On measuring skewness and kurtosis

Ðorić, Dragan; Nikolić-Đorić, Emilija; Jevremović, Vesna; Mališić, Jovan

doi:10.1007/s11135-007-9128-9

Cited by 40 publications

(28 citation statements)

References 12 publications

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“…The absolute values of S and K are usually positively correlated (Wyszomirski ) making S and K not entirely independent from each other (Blest ; Dorić et al ; Jones et al ). That is, high values of S and low values of K (bimodality) rule out one another, as a distribution with two distant maxima of similar magnitude cannot be highly skewed.…”

Section: Materials and Proceduresmentioning

confidence: 99%

Analyzing the shape of observed trait distributions enables a data‐based moment closure of aggregate models

Gaedke

Klauschies

2017

Limnology & Ocean Methods

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The shape of trait distributions may inform about the selective forces that structure ecological communities. Here, we present a new moment‐based approach to classify the shape of observed biomass‐weighted trait distributions into normal, peaked, skewed, or bimodal that facilitates spatio‐temporal and cross‐system comparisons. Our observed phytoplankton trait distributions exhibited substantial variance and were mostly skewed or bimodal rather than normal. Additionally, mean, variance, skewness und kurtosis were strongly correlated. This is in conflict with trait‐based aggregate models that often assume normally distributed trait values and small variances. Given these discrepancies between our data and general model assumptions we used the observed trait distributions to test how well different aggregate models with first‐ or second‐order approximations and different types of moment closure predict the biomass, mean trait, and trait variance dynamics using weakly or moderately nonlinear fitness functions. For weakly non‐linear fitness functions aggregate models with a second‐order approximation and a data‐based moment closure that relied on the observed correlations between skewness and mean, and kurtosis and variance predicted biomass and often also mean trait changes fairly well and better than models with first‐order approximations or a normal‐based moment closure. In contrast, none of the models reflected the changes of the trait variances reliably. Aggregate model performance was often also poor for moderately nonlinear fitness functions. This questions a general applicability of the normal‐based approach, in particular for predicting variance dynamics determining the speed of trait changes and maintenance of biodiversity. We evaluate in detail how and why better approximations can be obtained.

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Section: Materials and Proceduresmentioning

confidence: 99%

Analyzing the shape of observed trait distributions enables a data‐based moment closure of aggregate models

Gaedke

Klauschies

2017

Limnology & Ocean Methods

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“…If the values are about the same as the normal distribution, it is mesokurtic. These phrases are frequently confused (see Fiori & Zenga, 2009, for a historical analysis; see also Đorić, Nikolić-Đorić, Jevremović, & Mališić, 2009). "Student" [Gosset] (1927, p. 160) offered a handy memory aid, depicted in Fig.…”

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confidence: 99%

Problematic standard errors and confidence intervals for skewness and kurtosis

Wright

Herrington

2011

Behav Res

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Many statistics packages print skewness and kurtosis statistics with estimates of their standard errors. The function most often used for the standard errors (e.g., in SPSS) assumes that the data are drawn from a normal distribution, an unlikely situation. Some textbooks suggest that if the statistic is more than about 2 standard errors from the hypothesized value (i.e., an approximate value for the critical value from the t distribution for moderate or large sample sizes when α = 5%), the hypothesized value can be rejected. This is an inappropriate practice unless the standard error estimate is accurate and the sampling distribution is approximately normal. We show distributions where the traditional standard errors provided by the function underestimate the actual values, often being 5 times too small, and distributions where the function overestimates the true values. Bootstrap standard errors and confidence intervals are more accurate than the traditional approach, although still imperfect. The reasons for this are discussed. We recommend that if you are using skewness and kurtosis statistics based on the 3 rd and 4 th moments, bootstrapping should be used to calculate standard errors and confidence intervals, rather than using the traditional standard. Software in the freeware R for this article provides these estimates.

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“…A total of 220 participants were included in the analyses. Before the main analysis, we checked the skewness and kurtosis of all the constructs [119]. Results showed the skewness ranged from -0.593 to 0.151, and the Kurtosis ranged from -0.278 to 1.40, which are all within the threshold, suggesting a normal univariate distribution that fulfills the assumption for further analysis [119,120].…”

Section: Design Of the Study And Analysis Of Datamentioning

confidence: 97%

“…Before the main analysis, we checked the skewness and kurtosis of all the constructs [119]. Results showed the skewness ranged from -0.593 to 0.151, and the Kurtosis ranged from -0.278 to 1.40, which are all within the threshold, suggesting a normal univariate distribution that fulfills the assumption for further analysis [119,120]. Although we adopted the original scale from previous literature in this paper, we still needed to check all of the item loads of the specific construct via the factor analysis.…”

Section: Design Of the Study And Analysis Of Datamentioning

confidence: 99%

The Sacred Power of Beauty: Examining the Perceptual Effect of Buddhist Symbols on Happiness and Life Satisfaction in China

Qin

Song

2020

IJERPH

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The theoretical relationship between Buddhism and subjective well-being has gained much academic attention in recent decades. However, the prominent determinants of religiosity remain limited for researchers to understand a holistic picture of religion-informed subjective well-being, particularly in the context of Buddhism. This study has applied a quantitative survey to verify the impact of the aesthetic effects of the Buddhist gesture symbol on Chinese people’s subjective happiness through sequential mediators of life satisfaction and the perceived religiosity. The significance of this study is threefold. Firstly, it aims to enrich the current academic understanding of the religion-informed subjective well-being by introducing a new determinant of the Buddhist symbols. Secondly, the current study investigates the mechanism of how Buddhist symbols could influence happiness by analyzing the sequential mediating roles of religiosity and life satisfaction. Thirdly, this study empirically examines the topic in the context of China to confirm and underpin the theoretical relationship between Buddhism and subjective well-being in relevant research, which has previously focused on Western culture. Our results indicated that the aesthetic perception of the Buddhist gesture symbol positively influenced perceived happiness and life satisfaction. In addition, perceived religiosity and life satisfaction sequentially mediated the perceived happiness after seeing the Buddhist gesture symbol. Our findings contribute to the current academic understanding of religious symbols and their impacts on subjective well-being.

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On measuring skewness and kurtosis

Abstract: Skewness, Kurtosis, Estimates of moments,

Cited by 40 publications

References 12 publications

Analyzing the shape of observed trait distributions enables a data‐based moment closure of aggregate models

Analyzing the shape of observed trait distributions enables a data‐based moment closure of aggregate models

Problematic standard errors and confidence intervals for skewness and kurtosis

The Sacred Power of Beauty: Examining the Perceptual Effect of Buddhist Symbols on Happiness and Life Satisfaction in China

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