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

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Usefulness of Z-normalization in Machine Learning

Z-normalization means rescaling the feature $X$ by subtracting the average $\mu$ and dividing by its standard deviation $\sigma$, i.e., $(X-\mu)/\sigma$. What is the usefulness of normalizing data ...
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2answers
200 views

Why is a Pearson correlation of ranks valid despite normality assumption?

I am currently reading up on assumptions for Pearson correlations. An important assumption for the ensuing t-test seems to be that both variables come from normal distributions; if they don't, then ...
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1answer
52 views

2x2 ANOVA - assess violations of homoscedasticity & normality

I have a 2x2 factorial unbalanced between-subject design, n = 355. My DV is a subjective probability estimate (i.e., a number between 0 and 100). My ANOVA model: ...
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1answer
35 views

What are appropriate tests for goodness of fit on glm with a small sample size?

I've thought quite a lot on large sample size inference where the strong law of large numbers is easily validated. In my case however, I'm trying to infer the sign and magnitude of an outcome where ...
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45 views

Do you need justification to transform non-normal data

First, a bit of background: I'm currently working on a project at work that produces variable width data. During a operation qualification I collected a bunch of data at low, nominal, and high ...
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11 views

Normality Testing of Productivity Data

I have a series of measurements from a construction production study I've been carrying out. I essentially measured the output rate of workers in terms of output/hr. The measurements varied each day ...
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10 views

Can non-normal data be used for factor analysis? [duplicate]

I would like to do factor analysis to derive a nutrient intake pattern. Many of these variables are not normally distributed. Is it gonna be a problem? And there are just 7 variables available. Can ...
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1answer
34 views

When reporting a CFA, is it desirable to assess univariate normality in addition to multivariate normality?

I am using SPSS AMOS to do a factor analysis and it produces statistics related to both univariate and multivariate normality. p35 of the AMOS Users Guide states that "[T]he observed variables must ...
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3answers
214 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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1answer
79 views

Why not always use bootstrap CIs?

I was wondering how bootstrap CIs (and BCa in barticular) perform on normally-distributed data. There seems to be lots of work examining their performance on various types of distributions, but could ...
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2answers
82 views

Regression, Independence & Normality of x and y variables (not residuals)

I am trying to predict productivity of inbound process of a warehouse using y-value = productivity in terms of pcs/hr x-value = # pcs and ratio pcs/SKU. (where SKU = stock keeping unit) Basic ...
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2answers
134 views

Normality tests for histograms

I understand that one quick way to test for normality is to create a histogram from my data and see if it "looks bell-curved". Alternatively, I can use some normality test like Pearson's chi-squared. ...
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72 views

Appropriate test for detecting a signal in normally distributed noise

I am doing some signal processing and I have a histogram which has a bell shape when there is only noise in the signal. (I have been advised that this is to be expected due to the central limit ...
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1answer
54 views

Transformation for negative skewness data

My analysis involved some behavioral data on swine. One measure we had was standing time (min) for pigs using accelerometers. Using SAS, I checked for normality, and results showed data to be ...
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47 views

Variable transformation in a ANOVA and multivariate analyses

I want to run an ANOVA, and the multiple correlation and regression analyses. Some of my variables to be included in these analyses are normally distributed and some are not. I log transformed the not ...
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3answers
474 views

Regression - How do I know if my residuals are normally distributed?

Performing a regression and need to find out if my residuals are normally distributed.
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1answer
66 views

how to interpret KS test or Shapiro wilk test for ordinal criterion variable?

Here Rank is my dependent variable from level (Strongly disagree to strongly agree) and Pre_Sales_support is one of the independent variable. Due to smaller sample size of 15, I am taking ...
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1answer
28 views

how to transform data of two experimental groups? one is positively skewed and one is negatively..

I have two experimental groups. Then I test their normality respectively. Result shows that one is positively skewed and the other is negatively skewed. In this case, how should I do the data ...
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1answer
122 views

Why does non-normally distributed errors compromise the validity of our significance statements?

There is a normality assumption when it comes to consider OLS models and that is that the errors be normally distributed. I have been browsing through Cross Validated and it sounds like Y and X don't ...
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1answer
111 views

Meaning of Qqnorm plot in R

I am testing the normality of a sample with R using qqnorm. I obtain this: I understand that the meaning of this plot is that the sample has fat tails. But what is the meaning of the values on the ...
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1answer
51 views

Kalman filter and Box-Cox

I'm interested in wind forecasting, which I have analyzed over some time by means of ARMA methods. Now I've being reading about Kalman filtering. Kalman filter is optimal when Gaussian assumption can ...
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1answer
28 views

Finding the probability of normality via Anderson-Darling, Shapiro-Wilk , and Kolomogrov-Smirov

I have quite a few distributions that were generated by some system, and I am trying to find the probability of accordance to normality for these distributions. So, the probability of accordance to ...
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1answer
51 views

how do normality check in ks test assess for equivalence or difference in data sets?

I have a series of data of photon counts versus time. These data are periodic, then I can fold them and obtain an average profile of the data. Nonetheless, some variations appear sometime in the ...
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24 views

SEM for Non-Normal Ordinal Data

In short, I conducted a satisfaction survey in which surveyees are required to answer on a satisfaction scale from 1 to 7: 285 observations, 37 satisfaction variables. Here is an example of what the ...
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1answer
26 views

Similarity Coefficient and Geochemical Correlation

I have a set of around 160 samples from different sediment bodies, or stratigraphic units, which I am attempting to correlate using geochemical analysis of 25 elements for each sample, and a ...
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1answer
290 views

Testing large dataset for normality - how and is it reliable?

