1.7 Using statistics for comparisons

Statistics are used primarily for making comparisons. Most typically, comparisons are made between different time-points and different regions.

Percentage change

Comparisons across different time-points usually aim to give some idea of the magnitude and direction of change. The magnitude of change is typically indicated in relative or percentage terms. If the population of London grows by 10,000, that translates into an increase of just over one-thousandth of the total population; if the population of Oulu grows by 10,000 persons, that means an increase of nearly eight per cent in the city's population. Percentage change is calculated using the following formula:

The percentage change indicates the proportion of difference between new and old observation concerned compared to baseline (=old observation).

If, for example, your weight goes up from 80 kg to 96 kg (i.e. by 16 kg), that is an increase of 20%. Losing the weight back to 80 kg, on the other hand, translates into a weight loss of just 17%, because now you compare the change to greater value of weight.

Indices

Statistical values are often translated into indices, which provide an effective tool for comparisons of change. For purposes of calculating an index the baseline observation is always entered as 100. The next time the same measurement is carried out, the observation is compared with the baseline result. The formula is as follows

If, for example, per capita consumption of 100% alcohol increases from 6.7 litres in 1995 to 8.2 litres in 2005, the index for alcohol consumption is obtained as follows:

The index shows the percentage change direct: alcohol consumption has increased in ten years by 22 per cent. The Table below also shows that coffee consumption has remained nearly unchanged (decreased by only 3 per cent), sugar consumption has decreased by 14 per cent and tobacco consumption has decreased by 22 per cent. In other words, indices are a good way to compare the rate of change of different items. Compared to the original statistics, indices provide a clearer picture of the relative magnitude of change. It is immediately clear from the index that the consumption of tobacco has decreased faster than the consumption of sugar.

Consumption of selected foodstuffs and stimulants per capita in 1995 and 2005

Source: Statistical Yearbook of Finland 2006, Table 449

An index calculated from a time series allows us to compare litres and kilograms, but only in relation to the magnitude of change. From the index values above we can draw no inferences about whether alcohol, sugar, coffee or tobacco consumption in Finland is high or low. We will need to have original consumption data in order to understand the significance of each item. For example, the significance of increasing alcohol consumption can only be understood when the level of consumption in Finland is compared to other European countries. (When comparing the examples one has to note that the taxation of alcoholic beverages was lowered in Finland in March 2004. This increased consumption, which can be seen in the table concerning the year 2005, but not in the international comparison table concerning the year 2003.)

Per capita alcohol consumption in selected European countries in 2003, litres of 100% alcohol

Source: Statistical Yearbook of Finland 2007, Table 689

Indices are most commonly used for purposes of comparisons over time, but they can obviously be used in any comparisons. For example, we can decide to set the Finnish value as the reference point at 100 and express the figures for other countries as indices in relation to this base value.

Per capita alcohol consumption in selected European countries in 2003, litres of 100% alcohol. Finland = 100 (index)

Source: Statistical Yearbook of Finland 2007, Table 689

Adding up indices

It is also possible to add up different indices if we know how the different items or aspects measured are related to one another. For example, the consumer price index (CPI) is the weighted average of the price indices of different products. For purposes of calculating the CPI, the price indices of different products or product groups are weighted according to their relative share of consumer spending in Finland. In other words, the housing price index has a greater weight in calculating the total index than health care expenditure because housing accounts for a much greater proportion (more than 20 per cent) of total spending than health care (less than 5 per cent).

CPI (2005 = 100) weight structure.
Bar length indicates the weight of each product category in the consumer price index (per cent).

Source: Statistics Finland, Prices and Costs 2007