Levels of Measurement.
17. February 2009 08:33
Nominal Data
With nominal data, as the name implies, the numbers function as a name or label and do not have numeric meaning. For instance, you might create a variable for gender, which takes the value 1 if the person is male and 0 if the person is female.
There are two main reasons to choose numeric rather than text values to code nominal data: data is more easily processed by some computer systems as numbers, and using numbers bypasses some issues in data entry such as the conflict between upper- and lowercase letters.
Ordinal Data
Ordinal data refers to data that has some meaningful order, so that higher values represent more of some characteristic than lower values. For instance, in medical practice burns are commonly described by their degree, which describes the amount of tissue damage caused by the burn. A first-degree burn is characterized by redness of the skin, minor pain, and damage to the epidermis only, while a second-degree burn includes blistering and involves the dermis, and a third-degree burn is characterized by charring of the skin and possibly destroyed nerve endings. These categories may be ranked in a logical order: first-degree burns are the least serious in terms of tissue damage, third-degree burns the most serious.
However, there is no metric analogous to a ruler or scale to quantify how great the distance between categories is, nor is it possible to determine if the difference between first- and second-degree burns is the same as the difference between second- and third-degree burn.
Interval Data
Interval data has a meaningful order and also has the quality that equal intervals between measurements represent equal changes in the quantity of whatever is being measured. Example of it – is the Fahrenheit scale, like all interval scales, has no natural zero point, because 0 on the Fahrenheit scale does not represent an absence of temperature but simply a location relative to other temperatures.
Multiplication and division are not appropriate with interval data.
Ratio Data
Ratio data has all the qualities of interval data (natural order, equal intervals) plus a natural zero point. Many physical measurements are ratio data: for instance,height, weight, and age all qualify.
Continuous and Discrete Data
Another distinction often made is that between continuous and discrete data.
Continuous data can take any value, or any value within a range. Most data measured by interval and ratio scales, other than that based on counting, is continuous: for instance, weight, height, distance, and income are all continuous.Discrete data can only take on particular values, and has clear boundaries .As the old joke goes, you can have 2 children or 3 children, but not 2.37 children, so “number of children” is a discrete variable.
Nominal data is also discrete, as are binary and rank-ordered data.
OReilly .Statistics in a Nutshell
With nominal data, as the name implies, the numbers function as a name or label and do not have numeric meaning. For instance, you might create a variable for gender, which takes the value 1 if the person is male and 0 if the person is female.
There are two main reasons to choose numeric rather than text values to code nominal data: data is more easily processed by some computer systems as numbers, and using numbers bypasses some issues in data entry such as the conflict between upper- and lowercase letters.
Ordinal Data
Ordinal data refers to data that has some meaningful order, so that higher values represent more of some characteristic than lower values. For instance, in medical practice burns are commonly described by their degree, which describes the amount of tissue damage caused by the burn. A first-degree burn is characterized by redness of the skin, minor pain, and damage to the epidermis only, while a second-degree burn includes blistering and involves the dermis, and a third-degree burn is characterized by charring of the skin and possibly destroyed nerve endings. These categories may be ranked in a logical order: first-degree burns are the least serious in terms of tissue damage, third-degree burns the most serious.
However, there is no metric analogous to a ruler or scale to quantify how great the distance between categories is, nor is it possible to determine if the difference between first- and second-degree burns is the same as the difference between second- and third-degree burn.
Interval Data
Interval data has a meaningful order and also has the quality that equal intervals between measurements represent equal changes in the quantity of whatever is being measured. Example of it – is the Fahrenheit scale, like all interval scales, has no natural zero point, because 0 on the Fahrenheit scale does not represent an absence of temperature but simply a location relative to other temperatures.
Multiplication and division are not appropriate with interval data.
Ratio Data
Ratio data has all the qualities of interval data (natural order, equal intervals) plus a natural zero point. Many physical measurements are ratio data: for instance,height, weight, and age all qualify.
Continuous and Discrete Data
Another distinction often made is that between continuous and discrete data.
Continuous data can take any value, or any value within a range. Most data measured by interval and ratio scales, other than that based on counting, is continuous: for instance, weight, height, distance, and income are all continuous.Discrete data can only take on particular values, and has clear boundaries .As the old joke goes, you can have 2 children or 3 children, but not 2.37 children, so “number of children” is a discrete variable.
Nominal data is also discrete, as are binary and rank-ordered data.
OReilly .Statistics in a Nutshell
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