I'm examining a part of my dataset containing 46840 double values ranging from 1 to 1690 grouped in two groups. In order to analyze the differences between these groups I started by examining the ...
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1answer
157 views

Using Univariate ANOVA with non-normally distributed data

If my data are non-normally distributed and I'm conducting a 2x2 ANOVA, what can I do to correct for this problem so I can report the main effect and interaction output appropriately? Only one ...
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1answer
29 views

Use pc scores to check mulitvariate normality

How can you check multivariate normality, using the scores from the PCA? Or what can we expect about the scores if the data is multivariate normal distributed?
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2answers
65 views

How much is moderate violation to normality for one sample t-test?

I want to test if my data have a mean equal to zero (Ho: mu=0). The sample size in not large (n=21). My variable is numerical with average -0.10 and sample_sd 0.05. I don't know the population ...
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1answer
96 views

Why is Shapiro–Wilk test considered to be the best normality test?

I have read somewhere in the literature that the Shapiro–Wilk test is considered to be the best normality test because for a given significance level, $\alpha$, the probability of rejecting the null ...
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1answer
31 views

ANOVA normality assumption for which variables?

When I want to conduct a repeated measures ANOVA pre and post test scores, which variables need to be tested for normality? Each the pre and post scores or the difference between them? I suppose ...
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69 views

Can I normalize a data proportion?

Is there any way to normalize this variable (attached)? In fact, this is a proportional data (a percentage). But I need transform it in order to do some contrasts. I try with arcsine transformation: 2 ...
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2answers
134 views

Standard error of regression coefficients without an assumption of homoscedastic normal noise

I have a time series that is affected by two (or more) kinds of events. When event $A$ happens, some signal is linearly added to the time series (the signal lasts, for example, for 100 time points). ...
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36 views

Determining the number of levels in a Repeated Measures ANOVA for multivariate or univariate within subjects effects

Maxwell and Delaney (1990) wrote that the multivariate approach should not be used for a repeated measures ANOVA for within subjects effects if n is less than "a + 10" (a is the number of levels for ...
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1answer
58 views

Total scores are normally distributed, but subtest scores are not; what to do?

I have two sets of data for males and females: $n=33$. I'd like to compare test results for both groups. I want to do a $t$ test, and I know my data should be normally distributed if I want to use a ...
2
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1answer
107 views

transformation to normality of the dependent variable in multiple regression

Is it really important to normalize dependent variables in multiple regression or are there any exceptions? My model is providing better results with more significant hypothesis when the DVs are not ...
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42 views

How to interpret probability plot?

I was reading about how to find the distribution of data from this question I generated the following probability plot from the scipy package.scipy prob plot Can someone please help me figure out ...
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21 views

Regarding transformation of a variable to follow normality [duplicate]

When I plotted histogram of a variable to see whether it follows normality, I got a highly positive skewed graph, more like that of a Poisson/exponential distribution. Now, what kind of ...
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1answer
94 views

Do all these estimates of kurtosis and skewness have the same (asymptotic) distribution under normal sample distribution?

I have seen five types of estimates of kurtosis and skewness: three from http://stats.stackexchange.com/a/84057/1005 one from page 9 of Analysis of Financial Time Series by Ruey S. Tsay one from ...
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1answer
79 views

Non-normal residuals - P-values higher or lower?

Background: I have estimated a model using panel data with the Arellano Bond estimator (see e.g., http://www.fordham.edu/economics/mcleod/Elitz-usingArellano%E2%80%93BondGMMEstimators.pdf) and n=300. ...
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84 views

Why do some researchers test for normality of sample data?

I once was a research assistant for a professor who wanted me to do some regressions, but before that he wanted me to test all the sample data for the variables to ensure they were normally ...
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1answer
2k views

Jarque-Bera normality test in R

Jarque-Bera normality test has significant p-values even when there is skewness and kurtosis. Does that mean test is infering data distribution is approximately normal?
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1answer
37 views

should both scores of 2 time points be of same scale in mixed ANOVA

I am running mixed ANOVA as repeated measurement analysis for cognitive score at 2 time points for 2 groups (blood pressure low vs. High). The the score at time 1 was normally distributed and at time ...
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3answers
150 views

Can a normal approximation assumption justify itself?

I am learning elementary statistics. I found an exercise, which asks to compute the desired sample size for some interval for standard error. The solution, in class slides, first assumes the sample ...
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1answer
23 views

Repeat normality check after modifying group cut-off?

I have a set of data which consists of one independent variable (2 groups) and one dependent variable. I successfully checked for normality (each group separately) and conducted a t-test. Now I want ...
3
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1answer
132 views

Proof that the log-likelihood is asymptotically quadratic

I was reading this article, where the author says that Maximum Likelihood (ML) estimates are asymptotically normal if the log-likelihood is asymptotically quadratic. I have heard or read other ...
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1answer
93 views

How to calculate power of different normality tests such as Shapiro-Wilk, Ryan test etc [closed]

Normality test for small samples with power comparison
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1answer
104 views

Does a Gaussian mixture model always imply a within-class multivariate normal probability distribution?

If I use a latent profile analysis (Gaussian Mixture Model) to model my observed multivariate probability distribution as a mixture (K-classes) of conditionally-independent normal pdfs, does this ...
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36 views

Derivation for the area formula for a sample data taken from a population that is normally distributed?

I need to understand where this formula comes from and what starting assumptions are required to get there: $ f_i = \frac{i-0.375}{n+0.25}$ where $i$ is the index (the position of the data value in ...
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2answers
90 views

Two-way ANOVA on not completely normal residuals

I have 2 factors, one (Page type) of 2 levels and the other (Intensity) of 4 levels. I did a 2x4 Full Factorial Design with 10 replications, so I did 80 experiments. Then I wanted to do a two-way ...