The problem with being ‘Average’
The word “average” is an everyday term that we all use almost without thought. In general terms, an average is a value that is meant to be typical of a set of measurements, usually thought to be roughly in the middle. But what does it actually mean?
For example, what does this statement mean: “The average age at the start of menopause is 52 years”? If you ask a statistician, they are likely to respond in their usual cryptic way – with a question: “What type of average is it?” You may well respond with your own question: “How many types are there?” which of course sets the statistician off and you will be lucky to get an answer to your first question. You may eventually find out that there are three main types of averages: the mean, median and mode.
Mean: Imagine a sample of women who are all at the start of menopause. If you laid bars with weights equal to each of their ages in order along a beam, the mean is the point at which the beam will balance. However, if one of the women is much younger or older than the others (an outlier in statistical terms), the point of balance will move towards her age. Therefore, the mean may not give a reliable indication of what is typical of a set of values in the presence of outliers.
Median: Going back to the beam illustration, the median is the value that will divide the group of women into two equal halves. Therefore 50% of the women in the group will have an age less than or equal to the median age. Therefore, in the presence of outliers, the median gives a more reliable indication of what is typical of a set of values than the mean does.
Mode: The mode is the most frequently occurring value that, at face value, appears to be the most intuitive of the three types of averages. It is notoriously unstable, however. Statements such as “Most women start menopause at the age of 50 years” refer to the mode and seem quite sensible. Imagine a group of ten women who start menopause at the following ages: 40, 45, 45, 47, 50, 53, 56, 58, 60, 61. The mode in this case is 45 – would you consider this to be typical of this group of women? Suppose, you later find an error for the sixth patient and she is actually 50 years of age. Now there are two possible values for the mode: 45 and 50. Which do you present?
The moral of the story: When presenting or interpreting results that include an average, think about what the most suitable type of average is for the values of interest. Invariably, the mean is what is presented in many cases. However, where there are outlying values that are not typical of the rest, almost all patients maybe above or below this ‘average’. In such cases, the median is preferable.
Measures of effect: The trouble with Odds
The odds ratio is a difficult concept to comprehend. Many researchers do not differentiate it from its counterpart, the risk ratio, and end up using it inappropriately. For example, statements such as the one that follows are commonly encountered in reference to an odds ratio of x: “.. intervention A was associated with an “x-fold” or “x-times” increase in the risk of …”. This statement would be correct if x was the risk ratio, but is incorrect when x is the odds ratio, as is the case here. The treatment effect is inflated, which may help the article get more attention, but is misleading.
Table 1 illustrates the differences in the computation of odds and risk ratios. Table 2 provides examples emphasising the differences between these ratios. Odds and risk ratios can sometimes be nearly equal, such as when the event rate is small, but even then, it is not helpful to present the wrong result in support of a supposedly ‘correct’ statement.
| Table 1: Illustration of calculation steps taken to derive odds and risk ratios |
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| Table 2: Illustration of calculated odds and risk ratios for comparison |
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| (Tables 1 and 2 have been copied (with permission) from a free online illustrative tutorial available at www.MedStats.org/Tutorials.htm.) |
Our advice: Whenever possible, calculate and use the risk ratio, rather than the odds ratio. The target audience of these reports are medical doctors and patients, who understand and use the term “risk” everyday, correctly translated to terms such as “twice/two-fold”. Computation of the risk ratio also easily extends to the provision of other useful measures such as risk reduction and the number needed to treat (NNT).
A word of caution: There is a time and place for the odds ratio in medical research. For example, it is used in case-control studies where a risk ratio can not be calculated directly, and is a