To capture the heterogeneity of the families, one can think of the probability parameter of the binomial model (say, probability of being a boy) as itself a random variable (i.e. random effects model) drawn for each family from a beta distribution as the mixing distribution. The resulting compound distribution (beta-binomial) has an additional free parameter. Another common model for overdispersion—when some of the observations are not Bernoulli—arises from introducing a normal random variable into a logistic model. Software is widely available for fitting this type of multilevel model. In this case, if the variance of the normal variable is zero, the model reduces to the standard (undispersed) logistic regression. This model has an additional free parameter, namely the variance of the normal variable. With respect to binomial random variables, the concept of overdispersion makes sense only if n>1 (i.e. overdispersion is nonsensical for Bernoulli random variables). As the normal distribution (Gaussian) has variance as a parameter, any data with finite variance (including any finite data) can be modeled with a normal distribution with the exact variance – the normal distribution is a two-parameter model, with mean and variance. Thus, in the absence of an underlying model, there is no notion of data being overdispersed relative to the normal model, though the fit may be poor in other respects (such as the higher moments of skew, kurtosis, etc.). However, in the case that the data is modeled by a normal distribution with an expected variation, it can be over- or under-dispersed relative to that prediction. For example, in a statistical survey, the margin of error (determined by sample size) predicts the sampling error and hence dispersion of results on repeated surveys. If one performs a meta-analysis of repeated surveys of a fixed population (say with a given sample size, so margin of error is the same), one expects the results to fall on normal distribution with standard deviation equal to the margin of error. However, in the presence of study heterogeneity where studies have different sampling bias, the distribution is instead a compound distribution and will be overdistributed relative to the predicted distribution. For example, given repeated opinion polls all with a margin of error of 3%, if they are conducted by different polling organizations, one expects the results to have standard deviation greater than 3%, due to pollster bias from different methodologies. Over- and underdispersion are terms which have been adopted in branches of the biological sciences.