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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26 views

2-sample t-test VS Mann-Whitney test - one group is not normally distributed

I'm comparing two groups of data. One group has a sample size of 30, and the other a sample size of 45. The second group is not normally distributed, and thus this violates the normality assumption. ...
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11 views

Check normality assumption for a 3 by 2 within-between (mixed) ANOVA

I'm conducting a 3 (within) x 2 (between) mixed ANOVA in SPSS and would like to assess whether my data satisfy normality assumptions. Do to so, I have saved the unstandardized residuals from the ...
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18 views

Coverage of confidence interval of non-normal distribution

I know that when a sample is non-normally distributed, I need to use non-parametric alternatives, as when the assumptions of parametric methods are violated, its coverage will decrease. Let's say ...
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How to understand the normality assumption of the errors?

We know one of the Gauss-Markov conditions is $\mathrm{Cor}[e_i, e_j]=0$ for $i \neq j.$ Also, we assume the errors are normally distributed, i.e., $e_i \sim \mathcal{N}(0, \sigma^2).$ My teacher ...
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Variable does not follow a normal distribution, can I trust its p-value from a Unit Root test? [closed]

If a variable does not follow a normal distribution, I should not trust in the p-value from a Unit Root test, right?
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64 views

GLMM for continuous response in $[0, 1]$

I am looking into GLMMs because my linear model residuals' plot has a weird pattern (some residuals form a diagonal pattern), and a lack of normality was also confirmed with a Shapiro test. ...
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1answer
40 views

What is a lay explanation for the numerator of W in the Shapiro-Wilk test?

I am trying to understand in basic terms what the Shapiro-Wilk test is doing, but the math in the original 1965 paper is beyond me. (For starters, why is the covariance matrix n x n? What do the $v_{...
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18 views

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 ...
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72 views

chi squared goodness of fit test to check for normality

I have the following data: I would like to use the chi-squared goodness of fit test to test whether it comes from a normal distribution. How shall I go about it? In particular, I would like to know ...
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Why does the linear regression algorithm assume the input residuals (errors) to be normal distributed? [duplicate]

I am trying to know the assumptions of linear regression (LR). I understand linear regression needs the relationship between the independent and dependent variables to be linear, but LR also assumes ...
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Possible tests for large sample, heteroscedastic, non-normal data?

I have downloaded all posts in a Reddit community over a set period of time. In this community, it is a requirement that any post is tagged with one of eight "flairs." I'm trying to test for ...
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64 views

Identification of discrete choice models

Consider the classical Logit model. In particular, let $\mathcal{Y}\equiv (0,1,...,L)$ be the set of options available to consumers, where $0$ denotes the outside option. Let $$ u_y\equiv \begin{...
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Transformed variable interpretation

In the analysis of my data, the dependent variable was non normally distributed. I used the two-steps approach by Templeton to transform the variable, and the normality was met. NOW: In the ...
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What is exactly the non-normality requisite for nonparametric tests? [duplicate]

As the title says, what is exactly what is being tested before deciding to use a non-parametric alternative test (as Kruskal-Wallis for ANOVA, or Mann-Whitney's U for student's t)? Most sources are ...
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Does rowwise distribution of random values in creating a normally distributed vector variable in matrix(rnorm(.), byrow=TRUE) damage normality?

(Reprodicible example added) 150-character-limitless full question is: Does the rowwise distribution of values in creating a normally distributed vector variable via ...
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Pooling Skewness, Kurtosis, and/or Shapiro Wilk Values in a Multiply Imputed Database

I am currently screening a database that has undergone multiple imputation (20 iterations). Unfortunately, SPSS does not provide pooled values for the Skewness, Kurtosis, or Shapiro Wilk. I am ...
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32 views

Normality Tests in samples with outliers

I'm making a code in R that contains some parametric and non-parametric tests, like ANOVA and Kruskal-Wallis. To know if I should use one or another I check the "normality" of the test sample. My ...
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Interpreting Shapiro-Wilk-Test, skewness and kurtosis in the light of a qqplot and histogram

Currently I'm trying to find out if my data with n=11 follows a normal distribution to decide how I process further. To find this out I use the Shapiro-Wilk-Test which gives me p < 0.05 and thus I ...
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Why is the type I error (power?!) for shapiro.test on studentized residuals on lm is 10% and for regular residuals is just 5%?

