Effective Sample Size (ESS)

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Effective Sample Size (ESS)

Companion and Reflect

The ESS for weighted data is a very important measure of the "weighting effect".

If data has had respondent weighting applied then there will be some loss of the collected data in the reports.  In the extreme case of some records having a weight of zero or close to zero, then these are effectively excluded from the analysis.

The ESS is a calculation of the Effective sample size and is always less than the unweighted figure.  The more targets that are used in weighting the wider the spread of weights and the further the ESS will drop.

In any respondent weighting scheme there will be a variety of weights applied to individual records and the wider the spread, the more data has been "lost" due to "weighting effects".

TIP: weighting schemes often need to be a compromise between the desirability of using many targets and not reducing the ESS too far.  If the ESS falls too low you may have to consider reducing the number of targets by not using them or combining them together.

In tables the ESS bases can be shown as a total row using Format ESR.

Example of ESS

The ESS is calculated as the square of the weighted total divided by the sum of squares of the individual weights.

Here is a trivial example:

Supposing five interviews are conducted and they were supposed to be one male and four females.  A mistake was made and one female and four males were interviewed.  If target weights are applied to rebalance to the desired sample then we will have four men with a weight 0.25 and one female with a weight of 4.0.  The weighted tables will still be based on 5 records but it should be obvious that it does not matter much what the men say because together they only account for a fifth of the accumulated figures and the single women accounts for four fifths.  For this weighting the ESS is 5 squared divided by 16.25 which is roughly 1.5.  This means that although the surveys contains 5 records, the tables are really only based on 1 and half records worth of data.

Efficiency

The term "weighting efficiency" is a term used to describe how much data has been retained and not "lost" due to weighting effects.  It is simply the ratio of the ESS to the unweighted number of records.  For example:

Efficiency of 100% means that no data has been lost.

Efficiency of 75% means that a quarter of the data has been lost.

Efficiency of 50% means that half the data has been lost.

Efficiency of 25% means that three quarters of data has been lost.