Refers to the normal distribution, the Gaussian continuous probability distribution.

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11
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3answers
224 views

“Reversed” Shapiro–Wilk

The Sharipo-Wilk test, according to wikipedia, tests the null-hypothesis ($H_0$) "The population is normally distributed". I am looking for a similar normality test with $H_0$ "The population is not ...
4
votes
1answer
46 views

non-normal residuals in ARIMA

I am trying to fit an ARIMA model and I have already evaluated a few variations which I finally selected ARIMA(1,1,3) model. The residuals seems to be uncorrelated and all the lags are significant. ...
2
votes
0answers
12 views

shape of distribution and indepencence

I have a sample of observation on which normality tests (Anderson Darling, Shapiro - Wilks, KS,...) would accept the assumption of normality. Nevertheless I know that there is a certain time - ...
-1
votes
0answers
26 views

Normality check for continuous data

The results of my normality check using Skewness and Kurtosis do not seem to be in support of normal data (my data has 1272 observations). Even after winsorising the variables (bottom 5% and top ...
0
votes
0answers
35 views

Significant Friedman's test vs. non-significant multiple comparisons

I am currently running a randomized, placebo-controlled, cross-over design for a new type of intervention. This intervention is compared to a placebo and another more conventional type of treatment. ...
2
votes
0answers
36 views

Departures from normality in factorial design

This paper (http://psycnet.apa.org/journals/med/6/4/147/) states that departures from normality can be tolerated for one-way ANOVA. "The results give strong support for the robustness of the ...
0
votes
1answer
44 views

Shapiro-Wilk test - are my data normal/non-normal?

Are my data normal/non-normal? How do you decide? I performed a Shapiro Wilk test and got the following results. How do you interpret this? ...
0
votes
1answer
36 views

Transforming Negatively Skewed Independent Groups

I have two independent groups, (roughly 30 in each) – and their performance on 3 different tasks, there are 10 scores in total for each group. The majority of them are negatively skewed so I know I ...
2
votes
1answer
19 views

Normality for Confirmatory analysis with Likert scale data

I'm running CFA on AMOS for an attitude scale and I got a good model fit after deleting three problematic items (less than .30 factor loadings). However, my data is not normally distributed. I was ...
1
vote
0answers
23 views

Heavy-tailed errors in mixed-effects model

I'm relatively new to statistical modelling and `R', so please let me know If I should provide any further information/plots. I did originally post this question here, but unfortunately have not ...
1
vote
0answers
28 views

Transform a sum of Likert items to normality

I am analysing data from a survey. There are 11 items, each to be answered on a 5 point Likert scale. It seems reasonable to summarize the results by taking their average, which can then be the ...
0
votes
0answers
40 views

Multivariate normality in Discriminant Analysis when using dummy variables

I've studied statistics now for almost two years and I'm starting to believe I have missed something very fundamental. I'm doing discriminant analysis where, as I understand it, I can use dummy ...
1
vote
1answer
25 views

Should data for both sub-groups be transformed when checking for sub-group differences when only one is non-normal?

Tabachnick and Fidell (2012) recommend examining the normality (outliers, skewness, kurtosis) of a variable separately/by group/sub-group if one is planning to do a group-based analysis (e.g., t-test, ...
1
vote
1answer
46 views

Using ANCOVA when the covariate is not normally distributed

I have conducted a repeated-measures ANOVA, but a reviewer suspects that the observed main effect of condition are due to a the difference between hit rates of two conditions (one of them is ...
2
votes
0answers
43 views

How should I deal with non-normality in geostatistics?

I am working with two parameters, one is normally distributed the other is not. I have read several different books and articles with different opinions on what to do with non-normal data. Since ...
0
votes
0answers
21 views

Tests of Normality using tool developed by CFA

I am doing a paired sample t-test pre/post intervention. I have used a tool where psychometric analyses included confirmatory factor analysis (CFA) and item response theory. For my data tests show ...
0
votes
0answers
23 views

(Pretty) large sample size, unequal variance, unequal sample sizes, non-normal distribution. T-test alternative?