I understand that the residuals from a regression model are not i.i.d. Hence, checking if they are normal (even when we know it is the case), should be a problem since they are dependent. The ...
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60 views

Normality testing with very large sample size

Hypothesis testing such as Anderson-Darling or Shapiro-Wilk's test check normality of a distribution. However, if the sample size is very large, the test is extremely "accurate" but practically ...
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46 views

How to check if means and variances are normally distributed?

From here I read that The t-test assumes that the means of the different samples are normally distributed; it does not assume that the population is normally distributed. By the central limit ...
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75 views

When, if ever, should a normality test be performed on real-world data?

I've recently come across some research studies and internal reports from my company where multiple mean-comparison tests are performed. The procedure is often as follows: first, the data is checked ...
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39 views

Apply normal or not-normal test to heterogeneously normal data sub-sets

I have a dataset made by measuring something on standard dilutions ranging from let's say 10, 100, 1000 and 10000. I checked how the results are distributed with the Shapiro-Wilk test, and it turns ...
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Not convinced about normality based on QQ plot, Shapiro and KS $p <0.001$

I have about 1000 data points, I'm trying to run a $t$-test because my points are divided in 2 groups and I want to compare them. The results of Shapiro-Wilk normality test: ...
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21 views

Opposite results from the residuals and JB result test?

I`m trying to forecast some forex returns of currencies couples. I build up my ARIMA model and test for normality of distribution after the arima is applied. I get different results from the Jarque - ...
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19 views

Data transformation on grouped data

I am running an Ax(BxCxS) mixed design. During data screening, I assessed for normality by splitting my data based on the two levels of Factor A. Some variables for one level are nonnormal (and normal ...
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1answer
68 views

Linear Regression Assumptions vs. Gauss Markov Theorem

I am wondering what is the difference between the Gauss Markov theorem and the assumptions of linear regression found here or here? For example, the third link says that the distribution of residuals ...
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27 views

Advantage of inputs/targets to be normally distributed?

Why is it advantageous for inputs/targets to most ML algorithms like neural nets to be normally distributed? I am not talking about mean normalization, but in some cases of skewed data, people perform ...
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1answer
31 views

Is one-way ANOVA robust to violations of homoscedasticity?

I read here that if group sizes are equal, ANOVA is robust against the violation of the assumptions of normality and homoscedasticity. I am wondering if this is the case, and if so why?
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77 views

Analysis of variance with not normally distributed residuals : how important is normality?

I am using gls and anova to analyse my data. I use gls to aply weights. I have one factor (tree genotype) and I analyse its influence on soil content. Here is an exemple of my data with one variable (...
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484 views

Logarithm of dependent variable is uniformly distributed. How to calculate a confidence interval for the mean?

My dependent variable is extremely non-normally distributed (Shapiro-Wilk gives $p=0.004$). However, taking its logarithm gives me something freakishly close to a uniform distribution. When I plot the ...
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44 views

What is point of transformation if the effects does not change?

with a question related to transformation. I have done a linear mixed model using the formula ...
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1answer
48 views

Assumption multiple regression: normality of residuals

I want to run a multiple regression analysis for a given dataset in SPSS. However, the dataset violates the assumption of normality of residuals, as depicted in the picture. The values for the ...
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43 views

How to make sure if the residuals are normally distributed? [duplicate]

Hello, I have a fairly big dataset containing 11000 data points. I am doing a ANOVA for my traits. But before that I have to make sure if the residuals are normally distributed or not. So, I did a ...
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27 views

Non-normal regression errors: consequences and solution

Doing an empirical econometrics project, I have managed to confuse myself on one of the basics and wonder if you could lead me on the right track. What I wonder about is the normality assumption of ...
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1answer
71 views

Why normality assumption on linear model implies equivalence between least square estimation and maximum likelihood estimation?

