# 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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### Selecting random effects in a linear mixed model when all participants complete all repeated measures?

Participants read 10 pairs of stories from Author A and Author B on 10 different topics (different topic for each pair). For each pair, they indicated whether they preferred Author A, Author B, or ...
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### What should I back transform beta coefficients when my dependent variable is fractionally exponentiated in R

I have this mixed effects regression model. To create a normal distribution in continuous scale dependent variable, I fractionally exponentiated it: ...
22 views

### Analysis of Variance Assumption Testing When Multiple Error Terms Are Used

I am conducting a repeated-measures analysis in R, where blocks were sampled repeatedly over a season. ...
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### Normality condition met with outliers in residuals

I am not sure if the normality condition for my multiple regression is met. Below are the graphs of my residuals. In the second graph (residuals vs fit) the red points are the outliers in the fitted ...
1 vote
66 views

### Normality of residuals in panel data

I ran a linear regression containing country- and year-fixed effects from a sample containing panel data (country by year). Since I'm using OLS, do my residuals have to look approximately normally ...
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1 vote
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### Transforming data with two groups for multiple regression analysis

I have a dataset includes 2 groups (HC, PT) and unfortunately, variables (8) are not normal. I'm trying to run a multiple regression to see if the relationship between the variable of interest ("...
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### In linear regression, in what situation(s) would you transform the response variable BEFORE having checked the assumptions?

I have a non-normally distributed, right-skewed response (dependent) variable which will be used in an (OLS) linear regression model. Why would I want to transform this before having checked the ...
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### Is it possible to perform a three-way ANOVA on non-normal data?

I am not very experienced in statistics so I'm not sure how to tackle this data. I have run an experiment where we recorded the proportion of time some beetles spent in 4 different habitats. Response ...
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206 views

### Can Wilcoxon be used in large sample with non-normal distribution?

I am doing my undergrad research, aiming to know the difference of before and after an intervention. our sample size is 37 which is already considered as a large sample right? However, when we test ...
27 views

### Linear Mixed Model Assumption Testing

I'm looking at my eye-tracking data, and I'd like to analyse the following gaze data (fixation duration) with a Linear Mixed Model in JAS. But I'm not sure if the residuals are (approximately) ...
563 views

### In linear regression, do the errors overall have a normal distribution, or do the errors at each value of x have a normal distribution?

In linear regression with fixed effects (i.e. with constant $x_i$, not random $X_i$), the model states that $\epsilon_i \sim N(0, \sigma^2), \ \ i = 1, 2, ..., n$ Does this say that the overall set ...
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### Handling Non-normality of Reaction Time Data in Mixed Models

I am examining the effect of 'Phase' on reactions time (RT) data using a mixed model in lme4. However, as is common with RT data, the residuals are non-normal. This is the first model, which is a ...
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### Is there a way to calculate lambda for a Box-Cox transformation when there are two categorical independent variables in R?

I have the following model where X is the duration of a particular event, A is a factor with five levels and B is a factor with two levels. I want to run a type III ANOVA analysis. ...
32 views

### True or False: If the distribution of Y|X is normal, then the regression of Y on X must be both linear and homoscedastic [duplicate]

I'm trying to interpret an early and pretty dense (to me) paper on the theory of linear regression: Bartlett, M. S. (1934). On the theory of statistical regression. Proceedings of the Royal Society of ...
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### For normality testing, should biological replicates be averaged or should all values of each subgroup be evaluated as independent data points?

I have performed an in vivo study evaluating splenic white:red pulp ratio as determined by AI on histopathologic slides (neural network trained and validated per published guidelines). The questions ...
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556 views

### Why does the normality assumption not affect Linear Regression in large samples?

I've read once that the normality assumption shouldn't be a problem and that you actually shouldn't care that much if your sample is large. Why is that? Can someone give me a mathematical explanation? ...
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### SEM: Multivariate normality of the residuals?

