A simple example given below will explain the difference among 4 basic measurement scales: Nominal, Ordinal, Interval and Ratio.

Let us take an example of “100 meter race” in a tournament where three runners are participating from three different states of Malaysia. Each runner is assigned a number (displayed in uniform) to differentiate from each other. The number displayed in the uniform to identify runners is an example of nominal scale. Once the race is over, the winner is declared along with the declaration of first runner up and second runner up based on the criteria that who reaches the destination first, second and last. The rank order of runners such as “second runner up as 3”, “first runner up as 2” and the “winner as 1” is an example of ordinal scale. During the tournament, judge is asked to rate each runner on the scale of 1–10 based on certain criteria. The rating given by the judge is an example of interval scale. The time spent by each runner in completing the race is an example of ratio scale.

Dear Monika,

I think this refer to the scale of measurement not the variable.We shouldn't say our variable is ordinal or interval,instead we speak about the measurement scale that we use to calculate data for our variables,so for one variable we can report different numbers which can be calculated by different scales.

For example think about length of sticks, our variable is continuous and can be measured with interval or ordinal scale,we can give numbers in inches(interval) or only give them number 1 if it is shorter than 1 inch and 2 if it is longer than 1 and shorter than 3 and so on(ordinal).

Although any of these scales have their own characteristics that make them different of each other ( you can find in statistics books) and should use for proper variables.

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"Interval and ratio level data are classified as quantitative or numerical data.

Interval data are measured and have constant, equal distances between values, but the zero point is arbitrary. The zero isn’t meaningful, it doesn’t mean a true absence of something. An example of interval level data is intelligence, as measured on some IQ test. We know that the scoring difference between a 100 and a 110 is equal to the scoring distance between 120 and 130, but there is no true zero on this test and an IQ of 140 is not twice as high as an IQ of 70.

Ratio level data are those which have equal intervals between values, and the zero is meaningful. Some laboratory tests are good examples of ratio level data. A person who weighs 100 kilos is twice as heavy as a person who weighs 50 kilos, and a measure of zero kilos is meaningful. Other examples include pulse rate and respiratory rate."

taken from this presentation :

www.med.wright.edu/sites/default/files/psych/.../6TypesofVariables.pptx

(it even provides a small test at the end !)

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A typical example is the temperature. It can be measured on an interval scale like °F or °C, as well as on an ratio scale in Kelvin (K).

When a ratio between two values of a quantitative/metric variable is meaningful, it's a ratio scaled variable, otherwise it's an interval scaled variable.

Not that the "variate" is some property one likes to analyse/measure. If one applies a defined measuring procedure to get some kind of values (names or numbers), then the result is the "variable". The way how a variate is measured defines the scale of the variable. For example, the variate "color" could be measured by naming the colors (the variable would be nominal with values "red", "green" ...). Also, the variate could be measured as "wavelength" in nm, what would give a quantitative variable. This variable is ratio scaled, since 0nm is a physically meaningful value and in fact the wavelength 200nm is twice as long as 100nm. As a third way, one could take a colored pallette system like the hue color system to measure the color (http://dba.med.sc.edu/price/irf/Adobe_tg/models/hsb.html). This gives values between 0° and 360°, again a quantitative variable. But here the 0° point is arbitrary, and a hue of 40° does not mean twice the hue of 20°. So it's an interval scale, but not a ratio scale.

A simple example given below will explain the difference among 4 basic measurement scales: Nominal, Ordinal, Interval and Ratio.

Let us take an example of “100 meter race” in a tournament where three runners are participating from three different states of Malaysia. Each runner is assigned a number (displayed in uniform) to differentiate from each other. The number displayed in the uniform to identify runners is an example of nominal scale. Once the race is over, the winner is declared along with the declaration of first runner up and second runner up based on the criteria that who reaches the destination first, second and last. The rank order of runners such as “second runner up as 3”, “first runner up as 2” and the “winner as 1” is an example of ordinal scale. During the tournament, judge is asked to rate each runner on the scale of 1–10 based on certain criteria. The rating given by the judge is an example of interval scale. The time spent by each runner in completing the race is an example of ratio scale.

