# Questions tagged [skewness]

Skewness measures (or refers to) a degree of asymmetry in the distribution of a variable.

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### Should I normalise a sample drawn from a skewed population?

I am interested in the effect of the number of inhabitants of political entities on certain political behaviours within these entities. It happens that the number of inhabitants is not evenly ...
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### log transform left data in r

I am having trouble finding the transformation operation for left/negatively skewed data. The catch? All of my values are between 0 and 1. As such, trying the standard log10 transformation command ...
1 vote
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### Why does a small shape parameter in the skew normal distribution invert the skewness?

I am using the rsnorm function from the fGarch R library. As one would expect, for shape parameter (xi in this implementation) that is sufficiently large (abs(xi) > 1), a histogram has a clearly ...
294 views

### Vintage of this lower bound on skewness for positive data with given mean and sd?

It turns out there is a lower bound on the skewness $g_1$ of any strictly positive set of data having a given mean μ and standard deviation σ: $$g_1 > \sigma/\mu - \mu/\sigma.$$ Although ...
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### zero-inflation analysis multilevel for continuos data (not count data)

I was trying to fit a multilevel model, but I discovered that my dependent variable is highly skewed and zero-inflated. Individuals report 5 times a day for 7 days their level of paranoia and the ...
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### Estimate Box-Cox Transformation Lambda Using Skewness and Kurtosis

I would be interested in a method to find an appropriate Lambda parameter for the Box-Cox transformation based on only the skewness and the kurtosis of a given sample. I.e, if the skewness and ...
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1 vote
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### How can a probability density distribution look negatively skewed on a graph but yield a positive skew result in Excel? [closed]

I am analyzing data from a young single mothers residential facility and I am seeing probability density plots that look clearly negatively skewed but Excel and calculates the dataset as being very ...
51 views

### Why do the skewness and kurtosis formulae have powers of the variance in the denominator?

We calculate the variance as the centered 2nd moment $E[(X-\mu)^2]$. So when it comes to the skewness and kurtosis, why are the 3rd and 4th moments divided by the 3rd and 4th powers of $\sigma$? Why ...
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### Is a product that has 4.9 stars from ten customers better than one that has 4.5 stars from a hundred customers?

In many areas, we encounter a situation where we compare averages of highly skewed statistics using two unequally sized samples. Typically, this happens when comparing items in an online store. For ...
408 views

### When does positive skew imply median<mean?

For a random variable $X$, the skew is defined as $S(X):={\frac {E\overline{X}^3}{(E\overline{X}^2)^{3/2}}}$, where $\overline{X}=X-EX$. It is often claimed that positive (resp. negative) skew implies ...
75 views

### Logistic regression with highly left-skewed data for the independent variable

I am using the in-built GLM function in R to identify the model that best predict frogs' occupancy based on survey data. One of the independent variable (saturation) is highly skewed, as 36 of the 57 ...
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### How to decide better threshold values for variables with skewed distributions

In the context of optimizing loan advance decisions for customers with gold loan history, I aim to establish threshold values (x and y) to categorize customers into four groups based on loan count and ...
1 vote
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### Tukey's IQR-method for outliers and highly skewed data

I am writing a thesis on performances on cognitive and linguistic measures. I have used the Tukey IQR method (Q1-1.5*IQR) to detect lower outliers in a non-normally distributed small sample of various ...
1 vote
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### Mean difference between four groups with

I have four categorical groups (A, B, C, D) each with one mean representing a numerical, skewed variable. The data structure is as follows: ...
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1 vote
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### How to convert Standarized Mean Difference to OR in skewed data?

There are many methods to convert Standarized Mean Differences to Odds Ratios for meta-analysis (ln(OR) = -1.8 SMD), but none that i have found really deals with skewed summary data. Do you think i ...
276 views

### Which model for highly skewed data

The response variable in the dataset is highly skewed with a "ceiling effect". The errors of a fitted regression model, will thus also be skewed. I tried to fit a regression but as expected ...
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### Can you do a log transformation for excess kurtosis, or is that mainly used for skewness?

I am planning on doing a regression analysis on STATA on the financial performance of private equity funds. On my descriptive statistics, I saw higher levels of kurtosis and skewness. I decreased ...
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1 vote
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### Should I transform my positively skewed predictor in hierarchical regression?

