Preliminary analyses examined the distribution, skew, and
kurtosis of all variables.
Given the large skewness and
kurtosis of three of its items, polychoric ordinal alpha was used to investigate the internal consistency.
Mean and standard deviation as well as the Skewness and
the Kurtosis of the 19 subscales of the CERS - M are reported in Table 2.
The kurtosis of the smaller project study was very flat.
That is,
the kurtosis of the model output would be flat, meaning pretty much equal probability of any outcome.
In particular a more thorough analysis would pay close attention to
the kurtosis of the distribution (i.e., the «fatness» of the distribution's tails) and would perhaps model it through a Generalized Pareto Distribution as is done in Otto et al., 2012 for example.
For that, the researchers rely on something called
the kurtosis of a distribution, which measures the size of its tails, or the rate at which the concentration of data decreases far from the mean.
Not exact matches
Comparison
of Diffusion Metrics Obtained at 1.5 T and 3T in Human Brain With Diffusional
Kurtosis Imaging.
They measure portfolio performance conventionally (Sharpe ratio), via effects on portfolio return distribution skewness and
kurtosis (as an indicator
of tail risk) and with investor utility metrics.
You get a VERY different result if you even use a lognormal prior with a standard deviation
of 0.65 - 0.85 (which maximizes width /
Kurtosis for a given mean).
If you have a situation where you are pretty sure that the likelihood will beat down the tails
of your distribution, then what you really want in an uninformative prior is one that maximizes your width rather than the extreme tails
of the distribution — relatively high standard deviation and relatively low
kurtosis.
You really need a fairly significant amount
of data before you can reliably estimate the skew or
kurtosis.
I think that we can be pretty confident that if done properly, the 1 SD would be pretty wide and
kurtosis flat, which can be expressed as «pretty much equal probability
of any outccome».
Re: quadratic interpolation... one
of the most interersting adaptive equalization methods I have seen is based on negentropy, approximated by squaring the
kurtosis (fourth order), an eighth order equation.
Ratings
of husbands» facial attractiveness were normally distributed in both studies (in study 1, skewness = 0.12,
kurtosis = − 0.42; in study 2, skewness = 0.43,
kurtosis = 0.20).
Preliminary analyses were performed to explore normality, linearity and homoscedasticity and the negative
kurtosis typically found in measures
of life satisfaction and relationship satisfaction were observed.
Due to some skewness and / or
kurtosis on some items on the SDQ and the DBD, polychoric ordinal alpha (Gadermann et al. 2012) was calculated instead
of Cronbach's alpha when more appropriate.
The
kurtosis varied between − 0.4 and 1.6, but in the case
of the subscale Conduct Problems it did reach high levels, up to 7.8 in case
of 11 - years old girls.
All variables demonstrated acceptable levels
of skewness and
kurtosis with the exception
of suicide ideation, which was transformed using the log - likelihood method to correct for non-normality.
Using the cutoffs
of two and seven for skew and
kurtosis, respectively (West, Finch, & Curran, 1995), all variables were normally distributed.
Correlation matrix
of behavior problem variables with means, standard deviations, skewness, and
kurtosis
Although none
of the NICU PCERA items used in the scales showed problematic skewness or
kurtosis (skew ≥ 2,
kurtosis ≥ 6), a few items showed limited variability.
Because
of the very skewed distribution (skewness = 3.27 and
kurtosis = 11.97) the outcome measure was recoded as a binomial variable (median split), in which 0 indicated a low Disgust mean and 1 a high Disgust mean.
Frequencies for all the independent and dependent variables were examined to ensure normality in terms
of skewedness and
kurtosis.
The
Kurtosis was also significant at 5.12 with a standard error
of 0.60.
To establish whether data was normally distributed, values
of skewness and
kurtosis were converted to z - scores (Field 2013).
On the basis
of distribution analysis using the Kolmogorov - Smirnov test and
kurtosis and skewness values, the decision was made to use parametric statistics.