Question

# What is the acceptable range of skewness and kurtosis for normal distribution of data?

It is desirable that for the normal distribution of data the values of skewness should be near to 0. What if the values are +/- 3 or above?

23rd Oct, 2018
Jessica E S Hoskins
University of California, Los Angeles
I believe the reason you are getting two general answers to this question is that different programs produce different values for kurtosis. I believe SPSS subtracts 3 (the kurtosis value for a normal distribution) so that negative values represent platykurtic and positive values reflect leptokurtic. In SPSS if you are unsure you can use the standard error to determine whether your value differs significantly from normal.
3 Recommendations

21st Jan, 2015
Javier Sánchez Rosas
National University of Cordoba, Argentina
The values for asymmetry and kurtosis between -2 and +2 are considered acceptable in order to prove normal univariate distribution (George & Mallery, 2010). George, D., & Mallery, M. (2010). SPSS for Windows Step by Step: A Simple Guide and Reference, 17.0 update (10a ed.) Boston: Pearson.
153 Recommendations

## Top contributors to discussions in this field

19th Apr, 2014
Casper J Albers
University of Groningen
It depends on mainly the sample size. Most software packages that compute the skewness and kurtosis, also compute their standard error.
Both
S = skewness/SE(skewness)
and
K = kurtosis/SE(kurtosis)
are, under the null hypothesis of normality, roughly standard normal distributed.
Thus, when |S| > 1.96 the skewness is significantly (alpha=5%) different from zero; the same for |K| > 1.96 and the kurtosis.
To manually compute the standard errors, see the formulae for the variance of skewness and kurtosis (https://en.wikipedia.org/wiki/Skewness, https://en.wikipedia.org/wiki/Kurtosis ) and take the square root.
19 Recommendations
19th Apr, 2014
Edgar Mesquita
University of Minho
A rule of thumb is -1 to 1 amplitude. Nevertheless, as said by Casper you should calculate CI 95% for adequate results reporting.
1 Recommendation
take a test on the distribution, e.g. Kolmogorov-Smirnov-test. After that you know whether you have a normal or not. then you need to test neither skewness nor curtosis.
5 Recommendations
19th Apr, 2014
Michal Illovský
Slovak University of Technology in Bratislava
I have come across another rule of thumb -0.8 to 0.8 for skewness and -3.0 to 3.0 for kurtosis.
2 Recommendations
This is not surprising since the kurtosis of the normal distribution is 3 :-)
2 Recommendations
20th Apr, 2014
Pedro Terán
University of Oviedo
A normality test which only uses skewness and kurtosis is the Jarque-Bera test. The idea is similar to what Casper explained.
(One remark: It has an asymptotic chi-squared distribution but the convergence is very slow and empirical tables exist for small samples.)
3 Recommendations
20th Apr, 2014
i think actually you want to check the normality , so instead go for any rule of thumb check jaurqe Bera test, it is based on skewness and kurtosis so acceptance of the null in this test will tell that skewness and kurtosis are i acceptable range for normality, and reject mean both are not in acceptable range for normality of the data
1 Recommendation
22nd Apr, 2014
Mohamed Benmerikhi Ph.D
I must agree with Peter.
1 Recommendation
24th Apr, 2014
Casper J Albers
University of Groningen
There are two different common definitions for kurtosis: (1) mu4/sigma4, which indeed is three for a normal distribution, and (2) kappa4/kappa2-square, which is zero for a normal distribution. It depends on your software settings which value is computed, although most software (Excel, SPSS, R-package 'moments') use the second definition.
When working with the first definition it is, as Peter states, not surprising to find kurtoses close to 3; when working with the second definition it is more surprising.
10 Recommendations
4th May, 2014
Norman Bravo
Independent Researcher
"Normal distribution" is a human concept, an example of this is "the best method to check normality is visual inspection", in this context, using the classification provided by Casper Albers (see above) (2) only 0 is classified like "mesokurtic", if it´s not = 0 then is platykurtic or leptokurtic...
