Reducing processing requirements to correct for bias in ratings data having interdependencies among demographic statistics

1. An apparatus comprising:

memory; and

a processor to execute computer readable instructions to:

access first beacon request messages received from a plurality of devices via a network to obtain impression data included in the first beacon request messages, the impression data associated with at least one of access or exposure to media via ones of the plurality of devices;

cause corresponding beacon response messages to be transmitted to the plurality of devices responsive to the first beacon request messages, the beacon response messages to cause the plurality of devices to transmit subsequent second beacon request messages to an online service;

access demographic data associated with the plurality of device from the online service;

process the impression data obtained from the first beacon request messages received from the plurality of devices and the demographic data accessed from the online service to determine attribute data associated with a sample population;

determine a plurality of weights based on a data structure having elements corresponding to pairings of ones of a plurality of demographic partition statistics and ones of a plurality of baseline demographic statistics obtained for a target population, the demographic partition statistics corresponding to a plurality of demographic partitions of the sample population, the demographic partition statistics based on the attribute data, a first element of the data structure to combine a first one of the demographic partition statistics with a first one of the baseline demographic statistics of the target population based on a first value and a second value, the first value based on a numerator term of an expression to calculate a corresponding first one of the baseline demographic statistics of the sample population based on the demographic partition statistics, the second value based on a denominator term of the expression, the weights corresponding respectively to the demographic partitions of the sample population;

adjust the attribute data based on the weights to determine ratings data for the target population; and

cause the ratings data to be transmitted via the network to a receiving device different from the plurality of devices.

2. The apparatus of claim 1 , wherein the data structure is a matrix.

3. The apparatus of claim 1 , wherein respective ones of the demographic partition statistics are based on respective numbers of individuals in the sample population that belong to corresponding ones of the demographic partitions.

4. The apparatus of claim 3 , wherein the processor is to determine the demographic partitions to form a mutually exclusive set that covers the sample population.

5. The apparatus of claim 1 , wherein the first one of the baseline demographic statistics of the target population is based on a first number of individuals in the target population that have attributes that correspond to a first one of a plurality of different demographic classifications.

6. The apparatus of claim 5 , wherein the corresponding first one of the baseline demographic statistics of the sample population is based on a second number of individuals in the sample population that have attributes that correspond to the first one of the different demographic classifications, and the first one of the baseline demographic statistics of the sample population is also computable from the demographic partition statistics based on the expression.

7. The apparatus of claim 1 , wherein the processor is to:

set the first value to one or zero based on whether the first one of the demographic partition statistics is included in the numerator term of the expression; and

set the second value to one or zero based on whether the first one of the demographic partition statistics is included in the denominator term of the expression.

8. The apparatus of claim 7 , wherein the processor is to determine the first element of the data structure based on the first one of the demographic partition statistics, the first one of the baseline demographic statistics of the target population, the first value, the second value and a third value, the third value based on an importance of the first one of the baseline demographic statistics relative to other ones of the baseline demographic statistics.

9. A non-transitory computer readable medium comprising computer readable instructions that, when executed, cause a processor to at least:

access first beacon request messages received from a plurality of devices via a network to obtain impression data included in the first beacon request messages, the impression data associated with at least one of access or exposure to media via ones of the plurality of devices;

cause corresponding beacon response messages to be transmitted to the plurality of devices responsive to the first beacon request messages, the beacon response messages to cause the plurality of devices to transmit subsequent second beacon request messages to an online service;

access demographic data associated with the plurality of device from the online service;

process the impression data obtained from the first beacon request messages from the plurality of devices and the demographic data accessed from the online service to determine attribute data associated with a first population;

determine a plurality of weights based on a matrix having elements corresponding to pairings of ones of a plurality of demographic partition statistics and ones of a plurality of baseline demographic statistics obtained for a second population, the demographic partition statistics corresponding to a plurality of demographic partitions of the first population, the demographic partition statistics based on the attribute data, a first element of the matrix to combine a first one of the demographic partition statistics with a first one of the baseline demographic statistics of the second population based on a first value and a second value, the first value based on a numerator term of an expression to calculate a corresponding first one of the baseline demographic statistics of the first population based on the demographic partition statistics, the second value based on a denominator term of the expression, the weights corresponding respectively to the demographic partitions of the first population;

adjust the attribute data based on the weights to determine ratings data for the second population; and

cause the ratings data to be transmitted via the network to a receiving device different from the plurality of devices.

