# Questions tagged [normality-assumption]

Many statistical methods assume data are normally distributed. Use this tag for questions about the assumption & testing of normality, or about normality as a *property*. Use [normal-distribution] for questions about the normal distribution per se.

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### How to assess normality under the OLS assumptions?

When we have a multivariate regression function, which assumption has to hold so that the OLS assumptions are not violated: ...
38 views

### I have a group that contains zero data, and I want to know whether it is considered normally or not normally distributed.?

I have a group (group2) that contains zero data, and I want to know whether it is considered normal or not normally distributed. I used the SPSS software, and it showed this result. I also tried R, ...
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### Why is non-normality of time series not a problem for ARIMA and GARCH?

My time series is very leptokurtic and non-normal, which is of course highly common for time series data. However, I don't exactly understand why that is not a problem for ARIMA modeling and GARCH ...
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1 vote
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### Do we need to check normality of the residuals when using 'CSS' method to fit ARIMA model?

I'm using auto.arima to fit my model. When I used the default CSS-ML method, I noticed that the residuals are not normal. So I ...
1 vote
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### Statistical analysis - Shapiro-Wilk test?

I apologize if this question will seem odd, but I am quite new to statistical analysis. I performed coinfection experiments with a total of 12 conditions, and I have 3 measurements per condition. I ...
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### R: Shapiro-Wilk test yields different results in descriptives and in One-Way ANOVA

I got a dataset of 60 people from a between-subject approach that I was trying to check for normality. (Since I need information about normality for ANOVA post-hoc tests.) They were split in three ...
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### Testing alternatives for Three-Way Anova that violates normality assumptions (outliers)

I am looking to do inference on Three-Way Anova model, but after looking at the residuals I saw a few violations: non-normality and a few outliers (as seen below). My question would be: How do I deal ...
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### What am I not understanding about semivariogram and Normal Score Transformation?

I have generated this two dimensional random field: This is done following this page. In particular, I have selected t=23 as dataframe and I have changed some parameters. As you can noticed, I have ...
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### Relationship between normally distributed errors (bivariate OLS regression) and bivariate normality of variables (Pearson’s r)

I have forty quite diverse statistical text books at hand but I cannot find a reliable answer. I’ve studied the following and associated threads, but they didn’t got into it that deep: here and here. ...
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### Transforming for assumption of normality (normality of residuals)

My model has a violation of normality assumption so the residuals are not normally distributed. I have tried log transformation and Box-Cox, but nothing worked. Any suggestion?
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### Is there a way to determine possible errors in data based on distribution

I am trying to find possible errors in the data. Below are the distributions of yield for 4 different fields. As the fields are large and non-homogenous, the distribution is not normal. Previously, I ...
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1 vote
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### What statistical test compare truncated distribution

I have been taking measures of two populations of mice. One population runs for 10minutes and the other can barely run for 2-3 minutes. The problem is that I have too many mice to keep testing them ...
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### OLS coefficient estimation with Poisson errors

Assume that in this regression $$Y=\beta_0+\beta_1 x+\epsilon,$$ where $\epsilon$ follows a Poisson distribution. Using OLS, estimate $\beta_0,\beta_1$ and $\text{cov}(\beta_1,\beta_0)$. I am ...
1 vote
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### How to know that a simple linear regression model is good enough if the independent variable is not normally distributed?

I would like to start saying that I am knew to statistics therefore yet a lot ahead of me. I ask for apologies if something sounds trivial. The problem We have a sample of 30 Nitrogen and Carbon ...
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1 vote
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### If the normality assumption in the for the GLS estimation fails, would you switch to GEE?

I want a marginal model, ideally fit via GLS. But the normality of residuals doesn't hold. It isn't much skewed, I don't want any transformations. It's just non-normal in shape. Yet still reporting ...
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### Both Shapiro-Wilk normality test results are non-parametric

I have 2 resuls from normality testing via Shapiro-Wilk test: and . If I understand correctly, both have p > α = 0,05 which indicates that both have normal distribution. So for my next analysis, ...
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### Calculating fixed effects in a mixed model with non-normality and heteroscedasticity with a 3-level time variable?

Due to non-normality and heteroscedasdicity, I use robustlmm and not lme4 for my mixed effects model. The variables look like this: ID: subject variable (random factor) var1: categorical between ...
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### Small sample skewed but population is assumed to be normal, is a two sample t-test still valid?

Let's say I have two samples with relatively small sample size and their distributions are skewed. The population distribution is assumed to be normal. It just so happens that these two particular ...
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1 vote
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### fast approximation of degree of normality, given order statistics

In a software application, I have access to the order statistics (without any extra computational cost) of a collection of $N$ samples (where $N$ can vary and is often quite large, usually on the ...
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### under what circumstances are regressors (x) correlated to the error term (u)?

suppose that Cov(Ui, Uj)=0 and Cov(Ui, X3i)≠0. What are some of the examples when one can expect a nonzero correlation between a regressor X3i and the error term Ui?
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### Transforming to address normality assumption (data with 0s)

I have done a regression analysis which violates normality assumption (shapiro.test yields <0.05 and plotting also shows that non-normality). Since my y has values less than 1 greater than 0, I ...
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### How can I perform a Tetrachoric and Polychoric Correlation on variables that aren't normally distributed?