4 Recommendations
12th May, 2014
Faizan Ali
University of South Florida Sarasota Manatee
I have also come across another rule of thumb -0.8 to 0.8 for skewness and -3.0 to 3.0 for kurtosis.
9 Recommendations
15th May, 2014
Alex Gilgur
Amazon
It's whatever range gives you an acceptable p-value for the Anderson-Darling test
1 Recommendation
23rd Jun, 2014
Karen Gold
Quanta Scientific, Monterey, CA
The scientific standard in research journals is to use the Kolmogorov-Smernov test. If it is not significant, the distribution can be considered normal. For very very small samples, this test may not be adequately powered and you fail to reject non-normality.
4 Recommendations
23rd Jun, 2014
Jochen Wilhelm
Justus-Liebig-Universität Gießen
As to my knowledge the Shapiro-Wilk test is more powerful than the Kolmororov-Smirnov test (Karen, please correct me when I am wrong). But performing a test to reject or accept a hypothesis (like "the sample is taken from a normal distributed population) is not (at least not directly) related to the question for an "acceptable range" of deviations. If one would use a test to get a decision about this question, one would need to define a reasonable alternative hypothesis. One must think of how/where to set alpha, and a well-defined alternative is required to set beta. Then and only then a test result might be sensibly interpreted. However, exactly the sensible choice of alpha and beta *requires* to have a reasonable idea about the size of relevant deviations (and this was the question about, as I understood).
I do not see that there might be a general answer. First of all it all depends on the purpose (why is normal distribution important in the particullar context). Secondly, the deviation is not "one-dimensional". Strictly, the dimensionality of the deviation is not defined, so there is no way to define *the* deviation at all. But one can look at some few particular aspects, like skewness and kurtosis. And even for these two it is likely important to consider their combination. I mean to say: the range of acceptable deviations for the kurtosis might depend on the actual value of the skewness (and vice versa). This is a 2-dimensional problem (think of the acceptable range as for instance an elliptic region on the plane over these two parameters). A correlation between kurtosis and skewness might also be important, so that not all combinations of values for theses parameters are possible, further complicating the whole story (the region of acceptable values might not be simply elliptic and have a rather complicated shape).
So I think the only way to answer this question is by experience: trial and error. If the results obtained are [not] good enough for the purpose for variables that deviate by a particular amount in kurtosis and skewness from a normal distribution, then these deviations (in the given combination) are obviousely [not] acceptable. Maybe one can extrapolate [un]acceptable deviations from similar data/studies that are already performed.
19 Recommendations
28th Jun, 2014
Ronán Michael Conroy
Royal College of Surgeons in Ireland
The trouble with the Kolmogorov Smirnov test is that it performs acceptably when the mean and standard deviations of the population are known. However, when we substitute for these the sample mean and standard deviation it does not perform well.
The other problem is implicit in your question : what do we mean by 'acceptable'? This has to depend on context. 'Desirable' for what?
If we're talking about the old canard about normally distributed data in regression, then the answer depends on simulation studies. But note that it is not the distribution of the predicted variable that is assumed to be normal but the sampling distribution of the parameter being estimated.
But you have learned from this discussion something important about rules of thumb. Everyone has a different thumb,
9 Recommendations
15th Dec, 2014
Pedro Joel Mendes Rosa
When your sample is very large, KS test becames very sensitive to small variations. Therefore I divide the sample skewness and kurtosis by their standard error to get the test statistic, which measures how many standard errors separate the sample skewness or Kurtosis  from zero:   If  Z values for skewness and kiurtosis are between −2 and +2, you reach conclusion that you sample might be symmetric.  I hope the attached file helps you. Cheers.
7 Recommendations
15th Dec, 2014
University of Tabriz
Aslam,
Everyone have different ways, but common purpose.
The first step for considering normal distribution is observed outliers.
