## Primary Scales of Measurement

There are 4 primary scales of measurement:

Interval and ratio à numerical scales

Example: Assigning a number to a person’s gender, say 0 for male and 1 for female, or vice versa.

When a nominal scale is used for the purpose of identification, there is a strict one-to-one correspondence between the numbers and the objects.

Example: Student identification number, Social Security number, PAN, etc.

Example:

One thing to note is that all the information that's contained in an ordinal scale is also contained in an interval scale, but the key difference is that with an interval scale, you can compare the differences between two points, between objects.

However, the location of the zero point or the zero reference point is not important, it's not fixed.

For example: Temperature. If something is 32 degrees Fahrenheit, and then a couple hours later, let's say it's the temperature, it's 34 degrees Fahrenheit, we can say that there was a difference of two degrees Fahrenheit. That's two degrees Fahrenheit is the same difference as between 60- and 62-degrees Fahrenheit. So, we can take the differences and compare those differences, and comparing those differences would have meaning. But if you think about the zero point, it's arbitrary. What is zero degrees Fahrenheit? It's an arbitrary point on the scale. It really does not have meaning. Whereas in the Celsius scale, the zero point, it's tied to the freezing point of water, but it's also an arbitrary point. The reason it's called interval scale data is that you can only look at intervals, the difference between two data points.

Thus, with ratio scale, we can identify or classify objects, rank the objects, and compare intervals or differences.

Example: height, weight, age

- Nominal
- Ordinal
- Interval
- Ratio

Interval and ratio à numerical scales

__Categorical scales:__**Nominal scale (order does not matter)**

Example: Assigning a number to a person’s gender, say 0 for male and 1 for female, or vice versa.

When a nominal scale is used for the purpose of identification, there is a strict one-to-one correspondence between the numbers and the objects.

Example: Student identification number, Social Security number, PAN, etc.

**Ordinal Scale (order matters)**

Example:

- class rank (freshman, sophomore, junior, senior – 0,1,2,3)
- Military rank (private, corporal, sergeant)
- Level in an organization

*Order matters*but we don’t know if these objects are spaced equally apart__Numerical Scales:__**Interval Scale**

One thing to note is that all the information that's contained in an ordinal scale is also contained in an interval scale, but the key difference is that with an interval scale, you can compare the differences between two points, between objects.

However, the location of the zero point or the zero reference point is not important, it's not fixed.

For example: Temperature. If something is 32 degrees Fahrenheit, and then a couple hours later, let's say it's the temperature, it's 34 degrees Fahrenheit, we can say that there was a difference of two degrees Fahrenheit. That's two degrees Fahrenheit is the same difference as between 60- and 62-degrees Fahrenheit. So, we can take the differences and compare those differences, and comparing those differences would have meaning. But if you think about the zero point, it's arbitrary. What is zero degrees Fahrenheit? It's an arbitrary point on the scale. It really does not have meaning. Whereas in the Celsius scale, the zero point, it's tied to the freezing point of water, but it's also an arbitrary point. The reason it's called interval scale data is that you can only look at intervals, the difference between two data points.

**Ratio Scale**

Thus, with ratio scale, we can identify or classify objects, rank the objects, and compare intervals or differences.

Example: height, weight, age

**Note:**We can go from ratio scale data up to less granular levels of data. The opposite, however, is not possible.