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I have this data:

Age         Pitch (Hz)       
10      312.53
15      280.12                  
18      250.66                  
21      240.66              
... 

My questions is if age interval scale or ratio scale? I don't have the data for some of the years (see table).

And is Pitch ratio scale? or is it also interval scale?

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Yes it depends on measurement. A somewhat elusive answer is that it does not really matter in most cases, as for most statistical purposes the two are identical (e.g. used the same and interpreted the same as a covariate in regression analysis).

As I see it, it does not matter much if you have measurement gaps or not (unless you have fewer than say, 5 ranks). An interval scale has meaningful and constant intervals between values which enables addition and subtraction. So you could say that the diff between 4 and 5 is exactly the same as the diff between 230 and 231. But this scale has an arbitrarily assigned zero.

A ratio scale has the first characteristic of the interval scale (interval) but also has a meaningful zero point---which means the absence of the attribute. This enables multiplication and division on the values.

Using the aforementioned definition, age is in a ratio scale. Age 0 = no age. A person who is 30 years old is half as old as someone who is 60, and twice as old as someone who is 15. compare this to temperature in Celsius if you will - 0 is arbitrarily chosen to represent the freezing point of water, not the lack of temperature. You can say that the difference between 20 and 21 degrees is identical to the difference between -1 and 0. You cannot, however claim that 10 degrees is twice as warm as 5 degrees - it makes no sense. So temperature in Celsius is on an interval scale.

Using the same principle Hz if defined by circles per second, is also in a ratio scale. 0 is non, 5 Hz is half as much as 10 Hz etc ...

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    $\begingroup$ Problems with age being ratio scale: Is zero (moment of birth) really a meaningful zero? Life started about 9 months before that ... But does it really matter? Most analysis I can thin of would not use moment of birth as a real zero. One could even ask if age is really, really interval---is the difference $1-0$years really the same as $11-10$years? $\endgroup$ Mar 3, 2020 at 13:03
  • $\begingroup$ In fact ratio scale is defined, according to Stevens, by the family of transformations that doesn't change the information content/meaning. For interval scales it's linear transformations f(x)=ax+b, for ratio scales only f(x)=ax. It all depends on whether you think that age can be meaningfully transformed by adding/subtracting a constant. Surely it can be meaningfully transformed by going from years to days etc. But as stated by others, if adding/subtracting a constant doesn't change the statistical analysis that is done, it doesn't matter. $\endgroup$ Mar 3, 2020 at 15:21
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Suppose you have 10g of liquid water at 0 degree C, If you apply 21 joules of heat the temperature rises to 5 degree C; if you apply 42 joules of heat the temperature is 10 degree C. So why can't you say it is twice as warm?

If you want to have zero heat, you need to reach -273 degree C which is zero K (Kelvin). People started the Celsius scale way before thermodynamics prove that zero K is the absolute zero that you cannot go any lower. So temperature has a natural zero, it is just that Celsius is off by 273 degree

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  • $\begingroup$ (-1) If I eat one pound of food I gain one pound in mass. If I eat another pound of food, I gain another pound: does that make me twice as heavy?? $\endgroup$
    – whuber
    Mar 3, 2020 at 13:07

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