Is rank measured by ordinal or interval scale?

[Ajey]

Is rank, (in case of students, 1, 2, 3...) measured by ordinal or interval scale? It does satisfy the definition of interval scale measurement, but is a categorical variable! Please explain your answer too.

[Statistics 1 Support 1]

Hello Ajey,

Rank in a class like 1, 2, 3... would clearly be interval scale as you mentioned as it satisfies the interval scale properties. If you talking about ranking like in military Major, Captain, Colonel then ranking is ordinal scale of measurement.

Thanks,

Ram,

Statistics-1 Course Support Team,

IITM Online Degree Programme

[Ajey]

Yeah, but rank, by itself, is a categorical variable, no? And categorical variables can only be measured by nominal or ordinal scales, ma'am stated in the last lecture. So if it will be measured by interval scale, is it an exception or is there some other reasoning?

On Friday, October 9, 2020 at 5:29:51 PM UTC+5:30, Ajey wrote:

[Statistics 1 Support 1]

Hello Ajey,

Rank by itself can be considered as categorical variable if you are just qualifying them but when you give the order in form of numbers like 1st, 2nd, and 3rd rank we clearly know that there is an order and has specific units. The difference between 2nd and 1st rank is same as difference between 3rd and 2nd rank. So, it becomes a interval scale. 

When ma'am mentioned ranking is ordinal scale ma'am meant there is an order and differnece between two consecutive values need not be the same. But in our case the difference is clearly the same. Hope this clarifies you doubt. 

Best.
Ram,

Course support team,

IITM online degree programme.

[Advaith Music]

I just saw the  course support sir stating

'The difference between 2nd and 1st rank is same as difference between 3rd and 2nd rank. So, it becomes a interval scale.'

How can the differences between the ranks be same(No same mark differences b/w ranks? If so shouldn't difference between temperatures also be same? Also if the differences in between are same, then shouldn't it be ratio scale? (I know in ranks there is no use in multiplication or division) . So shouldn't ranking mean Interval scale Or if not coding of ordinal variables? 

[Anand Iyer]

Advaith,

DIfference between the ranks of an interval scale is the same, but that doesn't mean you can do ratios among them.

In the case of temperature, it's interval scale, and a temperature reading 10 has the same difference from 20, as it has from 0.  But, can't say 20 is double as hot as 10.

Essentially, interval scale can be subjected to subtraction, but only ratio scale can be subjected to division.