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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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 ...
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35 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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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: ...
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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 ...
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1answer
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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 ...
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1answer
20 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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27 views

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 ...
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33 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; ...
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54 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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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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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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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 ...
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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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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 ...
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Checking the normality of a large sample?

If I want to analyze a large sample size (N = 50.000) of continuous data ($ revenue) from an A/B test, what would then be the best way to check for normality? Thanks in advance!
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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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Normality of residuals of arima model

Is the normality of data important if I have more than 100 observations ? I have a time series data which include 143 monthly observations, I used ARIMA to fit the data and due to the absence of ...
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4answers
141 views

Assumption of normally distributed residuals in linear regression [duplicate]

Let us consider the simple linear model $y = \beta_0 + \beta_1 X + \epsilon$, where $y$ is real number, $X$ a matrix of reals and $\epsilon$ is the random "noise". The least-square estimate of the ...
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Approximate discrete data by the normal distribution before doing a statistical test assuming continuity? [closed]

I have n subjects in my experiment, repeating 3 times an action, each time resulting in a success or a failure. These 3 repetitions are IMO not independent because the subject could improve over time. ...
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1answer
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Limitations of Kolmogorov–Smirnov test

In this article, it is said that the test statistic tends to be more sensitive near the center of the distribution than at the tails. Can some please explain this what it means? (with a simple example ...
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1answer
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Checking the normality assumption for ANOVA test [duplicate]

Let's see if I understand this correctly. The normality assumption means that for each group I am testing the response within each group is normally distributed. So in order to check all the groups ...
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Comparing excess returns using t-test [duplicate]

I am working with analysis on multiple mutual funds. I would like to find out if the average excess return of one of them is significantly lower than the average excess return of another one. I have ...
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How to transform $P[k_1\leq (x_i-\mu - \sigma\cdot Z)^2 \leq k_2]$ to $P[k_1\leq \frac{(x_i-\mu)^2}{\sigma^2}+e \leq k_2]$?

Taste estimation As an example consider an experiment conducted to determine the optimal concentration of salt in popcorn. The concentration of salt in sample $i$ is denoted by ${x_i}$. The subject ...
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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 ...
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3answers
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How can I check if nominal and ordinal data is normally distributed (for z-test of proportions)

This section deals with concepts and procedures for testing inferences about proportions that involve the normal distribution. Following a discussion of the concepts related to tests of ...
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2answers
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Regarding alternatives of t test when time series data is not normal

I want to test whether a investment strategy generates significant return or not. For this I have to apply t.test. But my time series data is not normal. It is negatively skewed and have heavy tails. ...
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Best choice of estimators in a CFA analysis without full dataset?

My team and I are working on an assignment that provided: A model to be tested, consisting of 2 Factors explaining 6 variables; $F1$ would be explained by $X1, X2$ and $X3$, while $F2$ would be ...
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Taking the square root of my DV solved problems with scewness in residuals. What does this mean?

As you could probably guess, I am -very- new to both statistics and R. SO the obvious answer would be that I have to get home and study more, but I would also appreciate some pointers here. I have ...
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2answers
98 views

Transformed data due to non-normal residuals - how to see if it actually improved the model?

I am trying to run a linear regression model (ideally) to see whether age (continuous variable) affects levels of stress hormone (also continuous, dependent variable), i.e. hypothesis testing. My ...
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1answer
25 views

Normality test without knowing a sample's mean

I've been searching for a way to approach my problem. This is a scenario from a Multivariate Statistics Assignment on Confirmatory Factor Analysis. We've been given only a correlation matrix on 6 ...
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what is the probability of detecting departure from H0?

The desired percentage of SiO$_2$ in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained ...
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Would you accept this normality for ANOVA? (asked yesterday, but data revised and different graph)

I posted yesterday asking for help with ANOVA assumptions, however I discovered the data I was given had several incorrect values. This data fulfills the assumption of homogeneity of variance, and the ...
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1answer
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One-Way ANOVA assumption: No Outliers in boxplot

I read in this link: enter link description here It said: ...
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2answers
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Help interpreting residual vs fitted plot and normality (ANOVA on R)

I'm carrying out a statistical analysis on R using ANOVA and am not sure if the data meets the assumptions of normality of residuals or homogeneity of variance. My data : And my plots: Any help is ...
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Is it okay if one of the residuals in a repeated measures ANOVA fails in Shapiro-Wilk test for normality

I am currently running a Shapiro-Wilk test on the residuals of a repeated ANOVA model. The repeated-measures ANOVA was conducted to measure two main effects A & B. The ANOVA summary is listed ...
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When assessing normality from a QQ-plot, can we use r (lin. cor. coeff.) to do so?

When assessing normality from a QQ-plot, I see online that many sources compare the linearity by plotting a straight line through the two points of intersection of quantiles 1 and 3. But does it also ...
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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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1answer
32 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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26 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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1answer
81 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
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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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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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1answer
105 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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2answers
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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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