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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12 views

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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52 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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43 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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2answers
72 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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1answer
38 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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3answers
77 views

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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20 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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15 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
38 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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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
24 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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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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475 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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43 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
43 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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17 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
68 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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29 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
41 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
35 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
27 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
44 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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2answers
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
227 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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17 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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47 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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19 views

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
41 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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31 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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57 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 ...
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2answers
79 views

Residual Bootstrapp based on GARCH models with student-t distributed innovation

I want to generate 500 simulations of my original return time series. My original return series (n = 4000) exhibits significant serial autocorrelation at lag 1 & 2, is non-normally distributed (...
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22 views

Shapiro–Wilk test for non-normal distributions

The Shapiro–Wilk test makes use of the correlation between the data (a.k.a. sample quantile) $x$ and its theoretical quantile $m$. As far as I'm concerned, it's a normality test simply because the ...
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69 views

Non-parametric alternatives for a three way nested ANOVA?

I am a student working on a graduate degree in the natural sciences. I am looking for advice on generals approaches and examples (R code and example data) which I might be able to follow to get ideas ...
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156 views

How to check SEM assumptions?

This question is related to SEMs that include latent variables e those that not include in lavaan package. SEM assumes normality/multivariate normality, but it is being very difficult to found a way ...
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20 views

Can I draw a histogram of the mean sample distribution (n=30) sampling from my dataset (n=200)?

I would like to test whether my data reasonably satisfies the normality assumption necessary to apply a t-test. My understanding is that, to apply a t-test, the distribution itself does not need to ...
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2answers
126 views

Why is the proposal in the MALA algorithm always normally distributed?

Notation: $\pi(x)$ is the target density. $(x_n)_{n=1}^{N}$ is the chain generated by the MCMC method. At the moment, I am doing some research in MCMC methods. Before, I was planning to dive into the ...
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testing normality for a two way anova, residuals as well as each sample? [duplicate]

to test a two way ANOVA do you have to test each sample for normality as well as normality for the residuals?
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1) Am i right in conducting an ANOVA 2) no p value because of lack of results

Im unsure whether I should conduct a two way ANOVA as GLM on minitab 17. Got seven mutant plants (with different knockout genes, including the wildtype and lines incase a knockout didnt occur). I'm ...
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22 views

Help with normalising data that has A LOT of 0s [duplicate]

I recently am analysing my results (behavioural, observation-based data), and I realised that my data are non-normal. No problem, this happens in behavioural data a lot, and I thought I just needed to ...
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2answers
74 views

Normality vs normality of residuals

I am currently trying to perform a hypothesis test on the difference between four means. Initially I was trying to use ANOVA but then realised I may not meet the assumptions for this test and may need ...
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25 views

Control chart control limits for non-normal data

I have the following control chart: To my understanding, control limits are calculated with μ ± 3σ. So basically it's setting boundaries using three standard deviations - and this assumes that the ...
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1answer
45 views

Pearson correlation coefficient: Gaussian data expected?

The Pearson correlation coefficient is sometimes referred to as a parametric statistic. Does this parametric nature imply that it is actually only applicable to data drawn from Gaussian distributions?
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1answer
39 views

Incomplete block design analysis

I have 4 treatments (6m, 12m, 24m, 40m) in 3 blocks, but all treatments are not replicated in these blocks: 6m, 12m, 24m are in Blk1 and Blk2 and Blk3 consist of only 34m (control plot) and 6m. How ...
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1answer
54 views

Types of Normality Test used in Minitab

I recently performed a normality test for a set of data. I noticed that when I use the AD test, the p-value is < 0.05; whereas when I use RJ test, the p-value showed is >0.05. My question here is: ...
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1answer
283 views

Why do two implementations of the Anderson-Darling test produce such different p-values?

I want to check the normality assumption of my series I am trying to figure out the way is computed the p-value of the Anderson Darling in R packages, goftest and <...
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80 views

Jarque-Bera Test for Normal Distrbances in a VAR

I did the test of he null hypothesis of Normal disturbances and found that it is rejected for Dlop and Dunp. Does this mean that I have a problem with my model specification? Or how can I rectify this ...
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Use of supportive inferential statistics (e.g. Levene's and normality tests) in underpowered samples

We know that underpowered statistics greatly increase the probability of a type II error (by definition), meaning a greater chance of failing to reject the null hypothesis despite the existence of a '...