# Questions tagged [normality-assumption]

Many statistical methods assume data or a model's residuals 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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34 views

### Anova model assumptions. How to go by?

I have a data frame that contains a continuous response variable measured on different species, at different elevation and month of sampling as explanatory variables. I want to analyze how the ...
33 views

### Normality assumption n=48 [closed]

Regarding normality assumptions for model evaluation I have been told by my supervisor that it is not needed in the case of analyzing but is needed in forecasting only. i am looking for an explanation....
29 views

### Does shapiro.test() automatically work out residuals on your data?

I'm quite new to R and I am trying to do some stats. I have a set of data and want to work out whether my data comes from a normal distribution. I was told to do the test on the residuals of my data, ... 47 views

### About the normality question with four conditions

I am encountering difficulties in determining the normality of data and distinguishing whether the data I have collected is parametric or non-parametric. I have gathered data using a 7-point Likert ...
28 views

### I am unable to relate the normal distribution dependency for regression . I need a mathematical intuition cum understanding for regression assumptions [duplicate]

What is the mathematical significance for the assumptions of linear regression to hold true for arriving at a single/multiple regression formula? Can anyone use the assumed normally distributed ...
58 views

### Hypothesis testing - Newbie blockers - Update and more

Brief : I'm from manufacturing industry, a processing machine in our production line used to do pressing, polishing and QA one after the other. Now we have a new machine that will perform these at the ...
9 views

### Robust ANOVA t2way unequal sample sizes?

I have some parameters that I would like to analyze with a two-way ANOVA. The treatment groups have unequal sample sizes (n=9, n=36, n=36, n=36) and the data do not fulfill the requirement of normal ...
21 views

### Decomposition of variance in linear regression, normality

Please correct me if I am mistaken, but I've read somewhere that the usefulness of normally distributed errors $e$ lies in the fact that we use independence to decompose  Var(y) = Var(y - \hat y + \...
194 views

### When to use Pearson's test and when to use Spearman's test?

I want to do a correlation analysis on a dataset of 28 samples. I want to correlate the age with the size of a reflex response. But I don't understand whether I should use Pearson's or Spearman's test....
147 views

### Assumption of Normality - do the residuals need to be normally distributed for each independent variable (or each level of an IV)?

Let's say I have 4 groups of football fans, and I want to see who screams loudest, and I want to run an ANOVA. My dependent variable is loudness, and my independent variable is Fan_Type, with 4 levels....
1 vote
30 views

### Doubt on checking linearity assumption in a mixed-ANCOVA design

I am a PhD student and I have to run a mixed-ANCOVA on some questionnaire scores (my dependent variable) according to the following model. Factors of ANCOVA are (a) Timepoint (pre-intervention, post-...
25 views

### How is it possible to compare powers of normality tests?

The famous paper  compares the power of several normality tests. Regardless of its result, my immediate question is, "How is that even possible?" Well, the definition of power in this ...
349 views

### How could Lilliefors use Monte Carlo if the estimand is not distribution-free?

Lilliefors test is a well-known statistical test for normality. Its idea is based on the Kolmogorov-Smirnov test, except the CDF is replaced by the CDF of the normal distribution with $\mu, \sigma^2$ ...
23 views

### A T-test for difference of means and normality assumption [duplicate]

I am a little bit confused about normality assumption in T-Test for difference of two independent means. My reasoning now as follows: If the distribution of the populations are non-normal, it's ok as ...
674 views

### I have applied many statistical tests to my data, but still cannot determine normality

I have run multiple tests to determine normality on my dataset, but I am unsure which one to adhere to, especially since my histograms, density plots, and QQ plots leave much to be desired in terms of ...
1 vote
91 views

### (Multivariate) normality assumption for dependent variable

In their book on multilevel analysis Hox et al. (2017) write in chapter 13: 'The main assumptions are [...] (multivariate) normality for dependent variables, which is the focus of the current chapter.'...
2k views

### Pearson or Spearman? [duplicate]

After using the Shapiro-Wilk test for Bivariate Normality, I found different values of p. For the ones which were p<0.05 I used Spearman and the ones which were p>0.05 I used Pearson. Is it the ...
1 vote
35 views

### Meta-analysis of log transformed and untransformed Y!

First off, it's difficult to title the question without the knowledge of the field, Please bare with me as I, very much a novice, attempt to explain the issue: I have summary statistics for over a ...
302 views

### Help with the normality of the residuals of my regression model

I am doing a regression in R on the effects of EU and UN economic sanctions on GDP. My model looks like this: ...
18 views

### ANOVA: variables evaluated for normality with various test. How to interpret? [closed]

2 different species (1 & 2). 17 variables (A-Q). N: number of meaurements. I needed to test for normality before performing ANOVA. Using the software PAST this is the result: I highlighted in ...
228 views

### How valid is the use of bootstrapping in my case?

I am currently working on the analysis of measurement data and have the problem of obvious non-normal data. Since most methods I want to use require normality (especially statistical process control ...
142 views

### Deriving 99th percentile in log-normal data using transformed normal distribution?

My aim is to calculate the 99th percentile of the log-normally distributed data on the left-hand side. There are various approaches described to do this, e.g. ranking data and then selecting the value ...
25 views

### Anova violates normality assumption for error data

I have a 2 x 2 repeated measures ANOVA (N = 51) with Error Rate data as the dependent measure. The error data violates the normality assumption, even when outliers are removed. I have looked at the ...
25 views

### Normalization of Time Series for GARCH

It is generally observed that financial times series is not normally distributed. So I want to clear the following doubts: Is it necessary to normalize time series data especially before proceeding ...
47 views

