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What is the level of measurement where outcomes are based on some underlying continuum where it is possible to speak about how much more a higher performance is than a lower one?

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The answer is interval level of measurement. In this level of measurement, the distance or space between points does have significance. For instance, when we measure temperature (in Fahrenheit), the distance from 80-90 is similar as the distance from 100-110. Thus, the interval between values is interpretable.

User SeriousLee
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