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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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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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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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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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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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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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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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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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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
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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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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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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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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 '...
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Tests of normality - qq and Shapiro-Wilk

I am new to the world of stats... My data had a log normal distribution, so transformed by log to get it nearer normal distribution. This is real-world data. From here I want to establish if my data ...
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1answer
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Is this a reasonable coarse test for normality?

I'm interested in assessing if the marginalized posterior of a parameter obtained through a Bayesian MCMC process is "more or less normal". I use quotation marks because I'm not trying to asses for ...
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1answer
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Wilcoxon signed-rank test or One Sample t-test?

I conducted a training session and for each of my users, I measured pre and post score (before and after training session). Each of my users (n=28) is measured twice, so my data is paired: Data: <...
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normality of independent variables [duplicate]

I am running a generalized linear model. The dependent variable is binomial and independent variables are categorical and continuous variables. My question is : 1. Does the continuous independent ...
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Which one of these is correct for linear regression?

Only one of these is supposed to be the correct one for simple linear regression. Which pair of plots would you say has constant variance and normal distribution? I feel like none of them have both ...
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checking normality in repeated ANOVA (residuals vs differences)

If I check for the assumptions of a repeated ANOVA (one IV with 3 measurements) I need to check for the normality of differences. From t-test for paired data I know, I calculate the difference and ...
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How to verify assumptions of a normal distribution? [duplicate]

I'm working with the iris data.I made a density plot And a qq plot For sepal Length.It looks Approximately normal With the left skew And a flat peak The points In the qq Plot Stay within The ...
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Quasi-likelihood Estimation and Linear GEE

I am trying to better understand some of the assumptions of the estimator I am using, which is linear GEE. It is my understand that linear GEE uses quasi-likelihood estimation and so it has weaker ...
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1answer
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Wilcoxon Test - non normality, non equal variances, sample size not the same

I know there are already a lot of posts out there, but I couldn't find this exact combination in any of them. Comparing two samples (Prices associated with men and with women), but I have neither the ...
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Normality of residuals in a VAR model

If I have these differents results for the normal distribution of the residuals, I should consider them normal or not? $JB JB-Test (multivariate) data: ...
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1answer
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Generalized Estimation Equations 3 levels

I have a dataset where students are nested within classes, and classes are nested within schools. I am interested in evaluating the effects of a treatment delivered at the student level. The response ...
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1answer
38 views

Correct normalty preconditions for the t-Test

Lately, I have had several data sets at hand that I want to use to study the effect of a treatment. The data is in the form of: \begin{array} {|c|c|c|c|} \hline \text{Participant} \quad & \...
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Pros and cons of using a ratio vs a difference score to compare group means

I plan to collect data from 2 groups of people (Gp_1 and Gp_2), some few hundred people in all. Each person will respond to 100 yes/no tasks, each response yielding both accuracy and reaction time ...
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How do I interpret the p-value from a Shapiro-Francia Test?

I have a situation where I have more than 50 samples in a given set of inputs and I cannot use the Shapiro-Wilk test as I don't have the numbers for the pyramid for $n>50$. I was then asked to use ...
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1answer
71 views

Comparing linear mixed effects models using ANOVA - underlying assumptions

I am trying to analyze some CPUE (Catch Per Unit Effort) data for a fisheries related analysis with lme models in R. So I have total of six models that are tested in groups of two to determine the ...
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1answer
68 views

Assumptions of linear mixed model not met

I have a repeated measures dataset with which I'm testing if individuals are consistent in their boldness scores (continuous variable) over time (trials). Towards this, I generated linear mixed ...
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1answer
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Is normality test a must for SARIMA forecasting?

My data is not normal and I have tried Box-Cox transformation, yet after Box-Cox transformation, it still fails under the Kolmogorov-Smirnov test, so can I skip the normality transformation and use ...
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“This is a lower bound of true significance.” in Kolmogorov-Smirnov. WHat does it mean?

