### Solution to question 2.1

• Number of teeth
The number of teeth can be counted so it is a metric discrete variable
• Age
Age can be measured to any desired degree of accuracy (in theory!) and the interval between succesive years is eaqual so age is a metric continuous variable
• Age last birthday (in years)
In one sense this is a metric discrete variable as all we are doing is counting off the years in indivisible units. It could be argued, however, that there is an underlying continuous variable. In practice it will probably make no difference to how we treat it. The key thing here is to recognise it is a metric variable.
• Has patient visited their dentist in the last year
There are only two possible values for this variable Yes and No. This is a binary or dichotomous variable. This is a type we haven"t mentioned in the notes. For all analytical and descriptive purposes binary variables are the same as nominal variables
• Social class
This is a categorical variable. Sometimes it is treated as an ordinal variable and sometimes as a nominal variable. The case for it being ordinal is that the categories can be put into order (I, II, IIIA, IIIB, IV and V). The case for it being nominal is that the ordering is not really meaningful. For example, there is not a direct correlation between income and social class. Also, you may find that a substantial number of any sample has to be placed in an 'other' category because they do not really fit into the classes as defined. For these reasons it often safer to treat social class as a nominal variable.
• Pocket depth
This is a metric continuous variable. Pocket depth is frequently only measured to the nearest millimetre, because if the inherent inaccuracy of measurement methods. The underlying variable, however, is clearly continuous.
• Hardness of filling material
It depends on how we are measuring the hardness. If it is being described by how far a point driven with a particular force will penetrate it then 'Hardness' is a metric continuous variable. If we use a scale such as 'Soft', 'Hard', 'Very Hard' then it is an ordinal categorical variable.
• Colour of filling material
This is a nominal variable. Colours cannot, in general, be put in a meaningful order.
• Type of radiograph
Again a nominal variable. 'Panoramic' or 'Bitewing' can be distinguished from each other but not put into a sensible order.
• Calcium:phosphorus ratio in teeth
This is a continuous metric variable. It can be measured on a scale which can take any value.
• Severity of gum disease
If we are measuring this using a scale such as 'None', 'Mild', 'Moderate', 'Severe' then it is an ordinal variable.

Back to questions