I am currently reviewing the assumptions related to structural equation modeling and I read the following in an article on the subject: "Second, the assumption of normality applies to the ...
110 views

### Large sample size and multivariate normality assumption

I am working on a student research project using structural equation models for longitudinal analyses and am currently checking the assumptions. My sample comprises around 300-400 people. If I have ...
56 views

### Possible reason for the Central Limit Theorem not to apply?

I have a multi-generator process which generates around 1200 data points per minute consisting of ~80 processes which contribute more or less evenly to the data points. Each singular process should in ...
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### Can I violate assumptions of normality for categorical linear regression models?

I'm using packages included in this R/rStudio tutorial to set up some linear regression models comparing a continuous dependent variable (eccentricity) to three categorical variables (year, bird ...
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### Partial Correlation and 1 Categorical Control Variable with 3 Categories

I'm trying to calculate the partial correlation between continuous variables $X$ and $Y$ while controlling for $Z$ (a categorical variable with three possible categories). Tutorials and answered ...
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### when focus on the pre-test for the normality test and ignore the pre-test for equality of variances?

When should a pre-test for normality only without a pre-test for equality of variances be performed before location tests like this paper did ((Rochon, J., Gondan, M. & Kieser, M. To test or not ...
234 views

### What are bounded distributions? and can a bounded distribution hold the normality assumption?

I heard that normal distribution should be unbounded, but I want clarification about that, aren't most distributions in the real world bounded, I mean they won't go to infinity they have minimum and ...
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### Can I transform two log variables into one using multiplication in VECM time series model?

I performed a Vector error correction model using Tourist Arrivals as a dependent Variable and Real GDP, Public Road Transport operated distance and Public Railway Transport operated distance as ...
49 views

### Do these graphs show normality of model residuals? [closed]

I have a linear mixed-effects model (lme4 R package) and I am trying to work out whether the model residuals meet the assumption of normality. However, by looking at the graphs below (model residuals ...
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### Sample size required for normal approximation - null hypothesis or estimate?

Consider a simple hypothesis test with a binomial distribution $Bin(p,n)$: $$H_0: p = p_0, \\ H_a: p \neq p_0$$ and my estimate for $p$ is $\hat{p}$. If I wanna do a normal approximation, a common ...
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### When to use parametric/GLM/ANOVA, in relation to data normality

In my experiment we looked at colour change (luminance) following a predatory stimulus (presence and lock of being the two treatments). The data consists of luminance before, after and the % change ...
356 views

### Normality test using normal Q-Q plot and histogram

I have plotted a normal Q-Q Plot and a histogram to check the normality of this set of discrete data. My interpretation is the data are not normally distributed since they do not fall on the linear ...
1 vote
69 views

### Normality assuption violation of time series data in the presence of outliers

I have a dataset containing information on district wise monthly dengue incidence from 2010 to 2021. I have found that there is a sudden increase in the dengue incidence due to a new variant in 2019. ...
161 views

### Impact of outliers to QQ plot

I'm trying to build an GLM regression (10k samples and 50 dimensions). I ran an analysis of the dependent variable since the regression has a normality assumption for the dependent variable. The QQ ...
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### Why is every predicted $y_i$ in linear regression equal to $E[Y|X]$?

I have some loose intuition with this but I don't understand it Say we have a scatterplot of data in 2 dimensions. Then we can propose a mean model where, for all $x_i \in X$ the estimated $y_i = E[Y]$...
130 views

### Addressing Non-Normality of Random Effects in Linear Mixed Model

I have a paradigm where participants complete a reaction time task with three different stimulus 'Conditions'. I generate two contrasts for my mixed model. I produced the plots below to assess the ...
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1 vote
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### Solving equations where unknown parameters are distributions

Let $\mathcal{D}_1$, $\mathcal{D}_2$ and $\mathcal{D}_3$ be three distributions defined on some space $\mathcal{X}$. Assume $\mathcal{D}_1 = \mathcal{D}_2 + \mathcal{D}_3$ and $\mathcal{D}_1$ is ...
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### Anova model assumptions. How to go by?