So, I've never had all these problems at the same time before, but I have: - Likert data, from a 9 point scale - n = 317 v 177 respectively - SD = 2.08 v. .274; 1.9 v. 2.6; 2.5 v. 2.9 etc. (you get ...
2
votes
1answer
57 views

Should ordinal variables be normalized for PCA?

I need to analyze my (ecological) data with PCA, but the data don't seem to meet the assumption of normality very well. The problem is, that out of my 9 variables only two are continuous and the ...
5
votes
1answer
107 views

Distribution of “normalised” Gaussian random variables

Let $X_1, \dots, X_n$ be independent normally distributed random variables. What is the distribution of: $$ Y_i = \frac{X_i}{\mathrm{stdDev}(X_1, \dots, X_n)}, $$ where $\mathrm{stdDev}(X_1, \dots, ...
4
votes
1answer
48 views

D'Agostino-Pearson vs. Shapiro-Wilk for normality

In the field I work in, there is a large amount of impetus to use Shapiro-Wilk testing as the default normality test (possibly due to NIST and some pubmed papers). I understand that one weakness of SW ...
1
vote
2answers
103 views

Normality of residuals - contradiction between 'symplot' and 'qnorm'?

After running a multiple linear regression analysis, I wanted to assess normality of residuals. I plotted a histogram which showed an almost normal distribution of residuals. I also used ...
0
votes
0answers
8 views

How to transform data back (after violation of normality)?

As for one of my variables the assumption of normality was violated, using this software: http://www.wessa.net/rwasp_boxcoxnorm.wasp I transformed my data and did the analysis with ANCOVA. Now I need ...
1
vote
0answers
22 views

Assessing Multiple Regression Normality

Normal distribution in data is one of the assumptions in multiple regression analysis. In the situation where the Skewness test, Kurtosis and Q-Q plot showed the evidence of normally distributed ...
1
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0answers
33 views

Which significance test can be used in this instance? - paired, non-normal means

I have a data set of behaviours for a herd of captive elephants which I have attempted to quantify to compare for statistical significance, i.e., if a behaviour is performed once during an observation ...
2
votes
0answers
24 views

What to do with this non-normally distributed and near-categorical data?

I have a dependent variable (monetary transfers made by 'dictators' in an experimental dictator game) that is non-normally distributed, and which also appears to be multi-modal (it was collected as a ...
0
votes
1answer
40 views

normality and standardization

I wonder if I can transform to meet the normality of the data and then standardize the data. There is an order? become normal or standardize first? I understand that the two analyzes are different ...
11
votes
2answers
249 views

Departure from normality assumption in ANOVA: is kurtosis or skewness more important?

Applied linear statistical models by Kutner et al. states the following concerning departures from the normality assumption of ANOVA models: Kurtosis of the error distribution (either more or less ...
0
votes
0answers
45 views

Normality violation in Two-way repeated measure ANOVA

I have a sample of around 25 in my within-subjects design, and two factors (music, and flanker type), each with three levels. My DV is reaction time (measured in milliseconds). This gives me 9 ...
2
votes
1answer
47 views

Normality requirements across tests

I would like to understand the reason why normality is required in many tests. T-tests: I read that what needs to be normal is the sampling distribution rather than the sample distribution. But since ...
3
votes
2answers
377 views

If my histogram shows a bell-shaped curve, can I say my data is normally distributed?

I created a histogram for Respondent Age and managed to get a very nice bell-shaped curve, from which I concluded that the distribution is normal. Then I ran the normality test in SPSS, with n = 169. ...
-1
votes
1answer
125 views

How can I determine if categorical data is normally distributed?

Is it true that a normality check should be used for continuous data only (ratio, interval level of measurement) and not for categorical data (nominal, ordinal)? Is there any way to check the ...
1
vote
0answers
61 views

Prove that the MLE $\hat{p}(1-\hat{p})$ is a asymptotically efficient

Consider when $X_1, ..., X_n \sim $ Bernoulli($p$). We want to estimate $p(1-p)$. Suppose $\hat{p}=\frac{1}{n}\sum_{i=1}^nX_i$. Prove that the MLE $\hat{p}(1-\hat{p})$ is a asymptotically efficient ...
2
votes
1answer
94 views

Why would I want to bootstrap when computing an independent sample t-test? (how to justify, interpret, and report a bootstrapped t-test)

Let's say I have two conditions, and my sample size for the two conditions is extremely low. Let's say I only have 14 observations in the first condition and 11 in the other. I want to use the t-test ...
4
votes
2answers
35 views

Should I take the Shapiro Wilk test with a pinch of salt here?

