Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [shapiro-wilk-test]

34 questions
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Quantitatively, how powerful is Shapiro-Wilk or other distribution-fit tests for small sample sizes?

I'm looking for an analysis (I assume a book or website, but feel free to put it all in comments here) that provides an in-depth discussion of the power/accuracy of normality assessments such as Shapiro-Wilk. In short, I understand that Shapiro-Wilk…
Porter
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Limitations of Shapiro test

Are there any possible limitations to the Shapiro test or the shapiro.test() function? After removing outliers in a data set it seem that using the shapiro.test shows that the data is no longer normal, although the test showed that the model was…
lambdaepsilon
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Can a sample larger than 5,000 data points be tested for normality using shapiro.test by applying the test to a subsample?

I have a number of samples that I would like to test for normality. One of the samples exceeds 5,000 data points, the limit up to which the shapiro test accepts samples. This is the data: c1 <- exp(rnorm(505)) c2 <- exp(rnorm(550)) c3 <-…
Chris Ruehlemann
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Can we use the R square of the q-q plot as the Shapiro Wilk effect size?

The q-q plot is a nice way to see a deviation from the normality. But this is only "eye estimation" Can the R square of the linear regression be the effect size of the deviation from the normality? for any normality test, not necessarily the SW…
OB1
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Testing the Central Limit Theorem with the Shapiro-Wilk test on dice rolling simulations

Rolling a single dice repeatedly will result in a uniform distribution. But if we roll multiple dice the sum would be the Normal distribution due the Central Limit Theorem (CLT). To verify this, simulated multiple dice rolls number of times to get a…
Denis Kazakov
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What is the difference between Shapiro-Francia and Shapiro-Wilk tests of normality?

I apologize for this easy/basic question. Please forgive me if this is a duplicate question. I've been researching the Shapiro-Wilk test (1965) of normality for a project. In doing so, I found an article by Royston (1982), which allows for a sample…
Macromika
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Shapiro-Wilk test on transformed data

I used RStudio to perform Shapiro-Wilk test for normality. In the following data set calling it $D$, I have performed Shapiro-Wilk test for normality with p-value=0.7698. 34.681 26.291 33.280 36.169 41.471 31.528 25.502 43.211 35.330 30.447 If I…
user45765
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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?
wacketsduffel
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Concept Clarification: Wilcoxon rank test vs two-samples T-test (UPDATE)

I am currently deciding whether to use the Wilcoxon rank test vs two-samples T-test to assess BMI between two unrelated groups. Using the following code to assess normality with(group1, shapiro.test(BMI)), I got p > 0.05 for group 1 (n = 10) but p <…
R Beginner
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Shapiro -Wilk assumptions

I am doing statistical analysis in a df and I am trying to check the normality of the data. I did the Shapiro Wilk test. I think I have to check if the data meets some assumptions, this is the case in the t-test. Basically I am trying through…
pipts
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Why is the Shapiro-Wilk $W$ statistic defined the way it is?

In the original paper (section 2.2.), we can see that derivation of the $W$ statistic goes along these lines: Let let $m_i$ be the expected value of the $i$-th order statistic of a random sample of $n$ numbers from the standard normal distribution…
Milos
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Best statistical test to compare two groups when they have different distributions

I am teaching myself to use and apply statistics to a big database. I have 2 groups that I wish to compare, healty controls (HC) and patients (P). The sizes are HC= 84, P= 196. Each group has many different clinical data collected as continous…
Pauliinaa
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How to test if data follows a half-normal distribution?

There are many ways to test if the data comes from normal distribution. like this post But the question is how to test if the data follows half-normal distribution? I know Ks-test, but as the post above states: "The KS test is well-known but it has…
Jiaqi Ding
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Data didn't pass normality testing for K-W and S-W but the skew and kurtosis were within range...advice please?

I am conducting a study on the relationship between rural/urban living, intentions and barriers to help seeking in adult males. I was planning to conduct a correlation and then pending that result, a MANOVA (no correlation) or a MANCOVA (should…
Rachel
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Compare Z-scores (weight) before / after with a T-test?

I'd like to ask you if it's possible to perform a T test to calculate Z-scores ( weight of persons ) https://www.cdc.gov/growthcharts/clinical_charts.htm with a t test in the same group ( paired t test) ? conditions : 1) N: 30 2)paired samples…
HappyMan
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