10. The non-transitory computer readable medium of claim 9 , wherein respective ones of the demographic partition statistics are based on respective numbers of individuals in the first population that belong to corresponding ones of the demographic partitions.

11. The non-transitory computer readable medium of claim 9 , wherein the first one of the baseline demographic statistics of the second population is based on a first number of individuals in the second population that have attributes that correspond to a first one of a plurality of different demographic classifications.

12. The non-transitory computer readable medium of claim 11 , wherein the corresponding first one of the baseline demographic statistics of the first population is based on a second number of individuals in the first population that have attributes that correspond to the first one of the different demographic classifications, and the first one of the baseline demographic statistics of the first population is also computable from the demographic partition statistics based on the expression.

13. The non-transitory computer readable medium of claim 9 , wherein the instructions cause the processor to:

set the first value to one or zero based on whether the first one of the demographic partition statistics is included in the numerator term of the expression; and

set the second value to one or zero based on whether the first one of the demographic partition statistics is included in the denominator term of the expression.

14. The non-transitory computer readable medium of claim 13 , wherein the instructions cause the processor to determine the first element of the matrix based on the first one of the demographic partition statistics, the first one of the baseline demographic statistics of the second population, the first value, the second value and a third value, the third value based on an importance of the first one of the baseline demographic statistics relative to other ones of the baseline demographic statistics.

15. A system comprising:

means for determining attribute data for a sample population, the means for determining the attribute data to:

access first beacon request messages received from a plurality of devices via a network to obtain impression data included in the first beacon request messages, the impression data associated with at least one of access or exposure to media via ones of the plurality of devices;

cause corresponding beacon response messages to be transmitted to the plurality of devices responsive to the first beacon request messages, the beacon response messages to cause the plurality of devices to transmit subsequent second beacon request messages to an online service;

access demographic data associated with the plurality of device from the online service; and

process the impression data obtained from the first beacon request messages from the plurality of devices and the demographic data accessed from the online service to determine the attribute data for the sample population;

means for determining ratings data for a target population, the means for determining the ratings data to:

determine a plurality of weights based on a matrix having elements corresponding to pairings of ones of a plurality of strata statistics and ones of a plurality of baseline demographic statistics obtained for a target population, the strata statistics corresponding to a plurality of demographic strata of the sample population, the strata statistics based on the attribute data, a first element of the matrix to combine a first one of the strata statistics with a first one of the baseline demographic statistics of the target population based on a first value and a second value, the first value based on a numerator term of an expression to calculate a corresponding first one of the baseline demographic statistics of the sample population based on the strata statistics, the second value based on a denominator term of the expression, the weights corresponding respectively to the demographic strata of the sample population; and

adjust the attribute data based on the weights to determine ratings data for the target population; and

means for transmitting the ratings data via the network to a receiving device different from the plurality of devices.

16. The system of claim 15 , wherein the means for determining the ratings data is to determine the demographic strata to form a mutually exclusive set that covers the sample population, and respective ones of the strata statistics are based on respective numbers of individuals in the sample population that belong to corresponding ones of the demographic strata.

17. The system of claim 15 , wherein the first one of the baseline demographic statistics of the target population is based on a first number of individuals in the target population that have attributes that correspond to a first one of a plurality of different demographic classifications.

18. The system of claim 17 , wherein the corresponding first one of the baseline demographic statistics of the sample population is based on a second number of individuals in the sample population that have attributes that correspond to the first one of the different demographic classifications, and the first one of the baseline demographic statistics of the sample population is also computable from the strata statistics based on the expression.

19. The system of claim 15 , wherein the means for determining the ratings data is to:

set the first value to one or zero based on whether the first one of the strata statistics is included in the numerator term of the expression; and

set the second value to one or zero based on whether the first one of the strata statistics is included in the denominator term of the expression.

20. The system of claim 19 , wherein the means for determining the ratings data is to determine the first element of the matrix based on the first one of the strata statistics, the first one of the baseline demographic statistics of the target population, the first value, the second value and a third value, the third value based on an importance of the first one of the baseline demographic statistics relative to other ones of the baseline demographic statistics.