Interval data and ratio data are two of the final levels of measurement. Here are the key differences and relationship between interval and ratio data:
- Definition and scope
Interval data is a mathematically quantitative data that has equal and measurable intervals between its values, but no true zero point.
For example, temperature in Celsius scale can be plotted as 10°C, 20°C, 30 °C, all have equal intervals of 10 points between them. And temperature of 0°C does not mean the absence of temperature. It is simply there to indicate the point where water solidifies into ice.
Ratio data has all the properties of interval data, in addition to that, it also has the property of having a true zero point.
For example, speed on a car meter shows 10 miles/ hr, 20 miles/ hr etc. Here it has equal intervals, and 0 speed indicates an absence of any speed and hence the vehicle is stationary.
- True “zero” point
A zero point on an interval data scale represents a state and not an absence. For example, a 0 on any test cannot represent an absence of what is being tested. Like a 0 on an IQ test doesn’t mean that IQ of that person doesn’t exist. A cat or dog cannot take an IQ test, so they get a zero, while we know that all animals have a certain degree to intelligence in them. Same with babies, a 2 year old will get a 0 on an IQ test, that doesn’t mean that they have no intelligence. As long as there is “awareness”, there is some form of intelligence present.
Taking it up even another notch, EQ is emotional quotient which is highly subjective when capturing on paper. A zero EQ certainly does not mean that EQ is not present.
Ratio data on the other hand are phenomenon that represents a.comppete absence with the value of zero.
For example, “distance” means movement itself and 0 distance means it’s stationary, in other words, distance doesn’t exist in this case. Same with “time”, time itself means movement “in time” be it past or future, and 0 time simply means the “the present moment”, or no movement in time. This is why many in spirituality say that there is no time in the present moment, that time only exists when we refer to the past or the future as a thought concept.
- Ratio-based mathematics (multiplication and division)
For any multiplication and division, a true zero value is required else the question becomes – from where should it multiply? For example, temperature cannot be multiplied. 20°C times 20°C means nothing in reality. It doesn’t mean 400°C because to reach 400°C the object’s original temperature is needed, and that can be any point below or above 0°C.
Similarly, for division also you need a true zero point.
This is why, between ratio and interval, only ratio data allows for multiplication and division.
- Addition and subtraction
Both ratio and interval data allow for addition and subtraction. In the same example above regarding temperature (interval data), in a lab you can check the temperature of two liquids and subtract the higher from the lower to estimate the temperature when they are mixed.