I have a data frame that contains a continuous response variable measured on different species, at different elevation and month of sampling as explanatory variables. I want to analyze how the ...
40 views

### Normality assumption n=48 [closed]

Regarding normality assumptions for model evaluation I have been told by my supervisor that it is not needed in the case of analyzing but is needed in forecasting only. i am looking for an explanation....
92 views

### Does shapiro.test() automatically work out residuals on your data?

I'm quite new to R and I am trying to do some stats. I have a set of data and want to work out whether my data comes from a normal distribution. I was told to do the test on the residuals of my data, ...
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63 views

### About the normality question with four conditions

I am encountering difficulties in determining the normality of data and distinguishing whether the data I have collected is parametric or non-parametric. I have gathered data using a 7-point Likert ...
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### I am unable to relate the normal distribution dependency for regression . I need a mathematical intuition cum understanding for regression assumptions [duplicate]

What is the mathematical significance for the assumptions of linear regression to hold true for arriving at a single/multiple regression formula? Can anyone use the assumed normally distributed ...
71 views

### Hypothesis testing - Newbie blockers - Update and more

Brief : I'm from manufacturing industry, a processing machine in our production line used to do pressing, polishing and QA one after the other. Now we have a new machine that will perform these at the ...
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### Robust ANOVA t2way unequal sample sizes?

I have some parameters that I would like to analyze with a two-way ANOVA. The treatment groups have unequal sample sizes (n=9, n=36, n=36, n=36) and the data do not fulfill the requirement of normal ...
24 views

### Decomposition of variance in linear regression, normality

Please correct me if I am mistaken, but I've read somewhere that the usefulness of normally distributed errors $e$ lies in the fact that we use independence to decompose  Var(y) = Var(y - \hat y + \...
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415 views

### When to use Pearson's test and when to use Spearman's test?

I want to do a correlation analysis on a dataset of 28 samples. I want to correlate the age with the size of a reflex response. But I don't understand whether I should use Pearson's or Spearman's test....
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### Assumption of Normality - do the residuals need to be normally distributed for each independent variable (or each level of an IV)?

Let's say I have 4 groups of football fans, and I want to see who screams loudest, and I want to run an ANOVA. My dependent variable is loudness, and my independent variable is Fan_Type, with 4 levels....
1 vote
49 views

### Doubt on checking linearity assumption in a mixed-ANCOVA design

I am a PhD student and I have to run a mixed-ANCOVA on some questionnaire scores (my dependent variable) according to the following model. Factors of ANCOVA are (a) Timepoint (pre-intervention, post-...
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### How is it possible to compare powers of normality tests?

The famous paper [1] compares the power of several normality tests. Regardless of its result, my immediate question is, "How is that even possible?" Well, the definition of power in this ...
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### How could Lilliefors use Monte Carlo if the estimand is not distribution-free?

Lilliefors test is a well-known statistical test for normality. Its idea is based on the Kolmogorov-Smirnov test, except the CDF is replaced by the CDF of the normal distribution with $\mu, \sigma^2$ ...
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### A T-test for difference of means and normality assumption [duplicate]

I am a little bit confused about normality assumption in T-Test for difference of two independent means. My reasoning now as follows: If the distribution of the populations are non-normal, it's ok as ...
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### I have applied many statistical tests to my data, but still cannot determine normality

I have run multiple tests to determine normality on my dataset, but I am unsure which one to adhere to, especially since my histograms, density plots, and QQ plots leave much to be desired in terms of ...
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1 vote
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### (Multivariate) normality assumption for dependent variable

In their book on multilevel analysis Hox et al. (2017) write in chapter 13: 'The main assumptions are [...] (multivariate) normality for dependent variables, which is the focus of the current chapter.'...
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