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# How data is apportioned and aggregated in Local Insight

### Data in Local Insight:

• All the indicators in Local Insight are published at statistical area level; Output Area (OA), Lower layer Super Output Area (LSOA) and Middle layer Super Output Area (MSOA).  To see at what level an indicator is published at you can view the list of all indicators in Local Insight and filter column H, Lowest Published Geography.
• Depending on the level the data is published at Local Insight either aggregates that data up to show at higher geographies or apportions that data down to show at lower geographies. The same aggregation methodology is used for aggregating data between standard geographical areas (eg LSOA to MSOA to LA) and for aggregating data to custom areas.The only difference between these two is that in some cases, we allow fractional component areas for custom areas whereas for standard geographies this is not the case.

### Aggregation

The process of summing data from component areas to give a value for a larger area.

• A central component of Local Insight is the ability to calculate the statistics for geographical areas from the statistics for the component areas. This process of summing data from component areas to give a value for a larger area is called aggregation.
• There are two types of aggregation methodologies, 'sum' and 'weighted_sum'. The formula and process for both of these is described here.

### Sum type aggregation:

• Sum type aggregation is used for indicators where the value of the larger geographic area is the sum of the values of the component areas. For example, indicators that measure numbers of people will be aggregated using sum type aggregation.

### Weighted sum type aggregation:

• Some indicators don't measure things that sum together. For example, it does not make sense to sum the life expectancies of two areas. Instead, the life expectancies should be averaged. For indicators like this, where the value of the parent area should be an average of the component areas, weighted sum aggregation is used.
• Weighted sum aggregation averages the component area data, with the contribution of each component area depending on the what proportion of the total population its population makes up. Here is a worded example.

Area C is made up of two component areas, area A and area B.

The population of area A is 100. The population of area B is 400.

The population of area C is therefore 500.

We want to aggregate the life expectancy of area A and B to area C.

Area A life expectancy is 73. Area B life expectancy is 83.

The mean life expectancy of these two areas is (73 + 83) / 2 = 78. However, since more people in area C come from area B, area B should contribute more to area C's life expectancy.

20% of area C's population is from area A. 80% of area C's population is from area B.

So the weighted sum of the life expectancies is given by:

(73 x 0.2) + (83 x 0.8) = 81

This is a more accurate estimate of the life expectancy of area C.

### Apportioning

The process of modelling data published at higher geographies (LSOA / MSOA) to get values for smaller geographies.

'Sum' type apportioning:

• For data that represents counts (for example numbers of people or amounts of money) we use 'sum' type apportioning (sum type since to aggregate this data to larger geographies we simply sum the values of the component areas). When apportioning, the value of the larger area is divided up amongst smaller areas according to the area's population. The naming is a little confusing here - the parent area is the area that data is apportioned to (in this case the geographically smaller area) and the component area is the area that data comes from.
• To give a worded example, 50 people in LSOA A are unemployed - in order to apportion this unemployment count for the component Output Areas that make up the LSOA we first need to establish the proportion of the total LSOA's population that reside in each of the component Output Areas e.g. if Output Area A contained 20% of the people living in LSOA A, we would calculate the unemployment count for Output Area A as 50*0.2 = 10.

'Weighted-sum' type apportioning:

• For data that represent averages (for example standardised mortality ratios) Local Insight uses a different approach. When aggregating rate data the value of a large geography is given by the weighted sum of the component area values, with area populations used for the weighting. When apportioning such data, we simply assign each of the smaller component areas the same value as the parent area. This ensures that the weighted sum of the smaller areas matches the value of the larger area, avoiding discrepancies that would arise when apportioning to areas with small populations.