# 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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97 views

### Normality test for discrete values of a continuous variable

I have a dataset with several hundred pH measurements from a factory line. This dataset will be used to infer process capability using Minitab. On a physical basis, pH is a continuous scale (being ...
11 views

### Model selection based on Jarque-Bera, Shapiro-Wilk and Ljung-Box tests

I am kinda new to econometrics I have six models with Jarque-Bera, Shapiro-Wilk and Ljung-Box results. How can I choose the best model using the tests mentioned above? Thank you
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### Why can we assume $\hat{\beta_1}$ is normally distributed?

I'm reading trough my textbook (“A Modern Approach to Regression” Sheather. Page 35) and it says that we can assume $\hat{\beta_1}|X$ is normally distributed because $Y_i|X$ is normally distributed ...
196 views

### Test whether the study population come from a normal or log-normal distribution based on mean, median, and number of subjects

I have MEAN, MEDIAN, NSUB (number of subjects) and SD data coming from different studies and different populations. These are the only available information in the studies. My data set contains the ...
25 views

### Some of my data is not normally distributed, what test should i use?

I am testing dating profile information and whether wanting children (yes, no, maybe) has an effect on how many attributes the seekers ask for. When testing for normality and homogeneity of variance ...
160 views

### Compare several means with different sample sizes (greater than 2)

I have seven different groups with different sample sizes and variances and I want to compare the means of their data. I'm not very informed in statistics, so could anyone help me out here? I've only ...
29 views

### Where does the Box-Cox Transformation actually come from?

I'm trying to figure out where the actual box-cox transformation comes from. I've looked at the original paper, and some of it's references, but for the most part, it seems that they just drop the ...
22 views

### How about finding a reliable answer for the normality assumption of the T-test

I'm working on a basic lecture about inferential statistics and I've tried to find a reliable and convergent answer in previous posts on Cross-validated. However, after reading several threads (like ...
429 views

### What is the CDF of the Shapiro-Wilk $W$ statistic?

I am trying to understand how Shapiro-Wilk test functions. So far, I have come across the following links: How are the values in the Shapiro Wilk weight table calculated? which explains how to ...
273 views

### Could this be considered normally distributed?

I have skewness and kurtosis values of 0.447 and -0.861 respectively. There are 540 observations and the standard deviation is 1.662. I have seen posts and suggestions saying between -1,1 and 2,2 ...
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### Determining the distribution of fitted values and residuals [duplicate]

For exam prep, we're supposed to answer this question (which we are supposed to be able to find the answer to in the course literature) For the model specified in a) and proper normality ...
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### Skewed outcome variable in moderation regression SPSS

I'm in desperate need of some help for my undergraduate dissertation. I'm looking for an interaction between a personality trait 'PLAY' and 3 parenting styles (which are separate continuous scores) on ...
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### Creating a prediction model with non-normal residuals on purpose

I am trying to build a model with non-normal residuals as it is supposed to overestimate rather than underestimate while being as accurate as it can be. So far I have not experienced a scenario where ...
2k views

### Assessing the power of a normality test (in R)

I want to assess the accuracy of normality tests over different sample sizes in R (I realize that normality tests may be misleading). For example, to look at the Shapiro-Wilk test, I'm conducting the ...
816 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 ...
1k views

### Confidence interval vs. prediction interval misunderstanding

Problem I have a time series data set with about 50 observations. I'd like to compute an interval that may contain the next/future value in the time series (the 51st data point). I tried using a 90% ...
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### How to perform van Zyl's (2018) ecf-based normality test in R [closed]

I have been reading quite a bit on empirical characteristic function (ecf) based normality tests, but cannot find any functions to perform such a test in R and lack the mathematical ability to figure ...
25 views

### Normality plot and shapiro test for repeated-measures ANOVA: near significant but not quite

I have a repeated-measures anova (Two-way), and I want to check for normality; my plots show this: ...
28 views

### My normality plot and Shapiro's test say different things

I have an LMER, and I want to check for normality; my plots show this: However, my shapiro test shows this: ...
18 views

### Confidence interval of bootstrapped difference of means

I am attempting to calculate a confidence interval for a difference in 2 populations by means of bootstrapping in order to compare this to an interval calculated via normal theory. I am getting stuck ...
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### Asumption of normality for two-way repeated measures ANOVA not met?

I have tested my data for a normal distribution (using a histogram on R studio) but the data were not normally distributed. I tried a sqrt, log and asin transformation on the dependent variable but ...
27 views

### Help identifying the features of this QQ-plot

I am wondering how to go about answering this question. I understand that the second option regarding the p-value is correct, as this graph shows non-normally distributed data - and the p-value states ...
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### Determining normality and model selection/specification

My data is as follows: Site Stim Pb_on Dest NR 1 S L L 41 1 S L R 13 1 S L F 6 1 S R L 11 .. .. .. .. .. I wish to determine what the ...
203k views

### Pearson's or Spearman's correlation with non-normal data

I get this question frequently enough in my statistics consulting work, that I thought I'd post it here. I have an answer, which is posted below, but I was keen to hear what others have to say. ...
164 views