The acceptable range for skewness or kurtosis below +1.5 and above -1.5 (Tabachnick & Fidell, 2013). If not, you have to consider transferring data and considering outliers.
So, if you could not take an acceptable range, you may not be getting correct analysis, especially CFA and other statistical analyses.
Hope help
5 Recommendations
13th Jan, 2015
Gabriella M. McLoughlin
Temple University
Hello fellow researchers,
I am having a similar issue. I too have small Skewness and Kurtosis values, however when running both these tests I receive significant values, indicating that the data are not normally distributed. In addition the G-plot graph shows fidelity to the expected value. I have a sample size of 792 and was investigating an independent variable.
Can anyone shed light on this issue? Is there something blatant that I could be disregarding?
Thank you,
Gabriella
1 Recommendation
13th Jan, 2015
Alex Gilgur
Amazon
If the question is of normality, go with Anderson-Darling (AD) test (KS does not perform as well as AD on the tails, making AD the golden standard of normality testing in industrial applications; not sure about research). If your primary concern is kurtosis, KS test is fine (I'm using it very successfully).  If you are concerned about skewness as well, then AD and Shapiro-Wilk (SW) are your friends.  Shapiro-Wilk test has the best power for a given significance, but it is slow when dealing with large samples, and AD follows closely enough.  There is a Royston's approximation for the Shapiro-Wilk test that allows to use it for bigger samples.
What was said about KS (and Shapiro-Wilk) requiring the apriori knowledge of mean and standard deviation is true, which is another advantage of AD test.  If you have to go with KS or SW, I would first remove outliers, estimate the mean and standard deviation, and then apply the test.
4 Recommendations
16th Jan, 2015
Rogerio Luz Coelho
The BIG QUESTION is ... "why do you need to test for normality" ... if your testing for normality is the form you use to choose your statistic, then it is intrinsically wrong !!
For big enough data (say in biological science above 100 or 200) the t-test and Wilcoxon have a 95% chance to tell you the same thing ... in today's fast personal computing you could even do both and see if they disagree, if they don't, use the t-test if you wish.
I like the non-parametric tests, and if you give them enough size they are very robust against the parametric ones.
5 Recommendations
21st Jan, 2015
Javier Sánchez Rosas
National University of Cordoba, Argentina
The values for asymmetry and kurtosis between -2 and +2 are considered acceptable in order to prove normal univariate distribution (George & Mallery, 2010). George, D., & Mallery, M. (2010). SPSS for Windows Step by Step: A Simple Guide and Reference, 17.0 update (10a ed.) Boston: Pearson.
153 Recommendations
22nd Jan, 2015
Anthony Muriithi Ireri
Kenyatta University
Some suggest that the most acceptable values for the two statistics should range between -1 through 0 to +2. check http://psychology.illinoisstate.edu/jccutti/138web/spss/spss3.html
3 Recommendations
24th Feb, 2015
Mary Nanyondo
Statistical significance levels of  .01, which equates to a z-score of ±2.58. is acceptable.
4 Recommendations
25th Feb, 2015
Norman Bravo
Independent Researcher
Skewness and Kurtosis can supply aditional info, when I coordinate a big project with 200 field researchers lifting data (distributed in 100,000 k2, 3.7 mll/hab, n=9850), and randomization I think "probably" will had a "bias" and analyzing one particular data from one field researcher (quality control) and have a doubt about "field reliability values" (age variable in Health-social research is useful to check "normality") with Shapiro-Wilk or K-S, then I check Skewness and Kurtosis "proportion", if Skewness error are bigger than Skewness value or Kurtosis error are bigger than Kurtosis value, "Houston...we got a problem", and I verify this "non normality" in empirical form "checking through talking" with the field researcher (methodology auditing/supervising); I don´t know about other researchers testing this.