Consider the following excerpt from the Alan Agresti's book on generalized linear models: "Having formed a model matrix $\textbf{X}$ and observed $\textbf{y}$, how do we obtain parameter estimates $\...
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39 views

Does a PCoA (or MDS) assume normality of the variables behind distances?

More precisely, if I conduct a cmdscale (classical multidimensional scaling) on an Euclidean distance matrix by considering $n$ observations of $p$ variables i.e. $D_{ij}=\sqrt{ \sum_p (x_{ip} - x_{...
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1answer
46 views

Checking normality for a t-test

I am following stats courses at the moment and I am a bit confused about performing a t-test. I know that a t-test assumes normality and enough sample size. In the course I am attending, the ...
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1answer
55 views

How safe is that to ignore homogeneity of variances test and continue with Post hoc test?

I want to know if average time people spending on their favourite social media are statistically different. I consider here five groups, and the total number of participant is 700 persons. I have ...
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1answer
38 views

Is it correct to do stats in log transformed metabolomics data?

I have a dataset from targeted metabolomics analysis, the units I am working with are ng/ml[creatinine] (I use creatinine concentration to normalize the data since the samples are urine and can have ...
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1answer
46 views

Testing normality for residuals

I have an Randomized block design experimental set up and a data consisting of species abundance. I would like to test for normality of the residuals, as in unexplained variance due tot the blocks. I ...
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41 views

Can one use parametric tests (e.g. ANOVA) if part of the data/ variables meet normality criteria but others not?

I want to compare differences between two groups(n1=26, n2=18) regarding their performance on different tests but also explore how each group performed on different times of these tests. I am ...
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1answer
424 views

Dealing with heteroscedasticity and non-normality in a mixed model

I am trying to fit a mixed model (person as random effect) on data which has heteroscedasticity and non-normality. I log-transformed the Y-variable but it did not fix the problem. Normality and ...
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24 views

Panel data regression - normality and testing issues

Im doing an event study using panel data regression with abnormal returns for 15 events and 38 stocks as the dependent variable, and different multiples (P/E, B/M etc.) as the independent variable. I ...
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70 views

How to choose cut off for winsorization/ flooring- capping? What is the impact of variable distribution on the decision

To perform logistic regression I wish to winsorize outliers in independent/ explanatory variables by flooring and capping independent variables. Can you suggest how I should choose cut-off for ...
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Usefulness of rejecting null in normality test [duplicate]

In this Stackoverflow answer Ian Fellows said, Normality tests don't do what most think they do. Shapiro's test, Anderson Darling, and others are null hypothesis tests AGAINST the the ...
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1answer
44 views

Are these the correct residuals to test for normality for a within-subjects 2-way anova?

I have data of an experiment where subjects performed a task under 4 conditions (A1B1, A1B2, A2B1, A2B2, where A1/A2 are the levels of factor IV1 and B1/B2 those of ...
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36 views

Is checking for normality and linearity in this way correct?

Testing normality using a significance test is a little bit useless especially when you have a large sample size So, recently I found a way to test normality by running a fake regression using ...
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30 views

Quality assessment for multiple imputation when joint distribution is not multivariate normal

I have a dataset with 100+ columns and 1000+ observations with significant amount (>60%) of data missing and fraction of missing data in individual columns varying from 10% to 90%. Data in none of the ...
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100 views

Adjusted Pearson Goodness-of-Fit Test - Rugarch Package

I fitted a GARCH(1,1), GARCH-M and EGARCH of first order (using maximum likelihood) to my return dataset using both, Gaussian normal and Student-t distribution assumption for the error term. When ...