# What is Risk?

Risk is a measure of how likely something – usually bad or undesirable &nd is likely to happen within a specified time period. Saying that the risk of something happening to a person is high doesn’t mean that it will happen to a particular person, just that it is more likely to happen than if the risk were low. It may not even mean that something is more likely to happen than not. Likewise, saying that something is of low risk doesn’t mean that it won’t happen, just that it is less likely.

Risk is usually measured by studying a large group of people, noting how many of them the ‘thing’ happens to, then looking for common factors among those people, and also among the rest of the group.

The overall number of ‘happenings’ in relation to the size of the group gives the overall risk for that group. If, for example, the ‘thing’ happens to x members of a group of N people, the risk of the ‘thing’ happening can then be expressed as x in N (or x:n), which is often reported as 1 in n, where n is N divided by x.

If a number of people in that group, say M people, have a common factor that the rest of the group doesn’t, and of those people y have the ‘thing’ happen to them, then the risk of the ‘thing’ happening associated with that common factor would then be y in M, or 1 in m (where m = M/y). If m was smaller than n, then the common factor would be said to increase the risk of the ‘thing’ happening, while if m was larger then the factor would reduce the risk.

If the group size being studied encompassed the whole population, then the measured risk levels would be completely accurate. However, it is rarely practical to study a whole population, and a smaller group size, or sample, of the population has to be studied instead. The measured risk levels are then only an estimate of the real values for the whole population, and the levels measured for one group could easily differ from those measured for a different group of the same size simply because the two groups happened, by chance, to include different numbers of people that the ‘thing’ happened to, or who had the common factor.

Therefore, for a change in risk level associated with a particular factor to be significant, the change has to be greater than might be expected from simple random variation in the sampling process.

In general, the larger the size of the group used in a study is, and the better the randomness of the selection process use to gather the group, the more accurately will the measured risk levels reflect the true levels for the whole population. Therefore the results from studies of relatively small groups of people should be used with great caution.

Also, the way in which changes in risk association with a given factor are reported can also be confusing, especially when reported as percentages. For example, a change in risk from 2:100 (2% or 1:50) to 3:100 (3% or 1:33) could equally well be reported as an increase in risk of 50% (2 x 1.5 = 3) or of 1% (2 + 1 = 3). Similarly, reporting that a particular factor increased an underlying risk of 2:100 by 50% could mean that the new risk level is 3:100 or that it is 52:100.

Large percentage changes in risk level are most likely to be of the multiplicative form, but could appear to exaggerate what is really a very small change in risk: a 100% increase in a risk level of 1:10,000 to 2:10,000 is still a very small risk.

Small percentage changes in risk, however, could be of either multiplicative or additive form, and in the latter case could hide a significant change in risk: a 5% increase in risk doesn’t sound much, but on an underlying risk of, for example, 1:100 it could mean a six-fold increase to 6:100 (1:17). An additive percentage change is sometimes reported in terms of 'percentage points' in order to help avoid this confusion.

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