### Asymptotic normality for nonsmooth objective functions

Assume that $f ({\bf x}; \theta): \mathbb{R}^p \times \Theta \to \mathbb{R}$, where ${\bf x}$ is the vector of inputs (with some distribution) and $\theta$ is the vector of parameters. Also, assume ...
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### Non-gaussian ML estimation with auto.arima in R

I am struggling with the details of auto.arima function in R. Particularly, I would like to estimate an ARIMA model with errors (i.e. regressors) for which: ...
37 views

### Are normally distributed sample means equivalent to normally distributed residuals?

According to t-test:Assumptions "The means of the two populations being compared should follow normal distribution" The one way ANOVA test in case of 2 groups equals the t-test but the ANOVA ...
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### Prediction interval for OLS with non-normally distributed residuals

I'm estimating a multiple linear regression model (found in equation 19 of "The volatility of realized volatility", Corsi et al. https://www.econstor.eu/bitstream/10419/25467/1/515328057.PDF) using ...
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### LDA vs. QDA when assumptions do not hold

If the Bayes decision boundary is linear and the underlying distributional assumptions are Normal, we expect LDA to perform better than QDA on the test set. But if the Bayes decision boundary is ...
71 views

### Normality of variables in correlation test and simple linear regression

A correlation test and a simple linear regression test both answer the same question, which is Is there a good chance that my data comes from a population where the correlation is positive rather ...
23 views

### Multiple linear regression with not normally distributed errors

I'm trying to analyze in R how the individuals from my sample use their income in terms of food/house rent/bills/holidays/etc. My database consists of 7 independent variables (gender, age, etc) and ...
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### Does the normality assumption hold? Is this an outlier?

I am trying to fit a multiple linear regression (OLS) model with IPO underpricing as dependent variable. As part of my master thesis I would like to analyze the effect of venture capital ...
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### Bland-Altman analysis in critical scenario?

I am analyzing some medical data about distance of tumor lesions from surgical resection margins, measured with two different protocols (say, protocols A and B). The overall idea would be to compare ...
87k views

### Assumptions of linear models and what to do if the residuals are not normally distributed

I am a little bit confused on what the assumptions of linear regression are. So far I checked whether: all of the explanatory variables correlated linearly with the response variable. (This was the ...
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### Angle of Line in a non-Normal Q-Q Plot

I'm currently working on a toy-problem of $n=15$ data-points and believe that my data may have come from a Truncated Normal Distribution with a lower-bound of $a=5.0$. I'm using the R's ...
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### ROC curve, d' A' - assumption-free?

In my research I want to know how reliably certain feature of a sentence indicates the class that sentence belongs to. So, according to that feature (=how many elements X they contain), the ...
44 views

### Two-way ANOVA when data is non-normally distributed

I'm trying to run a two-way ANOVA on a 375-sized dataset. I'm trying to navigate my way through the assumptions but need some assistance. Specifically, I have two groups as the IVs (1: Boys and Girls; ...
481 views

### Sobol variance based decomposition

I have 6 input variables, each of which is normally distributed. Can I use Sobol variance-based sensitivity analysis? I have read some articles where they said that input variables must have uniform ...
58 views

### normal distribution is essential in t test to compare two independent samples?

In student t test to compare the means of two samples, whether the normal distribution of each sample is prehypothesis or not? As we know, t test is used for comparing two independent small samples ...
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### Alternatives to Pearson's correlation given small sample size and normality hypothesis rejected?

I would like to use Pearson's $r$ to determine the correlation strengths among around $20$ variables. Unfortunately, I had to reject the hypotheses that the data from some (around $5$) comes from ...
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### R LambertW package - Gaussianize(): Why is transformation not possible? “Error in delta_Taylor(z.init) : kurtosis.y > 0 is not TRUE”

I am using the R package LambertW, specifically the function Gaussianize(). I have the following vector: ...
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### How to transform two non-normal samples to perform parametric test (t test)?

I have two samples of different size (Ratio = 1:12) which are non-normal in nature. The samples are sensor values from Machine working in normal condition and when it is about to fail. I have ...
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### Dealing with heavy-tailed residuals when fitting hierarchical linear models using lme4

This is my first time posting, so please excuse any issues with respect to my description of the problem and the presentation of the data and code I have supplied. Summary of the Design 30 listeners ...
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### What have to be normally distributed: groups or whole sample?

It is a general and maybe basic question, but it will help me to avoid a mistake. To test the dependence of continuous variable on nominal with parametric test (t-test, ANOVA), "the data has to be ...
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### Testing for normality in SPSS: Procedure for two or more independent variables WITHOUT levels/groups [duplicate]

In order to do a linear regression, I need to test my data set for normality. I have one dependent variable plus three independent variables. The independent variables are all scale variables, i.e. ...
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### there is a significant different result between qqplot and lillie,test for normality test

In R, when I test the normality of Decathlon dataset, the results of qqplot and lillie.test are very different. The size of the ...
685 views

### If a sample is not normally distributed, can a subset of the sample be normal?

I have used a Shapiro-wilk test on all of my data and the results show that it is not normally distributed. However, could this mean that a subset of my data could still be normally distributed?
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### Deviation from Normality Assumptions - t-test and f-test

Note that I am not a statistics major, but someone who is applying a workflow informed by statistics to a technical problem encountered at work. I've done some statistics at University, however the ...