In addition, the normal distribution has few values outside of two standard deviations from the mean. Hardly any nutrient or food group data fit this description. Rather, most are right positively -skewed, meaning that the tail on the right side is longer than the one on the left side and the bulk of the values lie to the left of the mean.
This is largely due to the fact that there is a very high upper limit on intake but there is a lower limit of zero. The presence of non-normal distributions can be diagnosed in several ways.
Visual inspection of a histogram of the nutrient dietary component is a useful but subjective procedure. Most statistical software packages contain a variety of formal statistical tests for the normal distribution hypothesis, such as the Shapiro-Wilk and Kolmogorov-Smirnov tests.
Because many [glossary term:] parametric statistical procedures assume a normal distribution, it may be necessary to normalize the distribution of skewed dietary data through transformation before analysis. Non-parametric statistical procedures do not have this requirement, and the dietary data can be used without transformation.
The normal distribution has a kurtosis of three, which indicates the distribution has neither fat nor thin tails. Therefore, if an observed distribution has a kurtosis greater than three, the distribution is said to have heavy tails when compared to the normal distribution. If the distribution has a kurtosis of less than three, it is said to have thin tails when compared to the normal distribution.
The assumption of a normal distribution is applied to asset prices as well as price action. Traders may plot price points over time to fit recent price action into a normal distribution. The further price action moves from the mean, in this case, the more likelihood that an asset is being over or undervalued. Traders can use the standard deviations to suggest potential trades.
This type of trading is generally done on very short time frames as larger timescales make it much harder to pick entry and exit points. Similarly, many statistical theories attempt to model asset prices under the assumption that they follow a normal distribution. In reality, price distributions tend to have fat tails and, therefore, have kurtosis greater than three.
Such assets have had price movements greater than three standard deviations beyond the mean more often than would be expected under the assumption of a normal distribution. Even if an asset has went through a long period where it fits a normal distribution, there is no guarantee that the past performance truly informs the future prospects. Advanced Technical Analysis Concepts.
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Unfortunately many authors assume precicely that, and test their data. Another common mistake is to assume statistical tests of normality were tests for normality, and to interpret a 'significant' outcome accordingly. Owing to their limited power, tests of normality can be very misleading for small samples, and we give a few examples where authors have used more appropriate graphical methods to assess normality.
Unfortunately though, we often find that insufficient detail of the methodology are given to enable a proper assessment of the results. Perhaps because of the importance of the normal distribution in the historical development of statistics, there are some very strange ideas around of what a normal distribution should look like.
We have included a couple of examples for your enjoyment The latter is much better on graphical methods of testing for normality, and is one of the few texts to cover rankits.
Thode is an advanced text covering all aspects of testing for normality.
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