All the respected responses explain the difference so simply and in detail that I don't think one has to say something new. Therefore, below is a short summary of all responses regarding ratio scale and interval scale of measurement:

1. Ratio measurement assumes a zero point where there is no measurement. Suppose you want to know straight line distance between your house and your college or university department, centre of your house will be taken as zero (0.0) and say distance between your house and your destination is measured as 10.523 km, it is ratio measurement (Keep in mind that measurement re seldom perfect even measured at nano-scale, rounding is always done). Values at this scale can be added, subtracted, multiplied and divided.

2. Interval scale never assumes as absolute zero (0,0). For example, temperature measured in degree C or F. Even in the condition of zero when some liquids or fluids solidified or condensed to solid as ice., we cannot say there is no heat (temperature) in them. Therefore, if at your place day temperature is 40 degree C and at nearby hill station it is only 20 degree C, one cannot say that your place is twice hot than that of the hill station and similarly one cannot say that hill station is 1/2 time less hot than your place. In the absence of absolute zero, we cannot multiply or divide interval values with each other. However, to arrive at a mean value, these values can be added and subtracted from each other.

I would simply ask two questions:

1. Does ‘zero’ mean ‘none’?

2. Does ‘multiplied by 2’ have the exact meaning of ‘twice as much as’?

If the answers to the both questions are ‘yes’, the scale of measurement used is a ratio scale.

The following example may be helpful:

Suppose a group individual is investigated and their heights in centimeter are recorded. The scale in this case is obviously a ratio one. Because:

0 cm height means ‘no height’

A person with 180cm is twice as tall as a person with 90cm height.

Now assume that the investigator could not find an exact measurement instrument for some reason and instead he chalks two lines on the wall to construct an interval. Then the interval is divided into ten equal divisions (units). The measurements are now made by the units marked on the wall. This in reality will give an interval scale of measurement. Because

0 unit height will not mean ‘no height’

A person with 8 unit height is NOT twice as tall as a person with 4 unit height.

Let a further assumption be made that marking the wall in equal units is also not feasible, and the investigator only draw one line on the wall and call the people having height above the line as Tall and people having height below the line as Short. This measurement only can be utilized to order the two groups in terms of height and hence will be an ordinal scale of measurement.

Finally consider that the two groups Tall and Short are just named as Height Group 1 and Height Group 2, the information contained by these two group names would not be helpful even for ordering the observations in terms of height. This is nominal scale.

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not sure that the following will make things clearer (a little background in physics may be needed) : consider the temperature

- when T is given in Kelvin, it has an absolute zero and kT (k the Boltzmann constant) has the dimension of an energy so that 400 K represents twice the energy coresponding to 200 K : ratio variable !

- the same temperature given in Celsius has no absolute zero (the melting point of ice at atmospheric pressure is just a useful but otherwise arbitrary point in the scale) but 10 more degrees correspond to the same energy difference whatever the point on the scale : interval variable !

the funny thing here is that it is the same quantity ; depending on its coding, it is either represented by a ratio or interval variable and the codings do not differ much : C = K - 273 (C in Celsius, K in Kelvin ; the absolute zero is about -273°C).

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woops, had overlooked Jochen answer above ! sorry for the spam ...

Ratio scale has absolute zero ex. Currency. where as in case of interval scale, absolute zero is not there ex. Temperature .

Dear Clerot,

you are right in terms of physics. It is possible at Boltzmann constant as when K=0, all molecular activity stops. But we don't know more what happens at -K. It is quite possible at K=0, the universe will become a cold waste.

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Dear Mohammad,

my answer was casted in the frame of "classical" thermodynamics, the one where the "temperature" is considered as the "real" variable of interest.

