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Consider

The variables show low correlation.

vs

The variables show a low correlation.

Is one version simply wrong? Is one more idiomatic than the other?

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"Correlation" is one of those tricky nouns that can be either countable or uncountable with the same meaning. In most cases it is used as a count noun (meaning it is countable). For instance:

We see clear evidence of a strong correlation between class attendance and exam scores.

We believe there is a correlation between texting and myopia.

However, it can also be a mass noun, especially when used to convey a negative sense, indicating a weak association or an unconvincing causal relationship.

Stocks do not respond to rate changes in the same way as bonds do, so there is little correlation between stock and bond value with respect to interest rates.

So the sentence you are asking about is perfectly grammatical without the indefinite article:

The variables show low correlation.

But the version with the article "a" is also fine and idiomatic. These two versions have a slight difference in meaning. When you drop the indefinite article, the sentence indicates a stronger sense of the correlation being low or next to nonexistent.

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In "show low correlation," correlation is a verb. In "show a low correlation," correlation is a noun. There's a not at all subtle difference.

As a verb, it's a statement of fact. As a noun, it's a statement of (informed) opinion. It's similar to the difference between the scientific definitions of "theory" and either "hypothesis" or "conjecture." In science, a theory is a well established principle that is as true as anything can be. An hypothesis or conjecture is something for which there is good evidence, but not sufficient to be accepted as true.

"show a low correlation" is more appropriate (likely?) to be used when referring to one or just a few research studies. "show low correlation" is more appropriate (likely?) to be used when referring to many research studies.

Not that everyone in math, science, and engineering know or bother about such things. But most technical editors will know the distinction.

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  • Thank you for the answer. However, I fail to see how "correlation" could ever be a verb. Could you clarify this?
    – Wang Tang
    Aug 26, 2018 at 7:39
  • Something can accelerate. When it is accelerating we call it acceleration. Something can vibrate. When it is vibrating we call it vibration. Something can correlate. When it is correlating we call it correlation. Acceleration is not an acceleration. Vibration is not a vibration. Correlation is not a correlation. Each of vibration, acceleration, and correlation is an active condition. Each of an acceleration, a vibration, and a correlation is an event.
    – oftenconfused
    Aug 26, 2018 at 8:52
  • You should probably edit the explanation above into your answer.
    – ColleenV
    Aug 26, 2018 at 11:51
  • "accelerate" is a verb, "acceleration" is not. AFAIK, as a nominalized verb, it is in fact a noun. However, it is indeed an interesting observation that the nominalized forms you mentioned seem to work with and without determiner, but with (slightly) different meaning, as you said between active condition (process?) and event. But separating these in specific use cases still seems hard for me. Might this just be a matter of focus?
    – Wang Tang
    Aug 26, 2018 at 16:04
  • No, correlation is not a verb in show low correlation. The difference between your two examples is not whether it's a verb or a noun, it's whether it's count or non-count, as Eddie Kal's answer explains.
    – user230
    Aug 27, 2018 at 2:51

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