From everything I have read, both tetrachoric and polychoric correlations assume normal distributions. However, the data I want to conduct these correlations with is not normally distributed. Does ...
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### Why we prefer normal distribution of data in linear regression

As I recalled, we can also assume the data points come from Laplace distribution and hence it will be the linear regression with absolute error. Why did so many texts assume the data points came from ...
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### Heteroskedacity and non-normality - What to do?

I conducted an experiment in which I am trying to model the relationship between my response weed_coverage [%] and the predictors soil moisture [%] + treatment + distance. Weed_coverage and ...
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### Comparing relative differences using paired samples t-test

I have the following problem: I have data from a small usability testing session where participants (n=22) had to perform the same task on the original and a modified interface. I have to compare data ...
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### Metric to measure how "standard Gaussian" a set of samples is?

Assume that I have a set of $N\in\mathbb{R}^{D}$ samples from some otherwise unknown multivariate distribution $p$. I seek a metric which might tell me how "close" $p$ is to a standard ...
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### Clarification about ANOVA assumption of normality [duplicate]

A few quick definitions: An error is the difference between an observed value and the "true" value A residual is the difference between an observed value and the "predicted" ...
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### How to deal with skewed data?

I want to examine 2 variables of experience: A. Regular practice - hours. B. Formal practice - days. Both variables are right-skewed, with extreme outliers (Experts) and many subjects with zero ...
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### What is the different between t(3) and Ca(0,1) distributions

I did a simulation study for empirical power for normality tests Shapiro-Wilk test and Anderson-Darling test against alternative t(3) and Cauchy distribution with parameters 0 and 1, I know both are ...
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### Asymptotic T-test validity for proportion values

I have a large sample of values, bounded in $[0, 1]$, divided into two conditions A and B, and I want to test the significance of one condition A having higher value than condition B. For the details, ...
1 vote
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### Comparing if there is a significant difference in two means of independent samples when the data is not normally distributed?

I am looking to see if the means obtained in previous clinical testing is significantly different to the means obtained by remote testing. I was planning on using a One sample T-test however the ...
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### Method selection - Linear vs. Logistic - Ordinal Outcome & Nominal Exposure

I proposed the method Ordinal Logistic Regression for the below analysis but received feedback that I should use Lasso Regression. Outcome: Ordinal scale (of 1-6) Exposure: Nominal categories ...
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### Can you correlate two variables when one has only 7 distinct values which repeat?

I have two variables which I want to correlate. Variable “X” has only 7 distinct values which repeat for each subject tested. The other variable, variable “Y”, is the rating of the subjects to each of ...
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### If a data set appears to be normal after some transformation is applied, is it really normal?

Suppose you have a data set that doesn't appear to be normal when its distribution is first plotted (e.g., it's qqplot is curved). If after some kind of transformation is applied (e.g., log, square ...
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### if I have a variable in my data that is not normally distributed, could I still use an ANOVA if my sample size is large enough?

I have a sample size that is more than 30 but one of my continuous variables is not normally distributed. The Shapiro-Willk test does say that my data is not normally distributed. I am going to ...
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### Small Sample - Confidence Interval Mean

I have a sample size of 14 and I plan to measure confidence intervals for the mean of different characteristics. I can say this about my data: ...
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1 vote
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### Unclear as to purpose of K-S test & U test in this study

I'm currently looking at this study's statistical measures: https://www.sciencedirect.com/science/article/pii/S0191886920302531?via%3Dihub Somewhere in the paper I noticed this: I have some questions ...
1 vote
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### What kind of normality tests that use comparison of moments?

I have these data of normality tests from a paper. What kind of normality test that use comparison of these parameters? Is there anyone here who can provide a reference link about this form of ...
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### Using z test or t test when $\sigma$ is unknown

Note: I realize similar questions have been asked here before but I couldn't find my specific doubt addressed (not in so many words, anyway). In testing a large sample for the population mean if the ...
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### Significant interaction in robust ANOVA but no significance in traditional ANOVA

In a 2x2 mixed design (2 groups measured at 2 times, n1 = 10, n2 = 12), a subsample violated the assumption of normality (Shapiro Wilk test). Thus, I used robust ANOVA (R-package ...
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### Is it okay to do a moderation anaylsis after the normality assumption failed (Shapiro Wilk)?

I am currently conducting a study on the suicide topic and entering the data analysis period. The Shapiro Wilk analysis reported that all my data failed the normality assumption. Most of the data's p ...
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### Is it reasonable to use the Kolmogorov-Smirnov test to assess the normality of a random variable?

Context I am confused by the following post where the accepted answer states that : You can't really even compare the two since the Kolmogorov-Smirnov is for a completely specified distribution (so ...
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### What does it mean if the Pearson's correlation is significant but Spearman is not?

I'm looking for a correlation between 2 parameters, neither of which is normally distributed. Hence from my (very limited) understanding of statistics, I should be running a Spearman correlation or ...
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1 vote
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### prop.test() in R assumptions?

Can anyone verify if the following assumptions are true for prop.test in R? I think it's a hypothesis test for differences in proportions between groups, no? Key assumptions(?): Samples are randomly ...
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### Do robust estimators like M-estimator still have higher variance than OLS in presence of non-normal errors and/or outliers?

In my studies I've learned that even with non-normality of the errors, the OLS estimator is still considered BLUE (Best Linear Unbiased Estimator). The texts also suggested using M and L estimators ...
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