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Art is a leveller - education, age, money, gender, faith are irrelevant - shared tastes and appreciation of art transcend these divisions.

The Arts Debate, Arts Council England 2007

Jargon Buster

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Index or comparative index

What does this mean?

A variation on the percentage, this is a single figure that shows the result of comparing a specific instance that you are interested in with the overall average for the whole from which this instance is drawn.

The formula for calculating an index is:

(The specific instance of interest ÷ the overall basis for comparison) × 100

For example, say that your arts facility was attracting 50% of its audience from a particular social grade, compared to the population of your catchment area which had only 20% of its population in that social grade. Then in this case the comparative index for the use of the facility by people having the specific social grade compared with the presence of people from that social grade in the catchment area as a whole would be:

50 ÷ 20 × 100 = 5 ÷ 2 × 100 = 2.5 × 100 = 250

As can be seen from the logic of this formula and calculation, a resulting index of 100 would mean you have levels of attenders from a particular social grade that are on a par with their levels in the catchment as a whole.

By extension, an index of 200 indicates something happening at twice the rate that might be expected from the basis for comparison, while an index of 50 shows it happening at half the rate of the basis for comparison.

How did we get this definition?

An ‘index’ is a single figure that shows the result of comparing a specific instance of interest with the overall norm for the data from which the specific observation has been taken (see above).This overall norm is also known as the ‘base’ or the ‘basis for comparison’. (for instance, the proportion of people matching a particular classification in one postal sector compared with the proportion of people matching the same classification in an entire catchment. Because of the way an index is calculated (see below), a value of 100 for the index shows that the specific instance being examined is happening at the same rate (or ‘on a par’) with its appearance in the wider basis for comparison. Hence a figure greater than 100 indicates something occurring at a greater rate than within the base, and an index of less than 100 indicates a rate of occurrence at a lower level than is happening in the base.

Also here, care needs to be taken that readers and users are not misled by what The Economist Numbers Guide [1991] calls ‘index convergence.’ This is an effect where different index values for different observations seem to converge on the norm. While this does not necessarily mean any findings are incorrect, it does highlight the sensitivity of indexes to what is chosen as the basis for comparison. For instance, the two charts below use the same data for the postal sectors shown, but compare it with different bases. Hence the first compares the Birmingham postal sectors shown with the averages for the catchment, and the second one compares the same data with the UK data. So the results look different. Please note here that the data used is not real and is for illustrative purposes.

[Graph showing indexes of proportion of ABs in postal sectors compared with proportion of ABs in entire catchment]

[Graph showing indexes for proportion of ABs in postal sectors compared with proportion of ABs in the UK population]

Related and similar definitions

The formula for finding a comparative index is:

(The specific instance of interest ÷ the overall basis for comparison) × 100

For example, say that your arts facility was attracting 50% of its audience from a particular social grade, compared to the population of your catchment area which had only 20% of its population in that social grade. Then in this case the comparative index for the use of the facility by people having the specific social grade compared with the presence of people from that social grade in the catchment area as a whole would be:

50 ÷ 20 × 100 = 5 ÷ 2 × 100 = 2.5 × 100 = 250