I' conducting a Normality Test for a numerical variable (level of a substance in blood) in a sample of 368 subjects. As I will need to run analysis of covariance (ANCOVA) and partial correlations, I ...
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Can the Berry-Esseen theorem tell us whether acceptable inference may be achieved by parametric tests?

I refer in particular to such choices: 1) t-test (or its generalizations: ANOVA or Hotelling's $t^2$) vs its non-parametric alternatives (e.g., U Mann-Whitney test and its generalizations); 2) Pearson'...
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1answer
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Meta analysis Cliff's delta

Cliff's delta is an effect size typically recommended whenever the normality and homogeneity assumption do not hold---and thus, Cohen's d cannot be used. However, I cannot see any reference ...
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Censored Regression/Tobit: coefficients decrease drastically when non-normal distribution is assumed

I am trying to use a Tobit/ censored regression model to estimate the effect of a certain political condition on a tax. Our dependent variable is zero-inflated because in most of our observations this ...
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2answers
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When checking for normality, would you prefer numerical methods or graphical methods?

I would like to know what is your preferred way to decide when the deviation from the normal distribution is relevant. when saying "relevant", I not saying necessarily "statistically significant". ...
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Why linear regression needs normality assumption [duplicate]

In this page, it mentions that linear regression requires residuals to be normally distributed. Why we need this assumption, and what will happen if this assumption does not satisfy?
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1answer
101 views

Normal distribution test ( D'Agostino and Pearson's) in Scipy - results don't make sense

I want to test if an array of numbers is approximately normally distributed. ...
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Relationship between t-test and normality

I haven't been able to find a definitive answer to my question in previous topics, so I'll post it here. I am sure this is a trivial question for many, but I do not have ny formal training in ...
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1answer
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What should I do after multiple imputation in the data?

I have a data set with missing observations. I used VIM package in R for imputation. After imputation, I will try to run a ...
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Asymptotic consistency and normality

I need help getting the following problem Let $X_1,..,X_n$ be independent $N(\mu,1)$-distributed random variables. Define $\hat{\theta_n}$ as the point of minimum of $\sum_{i=1}^n(X_i-\theta)^4$...
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1answer
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Paired t-test of a non-normal data with sample size 66

I have a paired data with n=66. I understand that normality condition of differences data should be met to conduct a paired t-test. However, from the histogram, it doesn't appear so normal. The p-...
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A powerful test for any distribution

Simulations by Razali et al (2011) showed that the Shapiro-Wilk test of normality provided the most power (at a fixed significance level) when compared to Anderson-Darling, Kolmogorov-Smirnov, etc. My ...
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Normality test and parametric vs non parametric tests

I'm pretty new in statistical testing and I'd like some help in what I'm doing. I have two groups of scores from 0-100. Group A has 10 values and group B has 70 values. Initially I'm testing normality ...
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1answer
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Instrumental variables with non-normal endogenous

Does it make sense to conduct an instrumental variables model where the endogenous variable of interest is continuous but not normally distributed? I know for normal regression purposes, there is no ...
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What is the difference between Shapiro-Francia and Shapiro-Wilk tests of normality?

I apologize for this easy/basic question. Please forgive me if this is a duplicate question. I've been researching the Shapiro-Wilk test (1965) of normality for a project. In doing so, I found an ...
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Point Biserial Correlation

In terms of testing the assumption of normality for a Point Biserial Correlation; I have a dichotomous variable (1 = microsleep, 0 = no microsleep) and a continuous variable (number of driving events ...
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Normality assumption for t/z tests

I have what is probably a silly question regarding normality assumptions for t/Z tests. As I understand, t/z tests require that sample data was obtained from populations following a normal ...
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Checking the Assumptions for T-tests

I am in the porcess of checking the assumptions of some data in order to perform a T-Test and had a few questions about how they should be set up. I was able to find the assumptions for a T-test here....