This "classical" thermodynamics is quite sufficient to interpret macroscopic properties and most microscopic ones ... but not all and, indeed, systems with negative absolute temperatures do exist, although their interpretation is more that these "negative" temperatures are "above infinity" (such systems have a decreasing entropy as their energy is increased, because they have a bounded number of high energy states ; in a sense, for such systems, the more you add energy, the more you are bound to fill in the low enregy states (as they are the only available) therefore reducing the entropy).

So well, well, well ... temperature may not be such a brilliant example (a scale that starts again beyond infinity ... definitely not interval nor ratio !!!) ... at least at the quantum level but this should not be a such a surprise as the relevant parameter for such systems is the conjugate of the temperature, the infamous "thermodynamic beta" !

for more details :

http://en.wikipedia.org/wiki/Negative_temperature

However, for macroscopic systems (from galaxies to superfluid helium,say), the three laws of thermodynamics provide an excellent framework and within this framework, the notion of temperature is reasonably well understood as a ratio variable (if expressed in Kelvin).

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No Oil In Rivers: The first letters of the scales in order from lowest to highest.

Nominal Scale: Property , Example: Gender.

Ordinal Scale: Properties , Example: the results of a horse race Note: The distance between scale points is not equal.

Interval Scale: Properties , Example: Survey rating- Strongly Agree, Agree, Neutral, Disagree and Strongly Disagree.

Ratio Scale: Properties , Example: Money

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@ Monika

regarding the different examples you list in your update, it seems that the temperature above is a good warning : measurements (aka "data") are not "variables" by themselves ; they only become "variables" (and variables of a given type) through a clear specification of the purpose of the analysis.

For meteorologists, temperature coded in °C is appropriate and therefore temperature measurements are conveniently considered as occurrences of an interval variable.

For solid state physicists, temperature is quite often considered as a proxy for the energy kT (with T in Kelvin) and the zero temperature has its classical interpretation as the absolute zero of the energy scale ; temperature measurements are therefore recoded in Kelvin and conveniently considered as occurrences of a ratio variable.

For quantum physicists, temperature is sometimes not the right parameter of interest and using it in the discussion of the results (because of tradition or just for the fun of writing about "negative absolute temperature" !) leads to more questions than answers !

In summary, it is not the nature of the measured quantity (the "data") which determines univocally the nature of the type of variables these mesurements will be recoded into. You have to consider both the nature of the quantity _and_ the way they enter the analysis.

In your example about units, it is the role of the analyst to decide whether s/he wants to use units or not. Once this choice is made and agreed upon, the type of variables is fixed and the analysis can proceed ... and no "ex post whining" about units if the choice has been made not to use them ! Instead, it is possible to start another analysis with units and compare results.

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When I this stuff I explain the point that 'zero has no meaning' in an interval scale by thinking about what it means to double the score. Does it really mean that you've doubled the thing you're measuring? For example, 50 degrees Fahrenheit is not 'half' of 100 by any physical or psychological way. I also make the point that there aren't many examples of scales that are interval but not ratio. All books use temperatures in Fahrenheit. Another example I use is years AD.

Ya I refer to the question and keep in mind that only ratio has a true zero. So if I am measuring hours of study, and I can have zero hours, then my data is ratio

Personally I think of age as interval because it is arbitrary that the West considers birth year 0; some south east Asian countries don't consider a child 'alive' until it reaches it's second birthday.

Nice example, Dory.

"Time from birth" is, by definition, ratio scale, because, for instance, 6 years from birth are just twice the time of 3 years from birth. But the intersting point you brought up is about the rationale of this variable (in scientific context). I do not see any biological, psychological or sociological variable that would be (even only vaguely) linearily associated with this "time from birth". (Nevertheless the measure is useful in the juristical context, and  there the scale is not relevant)

I am happy to have accessed this site. I was facing the same difficulty in explaining the subtle differences between these variable categories particularly the ratio and interval ones. Thank you all for the nice examples and explanations.

i have the same problem

i consider it as interval if

-no true zero

- cannot multiply or divide