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I'm writing up the results of a measure of emotional management, and I'm hypothesising that under- or over-management of emotions leads to negative consequences.

I'm looking for a term which expresses that both a very high, or a very low score, on this measure, is suboptimal (unlike, for example, IQ, in which a higher score is always considered superior to a lower one), but I can't think of, or find an appropriate term.

It was suggested to me, by a colleague, to use the term "curvilinear", but I don't think that expresses what I want.

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    $\begingroup$ Your colleague is correct. When you refer to an inverted U shape the term you want to use is curvilinear relationship if you are describing it statistically. $\endgroup$ – Rooirokbokkie Mar 31 '16 at 13:30
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    $\begingroup$ Curvilinear could go the other way, though (Optimal at either end, suboptimal in the middle). $\endgroup$ – K A Apr 1 '16 at 16:38
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I recommend looking at non-scientific writing describing when too much AND too little of something is not good-- when average/in the middle is best for a certain outcome. This is true in many aspects of life, so you'll find a variety of words that may express what you want to convey about these high-end suboptimal and low-end suboptimal scores.

English StackExchage wordies may know an existing noun/adjective for exactly what you want. If there isn't a word to express what you mean, you're free to create one. Perhaps pairing the prefix "extra-" in the sense of "outside the optimal range", or the prefix "dys-" in the sense of "unfavorable scores" with word(s) relevant to the measure.

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I think Inverted U is what you're looking for.

The specific example given by Wikipedia is the Yerkes–Dodson law, which essentially states that arousal levels that are too high and too low have negative effects on performance of certain tasks.

There are many other examples of this type of relationship. Here is another example, showing that the level of alpha (10 Hz neural oscillations) before a visual stimulus has an inverted U shaped relationship with the evoked response to the stimulus.

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