So I'm trying to determine whether the residuals from a seasonal ARIMA model are normal or not. Upon using the shapiro wilk test, I get a staggeringly low p-value leading me to think that the ...
2
votes
3answers
74 views

How do I know if my data is meaningful?

I am a 17 year old conducting a very scientific experiment into the best method for pulling Christmas crackers in order to get the highest chance of winning the prize. I have 1000 crackers and a team ...
2
votes
2answers
62 views

Log transformation for data?

If the data is between (0,1) because of some kind of vector normalization to get rid of background noise, is it still OK to do log transformation to improve normality? Or we have to do logit ...
0
votes
1answer
46 views

Cannot perform tests for multivariate normality. Is my data set too large?

I'm examining the performance of quadratic and linear discriminant models at classification. My dataset has 250,000 observations, 2 groups and 30 explanatory variables. I thought it would be worth ...
3
votes
1answer
82 views

calculating percentiles for transformation into standard normal quantiles

I'm trying to hand calculate a standard normal quantile plot. The first step involves transforming the data into percentiles. That sounded like the easy part, but apparently there are several ...
0
votes
0answers
42 views

verify the central limit theorem of chi sq distribution

hi i have a question on verifying the central limit theorem using R. the question was to use data generated from different statistical distribution n see if the sample means follow normal ...
0
votes
1answer
28 views

What is the design of this experiment and what tests are appropriate?

My experiment has the response variable F the experimental unit is a cage the Treatment is rear (1/2 get standard rear & 1/2 get non-standard rear) and there are multiple measures of F over 12 ...
4
votes
1answer
999 views

R: test normality of residuals of linear model - which residuals to use

I would like to do a Shapiro Wilk's W test and Kolmogorov-Smirnov test on the residuals of a linear model to check for normality. I was just wondering what residuals should be used for this - the raw ...
1
vote
0answers
214 views

Ap Stats Need Help on Assessing Normality

Grey Kangaroos are large, social marsupials, indigenous to Australia. The Eastern Greys are a light grayish brown, while the Western Grey is a copper brown color. As part of a study of the ...
1
vote
1answer
130 views

Testing whether random effects are normally distributed in R

I've been working on a GLMM in R and I see that an assumption of the test is that the random factor must be normally distributed (that is, unless you're using a package like ...
1
vote
2answers
317 views

Normal approximation for large data set?

I have a dataset that is highly skewed. See image below: When I transform the data I get the following histogram that makes it look normal: This data however is not normal. I get a p-value of ...
0
votes
0answers
114 views

Need to transform data before running mediation/model with bootstrapping (PROCESS)?

I am reading through Hayes' book on mediation and moderation analysis (2013) which describes the PROCESS macro he created to use bootstrapping in order to arrive to confidence intervals to check the ...
1
vote
0answers
17 views

Transforming data with a limited range (0,1,2) for parametric testing (ANOVA) [duplicate]

I've collected data on accuracy of recognition of images. Accuracy is a score out of 2 with points 0,1,2.. participants can score a 0. I am aiming to use a parametric test (ANOVA mixed design) to ...
1
vote
1answer
34 views

Comparing treatment means with lots of zeros

I am trying to compare the means of two treatments on a continuous variable with a lot of zeros in it. I've tried a log(n+1) transformation but that did not get me to a normal distribution. Any ...
1
vote
2answers
264 views

Estimating “Probability” in normal probability plot

I plotted normal probability plot in R using qqnorm and qqline. I want some help on: How to estimate "probability" that a data ...
1
vote
1answer
208 views

small sample size, large number of variables (most categorical) - how to proceed?

I would be grateful for general guidance/advice about data analysis with some data that is problematic for me because of the small sample size, and the large number of categorical data. I realize this ...
0
votes
0answers
35 views

Normality test with p-value equal to zero [duplicate]

I have an array dataset of about 650.000 points. I want to test if the dataset follow a normal distribution or any other distribution. The first thing I did was to split the data in groups, find the ...