I'm doing a hierarchical regression trying to understand how intelligence (first predictor) and personality traits (second predictor) influence general knowledge (dependent variable). The problem is ...
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### Is "skewing the data" and "skewing the results" just selection bias?

I recall various conversations with biologists, ecologists, and foresters that I neglected to ask for clarification on at the time. It doesn't occur in any of my statistics references. Sometimes in ...
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### How to test overall skewness / normality in a large data set of ordinal data in R?

I want to test overall skewness / normality in a large data set of ordinal data from survey questions and was wondering how this can be done? (I couldn’t use Shapiro wilk as I received an error saying ...
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### Centering a skewed predictor variable in a multilevel model that is involved in an 2-way interaction

Is there a correct method to center (mean or median centering) a skewed predictor variable in a multilevel model? The predictor is a skewed, count variable and will feature in a two-way interaction ...
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### In a skewed sample with a large n, does Central Limit Theorem dictate that a t-test can be used, even if the mean cannot be interpreted? [duplicate]

I understand that, in the case of a highly skewed population and sample, the sampling distribution of the mean can still be normally distributed if the sample size is large, according to Central Limit ...
38 views

### Fixed Effects Regression, weird Residual Plots

I am running regressions analysing drought impacts on electricity generation based on fueltype of the generator. I transform the outcome variable (daily_generation) using an inverse hyperbolic sine ...
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### Increasing probability of middle-large values decreases skewness more than large values?

I found this counterintuitive result and want to check with you folks if I did not make any mistakes. Imagine a simple uniform distribution, of all values between 1 to 100. I would expect that ...
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### Differences in Pearson skewness coefficients [duplicate]

I downloaded this and that file. Then, I created histograms showing the daily cost and annual expenses per country. We observe that the histogram of cost21 is more symmetrical than the histogram of ...
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### Negative Coefficients for Interaction Term in Dichotomous Variables

I've come across an issue while analyzing some data and haven't been able to find a similar question on the site. I'm working with data concerning the impact of certain genes and smoking on the ...
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### How do I transform an extremely skewed distribution to use it for linear regression?

I'm currently working on a data set where the goal is to predict the number of rented bikes in Seoul, given information about the weather at the time. The data set can be downloaded here: https://...
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### Influence of Large Data Size on Logistic Regression Fit and McFadden's $R^2$

I am currently working on a logistic regression analysis and have encountered a situation where I have approximately 16 million data points. I am interested in understanding the influence of such a ...
166 views

### Can positive values with sd > mean have skewness = 0?

I'm trying to create an example of a distribution with all positive values, standard deviation > mean, and skewness =0 (third moment). I cannot. Is that possible? Can you prove it mathematically? ...
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### Comparing probability distributions from the same ML algorithm

Background: We are using a research tool that uses computer vision to quantify facial expressions (ie whether someone is smiling) from a webcam. The raw output for this tool is time series data ...
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### Log-likelihood skew-t

I am trying to write down the log-likelihood for the multivariate skewed student-t distribution, but I don't really get how to define it exactly. Could someone please tell me the definition as in how ...
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### Can I do skewness on multiple standard deviation?

I have a 1000 sample of an electrical test at each 4 different time, so I do simple descriptive statistic to obtain standard deviation at each 4 different time. Can I then use skewness on standard ...
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### Meaning of Skewness and Kurtosis values of Residual Errors in Time Series Forecasting Problem using LSTM

I have developed different kinds of RNNs (such as LSTM,GRU etc.)to predict future values of thermocouple measurements. The residual errors look like they do not follow normal distribution, so I wanted ...
501 views

### Cut off value of +/- 1.5 for Skewness and Kurtosis (Tabachnick & Fidell)

I've read multiple posts/papers citing Tabachnick and Fidell's cut off of +/- 1.5 as the acceptable range for skewness and kurtosis to determine normality; however, I cannot find it in their book. Can ...
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### Hazard ratio and skewness

Suppose the distribution $F$ is absolutely continuous. Is there a way to compare (i) the monotonocity of the hazard ratio (i.e., strictly decreasing/increasing); (ii) the skewness of the distribution (...
1 vote
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### Power analysis to detect non-zero skew/kurtosis

Tests exist to determine whether a distribution is normal. For example the Shapiro-Wilk’s method. I'm wondering how to determine whether I'm powered to detect that my distribution is non-normal (e.g., ...
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