What is usually meant by logit scale or log scale?

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This question is more about the math terminology than about the math itself. Say we have x = logit(p). If one says "logit scale" does he mean:

1. the scale of p, or
2. the scale of x, i.e. the scale of logit(p)?

The same principle would probably apply if I asked about "log scale", right?

Thank you very much!

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2 Answers

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It is the possibility 2, i.e. the term "log scale" or "logit scale" refers to the scale of the function's output, not to the scale of its input parameter.

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Logit and Log scale are different. Both involve transforming by an increasing function, hence preserving the notion of scale. See the graphs at these links. $\text{logit}(p)=\log(\frac{p}{1-p})$.

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