Generally speaking, data can be classified as qualitative or quantitative, though the distinction is illusory (qualitative data can be represented numerically, and vice versa).Qualitativedata contains categorical variables and quantitative data contains numerical variables. Categorical variables come in nominal or ordinal flavours, whereas numerical variables can be discrete or continuous. The type of data tends to determine the level of sophistication one can achieve with their statistical tests.
This chapter answers parts from Section A(c) of the Primary Syllabus;"Describe the different types of data". It has no corresponding topic amongthe Fellowship exam revision chapters. Among the Primary papers, it is represented only byViva 1from the second paper of 2007 andQuestion 17from the second paper of 2015."Any reasonable classification was awarded marks", according to the examiners. Usually, examples are required in such questions, and the author has made some effort to offersome.
"Standard textbooks well describe this topic, often in their opening chapter" according to the primary examiner's answer toQuestion 17. They were clearly referring to Myles and Gin, where (at least in my 2000 edition) "Data Types" is the title of Chapter 1. Most of this summary was created using this chapter as the main source. An alternative resource is"Types of data"byDerek Richards (2007).
In summary, types of data can be rapidly classified in a nested list:
- Qualitative data:described by a characteristic
- Categorical (i.e. described as a category)
- Nominal data: an unordered list of categories
- Categorical (i.e. described as a category)
- Quantitative data: described bya numerical scale
- Numerical(i.e. described as a number)
- Ordinal (in a scale, or ordered by magnitide)
- Discrete (where the data plugs into a limited range of values)
- Continuous (where there is an infinite range of possible values)
- Interval (no true zero value)
- Ratio (there is a true zero value)
- Numerical(i.e. described as a number)
Qualitative vs. quantitative data
Qualitative data:defined by some characteristic. An example might be blood groupor gender.
Quantitative data:measured on some numerical scale. An example might be heart rate or blood pressure.
Categorical vs numerical variables
Categorical variable:a variable can only have one value from a limited range of values. For example, blood group andgender areforms of categorical data. The values belong to some sort ofcategory, on the basis of a qualitative property. Essentially, "categorical" is a synonym for "qualitative".
Numerical variable:when the variable takes some numerical value. An example might be heart rate or blood pressure.
Nominal vs ordinal data
Nominal data:the range of valuesis not ordered in any sense, but simply named (hence thenom). Again, blood groups, gender, etc. This is a form of categorical data.
Ordinal data:the range of values is ordered along a scale,e.g. disease staging (advanced, moderate, mild) or degree of pain (severe, moderate, mild, none).
Discrete vs. continuous data
Discrete data:when the variableisrestricted to specific defined values. For example, "male" or "female" are categorical discrete data values. Mortality(eg. 20 patients dead at 6 months) is an example ofnumerical discrete data values. There can be no 20.5 dead patients.
Continuous data:when the variable is unrestricted and can have any value from a potentially infinite range, eg. "blue" and "red" might be the categorical data range but the true value can be any subtle shade of purple. An example of numeric continuous data is weight - i.e. one does not have to be exactly 65 or 70 kg; one may easily be 67.5567kg.
Scales of Measurement
Nominal scale:only an identity; values assigned to variables are merely descriptive. An example is gender.
Ordinal scale:values have both an identity and a magnitude. A familiar ordinal scale is an examwhich ranks you first, second or third. You know the rank, but you don't know by how much you failed.
Interval scale:values have identity, magnitude, and equal intervals. An example is temperature (every degree Celsius is the same interval).
Ratio scale:values have identity, magnitude, equal intervals, and a minimum value of zero. An example of this is weight.
Importance of data types
Why do we need to know this? Well: data types determine the sort of statistic tests which are applicable.
- If your measurement scale is nominal or ordinal then you usenon-parametricstatistics
- If you are using interval or ratio scales you useparametricstatistics.