6 Recommendations
12th Mar, 2015
Norman Bravo
Independent Researcher
6 Recommendations
27th Mar, 2015
Rabia Khawar
i do not know much about other disciplines, yet to my knowledge, most of the researchers in the field of social science are following a less stringent criteria based on the suggestion by Kline (1998, 2005). Data with a skew above an absolute value of 3.0 and kurtosis above an absolute value of 8.0 are considered problematic.
8 Recommendations
7th Jun, 2015
Khalid Hassan
University of Diyala
The best test for normality is Shapiro-Wilk test , you can use SPSS for this purpose , but in other hand , you can use many other methods to test normality , one of these methods is skewness or kurtosis and the acceptable limits +2 / - 2 .
5 Recommendations
10th Jul, 2015
Indian Institute of Public Health Gandhinagar (IIPHG)
It is very arbitrary judging the normality of variables only from skewness; pls see sapiro-wilk or kolmogorov-smirnov tests from SPSS.
2 Recommendations
3rd Sep, 2015
Eddie T.C. Lam
Cleveland State University
Absolute values > 0.2 indicate noticeable skewness (Hildebrand, 1986).
1 Recommendation
10th Oct, 2015
James A. DiGabriele
Montclair State University
In my travels the rule of thumb I have come to know for both is between -1 to 1. In Stata you have to subtract 3 from kurtosis.
Closer to zero the better.
2 Recommendations
7th Dec, 2015
Nor Hisham Haron
Universiti Utara Malaysia
According to Bulmer M. G. (1979), Principles of Statistics.
it can be consider normal when  -1<skewness<1
3 Recommendations
14th Dec, 2015
Mohd Azmir Mohd Nizah
USIM | Universiti Sains Islam Malaysia
Byrne, 2010 suggest kurtosis value of 3 for a normal, while values exceeding 5 indicates data are nonnormallly distributed ( Bentler, 2006).
But, again, Jochen answers also need to consider.
6 Recommendations
14th Dec, 2015
Janet Hanson
Azusa Pacific University
Naeem,
I have learned much from reading the wonderful answers provided by other researchers to your questions. I was recently asking the same questions related to exploring the normality of my data-set before deciding the use of parametric analysis to confirm or reject my research hypotheses. What I learned was that the indicator value range I choose for the skewness and kurtosis of my data were important for several reasons:
• the indicator values I choose give me a range that I can use to evaluate whether any of  the individual items on my survey questionnaire are outside of "normal" range and if there is a problem that I need to address
• the values I use must be justified by the literature on statistical analyses methods and recommended by experts in the field
• the indicators values provide justification for my decisions in the study for the statistical methods I choose for analyses (ex: parametric or non-parametric procedures)
• the indicators I choose support the conclusions drawn from my analyses (For example, I predicted my data set would be skewed slightly to the right because of self-selection bias. People who volunteer for human subject surveys tended to be more positive in their responses. I found the results did skew right though still were in acceptable ranges I had set. However, I am exploring methods to adjust for skewness in the data when performing the EFA and CFA)
I used indices for acceptable limits of ±2 (Trochim & Donnelly, 2006; Field, 2000 & 2009; Gravetter & Wallnau, 2014) Hope this helps!
Janet
References:
Trochim, W. M., & Donnelly, J. P. (2006). The research methods knowledge base (3rd ed.). Cincinnati, OH:Atomic Dog.
Gravetter, F., & Wallnau, L. (2014). Essentials of statistics for the behavioral sciences (8th ed.). Belmont, CA: Wadsworth.
Field, A. (2000). Discovering statistics using spss for windows. London-Thousand Oaks- New Delhi: Sage publications.
Field, A. (2009). Discovering statistics using SPSS. London: SAGE.
Just for fun I paste a link for an article by Firefox researchers on self-selection bias for you to review. The article discusses their  considerations when performing survey research on specific populations. I also provide a link to a PPT on how to transform skewed data.
147 Recommendations
10th Aug, 2016
Sanaullah Panezai
University of Balochistan
The values within the range of +1.96 and -1.96 are the said to be acceptable. Beyond these limits can be called skewed data !!
