In practice, the conclusion about the validity of, for example, the normality assumption is then implicit rather than explicit: Because insufficient evidence exists to reject normality, normality will be considered true.
For example, the normality of spread on equity returns (say, returns on a portfolio that is long on Dell stock and short on HP stock in equal dollar amounts) can be rejected, yet such a normality assumption is implicit in the posited model.
In addition, the corrections themselves involve many assumptions, for example about normality of distributions and randomness of effects, which are rarely articulated in primary reports (Murphy, 2003).
However, as Bland and Altman note, and seen within our example, departures from normality between method differences will not usually have a great impact on the limits of agreement [ 6].
Use of PMM and LRD is typically motivated by the notion that they provide a degree of robustness when the imputation model is misspecified, for example if the normality assumption is in question, residuals are heteroscedastic, or associations are non linear.
The specification of the distribution of the random effects does not always have an impact on the estimation of the parameters of interest (Aitkin, 1999), but there are examples where the normality assumption leads to bias (Muthén and Asparouhov, 2009).
It's less exciting, perhaps, but a good example of the peaceful normality the only Afghan to have visited space wishes for his own country.
Second, the reported summary statistics can help the reader to refute the assumption of normality, for example, when a strictly positive variable has a standard deviation close to or even larger than its mean.
There are related worries that the human genome reference sequence will arbitrate a standard of genetic normality; for example, the application of concepts like "genetic error" and "damage" to the genome institutes a call for correction or repair (Limoges 1994; also Murphy 1994).
Yasumasa Kanada has performed detailed statistical analyses on the decimal digits of and found them consistent with normality; for example, the frequency of the ten digits 0 to 9 were subjected to statistical significance tests, and no evidence of a pattern was found.
