# 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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### Determining normality and model selection/specification

My data is as follows: Site Stim Pb_on Dest NR 1 S L L 41 1 S L R 13 1 S L F 6 1 S R L 11 .. .. .. .. .. I wish to determine what the ...
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### Are normally distributed sample means equivalent to normally distributed residuals?

According to t-test:Assumptions "The means of the two populations being compared should follow normal distribution" The one way ANOVA test in case of 2 groups equals the t-test but the ANOVA ...
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### Non-gaussian ML estimation with auto.arima in R

I am struggling with the details of auto.arima function in R. Particularly, I would like to estimate an ARIMA model with errors (i.e. regressors) for which: ...
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### Prediction interval for OLS with non-normally distributed residuals

I'm estimating a multiple linear regression model (found in equation 19 of "The volatility of realized volatility", Corsi et al. https://www.econstor.eu/bitstream/10419/25467/1/515328057.PDF) using ...
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### LDA vs. QDA when assumptions do not hold

If the Bayes decision boundary is linear and the underlying distributional assumptions are Normal, we expect LDA to perform better than QDA on the test set. But if the Bayes decision boundary is ...
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### Normality of variables in correlation test and simple linear regression

A correlation test and a simple linear regression test both answer the same question, which is Is there a good chance that my data comes from a population where the correlation is positive rather ...
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### Multiple linear regression with not normally distributed errors

I'm trying to analyze in R how the individuals from my sample use their income in terms of food/house rent/bills/holidays/etc. My database consists of 7 independent variables (gender, age, etc) and ...
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### Angle of Line in a non-Normal Q-Q Plot

I'm currently working on a toy-problem of $n=15$ data-points and believe that my data may have come from a Truncated Normal Distribution with a lower-bound of $a=5.0$. I'm using the R's ...
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### ROC curve, d' A' - assumption-free?

In my research I want to know how reliably certain feature of a sentence indicates the class that sentence belongs to. So, according to that feature (=how many elements X they contain), the ...
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### Two-way ANOVA when data is non-normally distributed

I'm trying to run a two-way ANOVA on a 375-sized dataset. I'm trying to navigate my way through the assumptions but need some assistance. Specifically, I have two groups as the IVs (1: Boys and Girls; ...
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### normal distribution is essential in t test to compare two independent samples?

In student t test to compare the means of two samples, whether the normal distribution of each sample is prehypothesis or not? As we know, t test is used for comparing two independent small samples ...
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### Alternatives to Pearson's correlation given small sample size and normality hypothesis rejected?

I would like to use Pearson's $r$ to determine the correlation strengths among around $20$ variables. Unfortunately, I had to reject the hypotheses that the data from some (around $5$) comes from ...
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### How to transform two non-normal samples to perform parametric test (t test)?

I have two samples of different size (Ratio = 1:12) which are non-normal in nature. The samples are sensor values from Machine working in normal condition and when it is about to fail. I have ...
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### R LambertW package - Gaussianize(): Why is transformation not possible? “Error in delta_Taylor(z.init) : kurtosis.y > 0 is not TRUE”

I am using the R package LambertW, specifically the function Gaussianize(). I have the following vector: ...
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### Testing for normality in SPSS: Procedure for two or more independent variables WITHOUT levels/groups [duplicate]

In order to do a linear regression, I need to test my data set for normality. I have one dependent variable plus three independent variables. The independent variables are all scale variables, i.e. ...
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### there is a significant different result between qqplot and lillie,test for normality test

In R, when I test the normality of Decathlon dataset, the results of qqplot and lillie.test are very different. The size of the ...
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### Dealing with heavy-tailed residuals when fitting hierarchical linear models using lme4

This is my first time posting, so please excuse any issues with respect to my description of the problem and the presentation of the data and code I have supplied. Summary of the Design 30 listeners ...
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### Deviation from Normality Assumptions - t-test and f-test

Note that I am not a statistics major, but someone who is applying a workflow informed by statistics to a technical problem encountered at work. I've done some statistics at University, however the ...
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### How Many Residuals Should There Be for a One-Way rmANOVA?

As explained broadly across this site and in the stats literature, it is useful to check the assumption of normality in your ANOVA (analysis of variance) by plotting a QQ plot of the residuals of your ...