2 Recommendations
29th Aug, 2016
Sertaç Sert
i cant find -+1.5 skewness-kurtosis in tabachnick and fidell, 2013. does anyone know which number in book?
1 Recommendation
• Hair et al. (2010) and Bryne (2010) argued that data is considered to be normal if Skewness is between ‐2 to +2 and Kurtosis is between ‐7 to +7.
• Multi-normality data tests are performed using leveling asymmetry tests (skewness < 3), (Kurtosis between -2 and 2) and Mardia criterion (< 3). Source Chemingui, H., & Ben lallouna, H. (2013).
• Skewness and kurtosis index were used to identify the normality of the data. The result suggested the deviation of data from normality was not severe as the value of skewness and kurtosis index were below 3 and 10 respectively (Kline, 2011). Source Yadav, R., & Pathak, G. S. (2016).
10 Recommendations
16th Oct, 2016
Meryem Berrin Bulut
Chalamalla thank you for useful contribution !
1 Recommendation
• The two most common tests for Checking Normality are
• 1) Shapiro-Wilks test
• 2) Kolmogorov-Smirnov test.
• Both Tests are used to calculate the level of significance for the differences from a normal distribution. But Most Preferable one is Sahpiro-Wilk Tests. Hair et al (2013, p.71).
• For n < 50, interpret the Shapiro–Wilk test. If test variable exhibits many identical values or for higher sample sizes, use the Kolmogorov–Smirnov test (with Lilliefors correction). Sarstedt, M., & Mooi, E. (2014, p.179).
1 Recommendation
16th Dec, 2016
Michael Teng Loong Ing
University Malaysia Sarawak
Dear Chalamalla Srinivas,
Multi-normality data tests are performed using leveling asymmetry tests (skewness < 3), (Kurtosis between -2 and 2) and Mardia criterion (< 3). Source Chemingui, H., & Ben lallouna, H. (2013).
May I get the reference for this statement?
1 Recommendation
@ Dear Michael Teng Loong Ing
• On Page No 584,
• Under Confirmatory factor analysis heading,
• Second Paragraph
• First Line.
• In Chemingui, H., & Ben lallouna, H. (2013). Resistance, motivations, trust and intention to use mobile financial services. International Journal of Bank Marketing, 31(7), 574-592.
1 Recommendation
16th Dec, 2016
Michael Teng Loong Ing
University Malaysia Sarawak
Dear  @Chalamalla Srinivas,
Thank you.
1 Recommendation
16th Dec, 2016
Marius K. Somda
Dear
Refering to some publications I conclude that skewness and kurtosis test for normal distribution of data could be ranged at limit ±2.
Thank
Marius
2 Recommendations
16th Dec, 2016
Dianning Qu
Central Stouth University,China
Thanks for the detailed information!@Janet Hanson
1 Recommendation
20th Dec, 2016
Thedorus Dwi Prasetyo Aji
University of Malaya
my professor in class said that both indicator should within +/- 1. But, from all references I found, +/- 2 is acceptable. By the way, thanks for the detailed information.
1 Recommendation
20th Dec, 2016
Janet Hanson
Azusa Pacific University
Thedorus,
Thank you for participating in the discussion. Would you be willing to share a bit about the different acceptable limits for skewness and kurtosis (provided in the literature) based upon the domain of the study, types of variables, and use of the data, such as for a survey versus testing instrument?
For example, high stakes testing using cognitive content requires high reliability, and therefore indices for all measures of analyses are narrower. When testing data using psychosocial variables and with high response numbers compared to items the analyses may not require such rigor to gain the same value because the factors themselves are broadly defined.
Kind regards,
Janet
1 Recommendation
2nd Mar, 2017
Yacine Hajji
Genfit
I'm sorry but I think you're all wrong (but one comment I read).
You don't ask the good question.
Normality's assessment firstly depends on the variable's mechanism: additive/multiplicative errors for normal/log-normal (or other mechanism).
