# Test scores out of 20: ordinal, interval or ratio

#### ThimoDS

##### New Member
Hello,

What scale of measurability do you assign to a dataset of test scores on an exam?

e.g. 5/20, 5/20, 7/20, 18/20

Is this ratio-scaled data?

King regards and thanks in advance

#### ondansetron

##### TS Contributor
Howdy! It may be useful to start with the definitions.

What is the meaning of a variable that is measured on the interval scale? How about on the ratio scale?

#### ThimoDS

##### New Member
Howdy! It may be useful to start with the definitions.

What is the meaning of a variable that is measured on the interval scale? How about on the ratio scale?

As I was taught, interval scaled data is quantitative data in which differences have a meaning (so for example when you add +1 it always adds the same), but ratios don't mean anything (so for example doubling doesn't mean anything) and there's no fixed 0. We saw temperature as an example (difference between 20-21 and 70-71 degrees is the same 1 degree, but 20 degrees isn't "twice as cold" as 10 degrees and 0 degrees does not mean an "absence of temperature". Ratio is also quantitative data, but there's a fixed 0 and ratio's do make sense.

Kind regards

#### Karabiner

##### TS Contributor
We saw temperature as an example (difference between 20-21 and 70-71 degrees is the same 1 degree, but 20 degrees isn't "twice as cold" as 10 degrees and 0 degrees does not mean an "absence of temperature".
But not if you mean degrees Kelvin. (SCNR)

Is this ratio-scaled data?
It depends on what is actually measured, and what it is intended to represent.. If the scores just mean "number of correct answers", then you could perform operations for ratio scales. If it represents "intellectual capability in field X" or something like this, a zero value probably would not mean Zero capability. The same as there's no zero intelligence, even if there are people who are not able to give just 1 correct response in an intelligence test.

What do you need the answer for?

With kind regards

Karabiner

#### ThimoDS

##### New Member
Not if you mean degrees Kelvin. (SCNR)

It depends on what is actually measured, and what it is intended to represent.. If the scores just mean "number of correct answers", then you could perform operations for ratio scales. If it represents "intellectual capability in field X" or something like this, a zero value probably would not mean Zero capability. The same as there's no zero intelligence, even if there are people who are not able to give just 1 correct response in an intelligence test.

What do you need the answer for?

With kind regards

Karabiner
Hello,

I was indeed talking about degrees celcius, should have mentioned that!

Thanks for your answer, it's very clear to me now. The distinction between number of correct answers and something like an IQ score is indeed a difference I did not immediately notice.

I don't need it for anything particular, I was practicing for an exam next Wednesday and was making some exercises I found online.

Thanks you very much and kind regards

#### ondansetron

##### TS Contributor
But not if you mean degrees Kelvin. (SCNR)

It depends on what is actually measured, and what it is intended to represent.. If the scores just mean "number of correct answers", then you could perform operations for ratio scales. If it represents "intellectual capability in field X" or something like this, a zero value probably would not mean Zero capability. The same as there's no zero intelligence, even if there are people who are not able to give just 1 correct response in an intelligence test.

What do you need the answer for?

With kind regards

Karabiner
Karabiner hit these both, and I would have provided the Kelvin example also because temperature is measuring kinetic energy/movement if I remember, and absolute zero is zero Kelvin, which is defined as the absence of movement/kinetic energy (no heat). Celsius and Fahrenheit, however do not measure the same thing at their respective zeros (if I recall, 0 C is +278 K and this would be 32 F).

If this is just simply a number of correct responses out of 20, this can be ratio.