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292:(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
360:, however, meanings have been transposed, so that overdispersion is actually taken to mean more even (lower variance) than expected. This confusion has caused some ecologists to suggest that the terms 'aggregated', or 'contagious', would be better used in ecology for 'overdispersed'. Such preferences are creeping into
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distribution is a popular and analytically tractable alternative model to the binomial distribution since it provides a better fit to the observed data. To capture the heterogeneity of the families, one can think of the probability parameter of the binomial model (say, probability of being a boy) is
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for one possible explanation) i.e. there are more all-boy families, more all-girl families and not enough families close to the population 51:49 boy-to-girl mean ratio than expected from a binomial distribution, and the resulting empirical variance is larger than specified by a binomial model.
197:. The Poisson distribution has one free parameter and does not allow for the variance to be adjusted independently of the mean. The choice of a distribution from the Poisson family is often dictated by the nature of the empirical data. For example,
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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
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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.
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means that there was less variation in the data than predicted. Overdispersion is a very common feature in applied data analysis because in practice, populations are frequently
300:, 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.
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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).
205:. If overdispersion is a feature, an alternative model with additional free parameters may provide a better fit. In the case of count data, a Poisson
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can be proposed instead, in which the mean of the
Poisson distribution can itself be thought of as a random variable drawn – in this case – from the
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thereby introducing an additional free parameter (note the resulting negative binomial distribution is completely characterized by two parameters).
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160:. However, especially for simple models with few parameters, theoretical predictions may not match empirical observations for higher
353:, the term 'overdispersion' is generally used as defined here – meaning a distribution with a higher than expected variance.
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As a more concrete example, it has been observed that the number of boys born to families does not conform faithfully to a
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as might be expected. Instead, the sex ratios of families seem to skew toward either boys or girls (see, for example the
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of the chosen model. It is usually possible to choose the model parameters in such a way that the theoretical
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Overdispersion is often encountered when fitting very simple parametric models, such as those based on the
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371:, overdispersion is often evident in the analysis of death count data, but demographers prefer the term '
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and will be overdistributed relative to the predicted distribution. For example, given repeated
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too. Generally this suggestion has not been heeded, and confusion persists in the literature.
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Over- and underdispersion are terms which have been adopted in branches of the
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Another common model for overdispersion—when some of the observations are not
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and hence dispersion of results on repeated surveys. If one performs a
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Presence of greater variability in a data set than would be expected
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463:"Analysis of the Human Sex Ratio by using Overdispersion Models"
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416:"The most widely publicized gender problem in human genetics"
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Stansfield, William D.; Carlton, Matthew A. (February 2009).
269:. Software is widely available for fitting this type of
133:) in a data set than would be expected based on a given
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is higher than the variance of a theoretical model,
49:. Unsourced material may be challenged and removed.
516:(Third ed.). University of California Press.
467:Journal of the Royal Statistical Society, Series C
254:(beta-binomial) has an additional free parameter.
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341:Differences in terminology among disciplines
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156:of the model is approximately equal to the
250:as the mixing distribution. The resulting
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461:Lindsey, J. K.; Altham, P. M. E. (1998).
311:(determined by sample size) predicts the
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129:is the presence of greater variability (
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47:adding citations to reliable sources
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201:analysis is commonly used to model
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540:Evolutionary Ecology of Parasites
390:Compound probability distribution
571:Probability distribution fitting
328:, the distribution is instead a
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543:. Princeton University Press.
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513:Quantitative Plant Ecology
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510:Greig-Smith, P. (1983).
373:unobserved heterogeneity
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263:normal random variable
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252:compound distribution
227:binomial distribution
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244:random effects model
195:Poisson distribution
164:. When the observed
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537:Poulin, R. (2006).
385:Index of dispersion
347:biological sciences
322:study heterogeneity
290:normal distribution
284:Normal distribution
275:logistic regression
239:beta-binomial model
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99:January 2008
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41:Please help
36:verification
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426:(1): 3–11.
158:sample mean
565:Categories
401:References
369:demography
203:count data
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123:statistics
69:newspapers
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