# Statistics - (Fraction|Ratio|Percentage|Share) (Variable|Measurement)

Ratio measurement gets its name from the fact that meaningful fraction (ratio or rational number) can be constructed with a ratio variable.

Ratio is the deepest, most meaningful level of measurement, and consequently, the most useful.

A variable measured at this level not only includes the concepts of order and distance, but also adds the idea of “nothingness”, absolute zero or True Zero.

Because of this absolute zero value (“true zero”), the ratio between any two values has a meaning

In the Celsius temperature scale the temperature at which water freezes is really an arbitrarily chosen number and does not represent the absence of temperature. As a result, the ratio between temperatures is relative.

## Meaningless

A ratio must have meaning. A ratio between two nominal variables is meaningless (i.e. a person who scores A did not necessarily do “twice as well” as a student who scored B )

## Type

Two type of ratio measure:

• Percentage measure
• Share measure

## Example

In each of these cases there is an absolute zero that has real meaning

• Height,
• Weight,
• Population (Population = 0 = extinct)
• Age (Age = 0 literally means NO age)
• Temperature K° (the Kelvin scale)

## on the importance of ratio, tic tacs sugar free

Tic Tacs are 94% sugar and yet claim to be sugar free…

The FDA says anything can be labeled sugar free if it has <0.5g of sugar, so each tic tac is 0.49g and they can claim they have 0 sugar on the label

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