### Residuals with mean 0 but with bigger standard deviation in regression

When I tried to fit a regression model to my data to predict a power variable using steam at entry and steam at exit variables in a thermal power plant, after taking care of outliers, etc... I fit the ...
1k views

### Kolmogorov-Smirnov test fails to recognize a normally distributed sample

I created a sample with 10000 normally distributed numbers. Subsequently, I used the Kolmogorov-Smirnov test to check if they are indeed normally distributed, and it turned out that they are not. How ...
17 views

### Log transforming + a constant for negative data- ANOVA

I have data (change in mass) ranging from ~ -400 to + 4,000. I'd like to run an ANOVA comparing change in mass in different treatments. When I plot the residuals they are not normal and the residual ...
49 views

### Test for "discrete normality"

I have implemented what I believe to be a sampler from a distribution over the integers. Its a specific discretization of the normal distribution so I know stuff like mean and variance of the ...
55 views

### Use linear mixed model or linear quantile mixed model for non-normal residuals?

I started with this initial model: m1 <- lmer(response ~ treatment + (1|subjectID), data = data) However, the residuals of the model are heavy-tailed (presumably enough to violate the normality ...
47 views

### CTL vs normal distribition of residuals

Hello, I submitted a study with a linear regression model. My sample size is >1000, so I invoked CTL. The statistics reviewer is requesting that we check assumptions of normal distribution (...
50 views

### Is my data normally distributed? [closed]

shapiro.test(U_ER) Shapiro-Wilk normality test data: U_ER W = 0.98093, p-value = 0.002173 agostino.test(U_ER) ...
37 views

### Consequences of violation of the normality of the residuals in Linear Rrgression

I am using linear regression and I see that if there is a violation of the Gauss Markov assumption and the estimates of the parameteres are not unbiased/ efficient. What are the consequences if the ...
31 views

### I have weekly averages, and weekly 2-minute peaks, can I estimate 30-second peaks?

I have been given weekly averages and weekly 2-minute peaks of flow to a process. I'd like to predict the 30-second peak. To clarify: By “weekly averages”, I mean that once a week, I get the average ...
265 views

### Understanding Why (or Why Not) a T-Test Require Normally Distributed Data? [duplicate]

This is a concept that I have always struggled to understand: We can write the formula for a Two Sampled T- Test (https://en.wikipedia.org/wiki/Student%27s_t-test) to compare the sample averages from ...
18 views

### Normal distribution in linear regression [duplicate]

There are some references like this that says in linear regression, this is not necessary for variables to have normal distribution. but I read some books that say otherwise: Joseph Hilbe in a book ...
41 views

### Can i add dummy variables before testing the residuals for normality?

I am using eviews 13 and I want to run these equations Co c yd yd(-1) Co c yd co(-1) With quantile regression I want to test the residuals for normality and ...
225 views

### Does mean centering work only for normally distributed variables?

In econometric analysis in some cases, such as models with interaction terms, multicollinearity between independent variables may exist. In such cases, some researchers suggest "mean-centering&...
31 views

### Comparing non-normal data between three groups

I am analyzing a dataset, where I have 3 categories (independent variable), and one continuous value (dependent variable). I am studying if the continuous value is significantly different between the ...
35 views

### Evaluating linear regression model [duplicate]

I understand that when performing linear regression, one common rule-of-thumb is that for a good 'fit', the residuals should be 1) independently distributed, 2) stationary and 3) not serially ...
1 vote
43 views

### Can I remove a single data point if it is changing drastically a Shapiro Wilk test?

I'm conducting a hyphotesis test to compare the mean of two independent samples. To do so, I need to check normality of both samples. I have two samples of size 20. A single data point, on both ...
20 views

### How to determine normalcy for a one group pre-test post-test? [duplicate]

My study is a retrospective one group pre-test post-test on multiple variables. Not every patient in the study had scores for all of the variables, so as long as a patient had both a pretest and a ...
103 views

### Distribution and variable analysis

I am doing a statistical test (program used is SPSS). On the basis of distribution and sample size, I have to chose the correct variable analysis. I also have to justify every decision. I have two ...
44 views

### Which statistical test should I use to compare two groups where their opinions are collected by using Likert Scale?

I want to find out a solution to the following question: "Is there is any impact of social media on the creation of entrepreneurial opportunity for rural women?" I have 2 groups: Online ...
225 views

### Help me understand this qqplot

I have plotted the qqplot of the residuals that my model generates with the python module statsmodel sm.qqplot(data, line ='r') and it looks like this The points are placed on a straight line but ...
1 vote
55 views

### Normality test for non-independent observations

I want to check if my data's distribution is normal. Thought of visual and formal test. One thing I'm not sure about – my observations are respiratory measurements of patient. Each patient measure ...
38 views

### Statistical tests for normality and log-normality testing?

I want to apply a filter to my data that assume its normality. The data comes from different sensors measuring the same quantity over the same period of time. Using a simple histogram plot, It seems ...
58 views

### Statistically testing MSE difference between models predictions without normality of squared residuals

I have a dataset that I have splitted for training - testing purpose (~2400 - ~600) . After training an XGBoost regression model on the training set, I would like to statistically test the fact that ...
19 views

### Is this data appropriate for a 2-way ANOVA? If not is there a non-parametric alternative?

I'm measuring the effect of tree Genus and location on % change in diameter at breast height of trees (converted to 0-100 rather than a %). I underwent a 2-way ANOVA using the following code: ...