# Questions tagged [normality-assumption]

Many statistical methods assume data or a model's residuals 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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64 views

### bimodal outcome - non normally distributed residuals

I have an outcome variable that is bimodal, this is because in about half the sample is measured from 0 to 5, and half the time from 0 to 7. Because of the different scales, I have decided to ...
9 views

### IV analysis for non-normal outcome distribution?

I now have a set of data where the outcome is continuous count data but does not follow normal distribution. IV analysis relies on linear regression, in which normality is an important assumption. Can ...
1 vote
39 views

### Test for bivariate normality assumption

Assume two time series $X_1$ and $X_2$, where $X_i=(x_{i,1},...,x_{i,T})$. How can we test the assumption of bivariate normality for these time series? (Assume each of the time series are stationary ...
272 views

### Understanding the assumptions of linear regression: residuals or data must come from a normal distribution? [duplicate]

I'm trying to better understand linear regression and have always heard that in order to meet the assumption of normality the data has to be normally distributed. However, I've also heard it's more ...
1 vote
12 views

### How to use side-by-side boxplots to assess assumptions of a 2 sample test?

Here is the context: So we can analyse this using a 2 sample t tests. The assumptions of t-test comparing the means of two independent samples are populations being compared should follow normal ...
455 views

### What is the reasoning behind expecting residuals in OLS regression to be normally distributed?

There are a lot of similar questions here but I have not found an answer to this specific question. Source: for example in https://peopleanalytics-regression-book.org/linear-reg-ols.html#norm-dist-...
73 views

### What to do when comparing mean of two populations and one is not normal?

I have a dataset with two populations (unpaired). First one with 36 observations, second one 74. The first passes the Shapiro normality test with p-value = 0.1521, ...
16 views

### Test for gaussian mixture fit when component assignment is known?

I have a process 𝑃 generating random variables X_1, ... X_n. From each of these I've sampled a set of samples ...
12 views

### Residual diagnostic for Boston Housing Dataset

I have some questions regarding the procedures for proper analysis of the "Boston Housing" dataset. My problem concerns the dysgnostics of the residuals and how to correct possible ...
18 views

### Significance test for accuracy - normal assumption

I have a dataset with pre-defined labels. I trained two machine learning classifier methods A and B to predict the labels and calculated the accuracy for each. I varied the dataset a bit and thus got ...
41 views

### Heavy tailed residuals in linear mixed model

I'm a new user of linear mixed models and I'm experiencing some troubles with that. I have a dataset with 680000 measures of milk production from 2017 to 2020, from a population of almost 37000 cows ...
1 vote
63 views

### Why use normality tests if we have goodness-of-fit tests?

What are the reason/s to use a nonparametric normality test (e.gr., Shapiro-Wilk, Jarque-Bera) instead of generic, parametric goodness-of-fit tests (good for any distribution including but not limited ...
1 vote
20 views

### Normality assumption of structural shocks in Vector Autoregression model

I’m currently working on forecasting yield curve evolution over time using a state space model where the transition dynamics are described using a vector autoregressive model of order 1. This model ...
33 views

### Normality Assumption - Help! [duplicate]

I am relatively new to statistics and struggle with the normality assumption (where and how it needs to be assessed). I understand that parametric tests need the data to be normally distributed. The ...
313 views

### 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: ...
43 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, ...
32 views

### 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 ...
1 vote
24 views

### 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
37 views

### 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 ...
1 vote
34 views

### 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 ...
9 views

### 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 ...
28 views

### 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 ...
20 views

### 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. ...
31 views

### 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?
11 views

### 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 ...
1 vote
43 views

### 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 ...
1 vote
41 views

### 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
41 views

### 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 ...
1 vote
19 views

### 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 ...
52 views

### 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, ...
35 views

### 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 ...
28 views

### 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 ...
1 vote
123 views

### 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 ...
12 views

### 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?
18 views

### 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 ...
45 views

### 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 ...
640 views

### 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 ...
43 views

### 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 ...
20 views

### 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 ...
38 views

### 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 ...
34 views

### 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" ...
63 views

### 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 ...
44 views

### 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 ...
108 views

### 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
45 views

### 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 ... 17 views

### 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 ...
31 views

### 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 ...
1k views

### 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 ...