is between -2 and -3, but that doesn't seem to be the correct notation. Furthermore, such notation is repeated several times in the table, seeming unlikely that it was an occasional mistake.

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#### hlsmith

##### Not a robit
First thing first, do you know what standardized values are. These values (in the table) appear to be for the proportion with a head, say smaller than 1 standard deviation below (negative) the mean. So for example 24/100 had a HC < 1 standard deviation below the mean HC. Without looking at the article, we can't know the data source, but for example, pediatricians look at Z-score BMIs based on a representative sample (population). So if a kid had a -2 Z-score it means their BMI is 2 SDs below the mean or given the standard normal curve, their BMI is at around the 2.5 percentile of all children given age and gender.

Let me know if this doesn't clear up your question. But I would refer you to the standard normal curve.

#### Lafargue

##### New Member
Dear hlsmith,

Thanks a lot for your response.

I am familiar with standard normal distribution, but I have just revised the subject, thanks for the advice.

You guessed it correctly, the data presented comes from a population with from which the head circumference was measured. The SD presented is always negative because it refers to children with microcephaly. Nevertheless, I am sending the article attached if you would like to have a look.

I believe I understood and interpreted correctly the data presented in the table. Perhaps my question was not clear, I will try to rephrase it. My question is if notations presented in the table like this: "-2 < HC > -3" or "-1 < HC > -2"; shouldn't be written instead like this: "-2 > HC > -3" or "-1 > HC > -2".

My question regards only to the direction of the inequality signs. For me it makes no sense to present something like "-2 < HC > -3", because it is the equivalent to saying that the head circumference is a measure greater than "-3" and "-2", which would be redundant and illogical in accordance with the other inequalities presented.

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#### hlsmith

##### Not a robit
Gotcha. Yeah, just a typographical error. I would say in most papers you can find some type of error in the reporting or text. It is hard to write 3,000+ words and results without any errors. You can also see that the numerators sum to the denominator across the subcategories, providing evidence toward it being a possible typographical error. Looks like this was published in BMJ, you may want to look to see if there was an associated erratum published