### 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.