A practical problem with large scale survey data is the potential for overdispersion.
Overdispersion occurs when the data display more variability than is predicted by
the variance-mean relationship for the assumed sampling model. This paper describes
a simple strategy for detecting and adjusting for overdispersion in large scale survey
data. The method is primarily motivated by data on the relationship between social
class and educational attainment obtained from a 2% sample from the 1991 census of
the population of Great Britain. Overdispersion can be detected by first grouping
the data into a number of strata of approximately equal size. Under the assumption
that the observations are independent and there is no variability in the parameter
of interest, there is a direct relationship between the nominal standard errors and
the empirical or sample standard deviation of the parameter estimates obtained from
each of the separate strata. With the 2% sample from the British census data, quite
a discernible departure from this relationship was found, indicating overdispersion.
After allowing for overdispersion, improved and more realistic measures of precision
of the strength of the social class-education associations were obtained.