Then it depends on the statistical test you want to use.
If you want to know if your kurtosis/skewness has an impact on the normality of your variable, you should first check the dependence of the power of the test used against different values of kurtosis/skewness.
Your kurtosis and skewness won't have the same impact on a one-way anova or on an ancova.
3 Recommendations
3rd Mar, 2017
Mehmet Guven Gunver
Istanbul University
we developed a new procedure in order to determine skewness. j.ponte.2017.2.34
1 Recommendation
3rd Apr, 2017
Andy Lawrence
I found this tutorial quite helpful :)
Do the t-test and ANOVA really assume normality?
1 Recommendation
16th May, 2017
Renato P. Dos Santos
I was looking for some understanding of this problematic and found this discussion.
As I see, most people simply use some normality test, such as D'Agostino's, Jarque–Bera, Anderson–Darling, Kolmogorov–Smirnov, or Shapiro–Wilk.
One opinion that came to my attention yesterday was that normality tests are 'essentially useless'! The argument was two-fold: 1) those are null-hypothesis tests *against* normality and, therefore, are only informative if the data is *not* normal; 2) for small datasets, those tests almost always give positive answers (incurring in false-positive errors), while for really large sets, almost always give negative answers (incurring in false-negative errors). As a consequence, many people advice forgetting about those tests and check only for comparisons of kurtosis and skewness with their standard errors.
2 Recommendations
17th May, 2017
Yacine Hajji
Genfit
Dear Renato,
You're totaly right about the use of normality tests.
Therefore, taking into account kurtosis and skewness won't be THE solution, they are more likely to be clues.
When assessing normality, one should take several clues in order to dig what underlying mechanisms the analysed variable is afected by.
QQplots, residual vs predicted values plot (very usefull graph when assessing normality and log-normality), histogram AND skewness & kurtosis are good clues. Don't forget also to take into account the sample size of your data which will tend to its real distribution with a high sample size.
Last thing would be to use a model on the variable you want to analyse before using all of those graphs and statistical parameters. Some variables could have an hidden effect on your variable (e.g. hypotermia experiments could bias animal's body temperature distribution).
YH
4 Recommendations
9th Jun, 2017
Satishprakash Shukla
Indian Institute of Teacher Education Gandhinagar
Different methods and formulae are there for calculating skewness. Different methods give different values of skewness for the same data set. So, it is very difficult to decide its acceptable range that can lead to believe that distribution is not skewed. The same thing happens with Kurtosis. Different computer software also give different values of each of them for the same data set. Moreover Kurtosis shows the pickedness of Normal Probability curve, it does not decide the normally of distribution. It has nothing to do with normality of distribution. So, to decide the normally of distribution, we should use certain Normality Test. I have discussed some such tests in my paper "Normality Test", which is available on RG.
2 Recommendations
8th Jul, 2017
jørgen nikolaj Schmith
Lund University
Use Robust statistics if you doubt, very easy and for small data you do it quickly in your hand
1 Recommendation
3rd Sep, 2017
Dr Mohsin
University of Central Punjab
1. For small samples (n < 50), if absolute z-scores for either skewness or kurtosis are larger than 1.96, which corresponds with a alpha level 0.05, then reject the null hypothesis and conclude the distribution of the sample is non-normal.
2. For medium-sized samples (50 < n < 300), reject the null hypothesis at absolute z-value over 3.29, which corresponds with a alpha level 0.05, and conclude the distribution of the sample is non-normal.
3. For sample sizes greater than 300, depend on the histograms and the absolute values of skewness and kurtosis without considering z-values. Either an absolute skew value larger than 2 or an absolute kurtosis (proper) larger than 7 may be used as reference values for determining substantial non-normality.
8 Recommendations
12th Sep, 2017
Ravi Prakash Jha
Dr. Baba Saheb Ambedkar Hospital, Delhi
I agree with Javier that The values for asymmetry and kurtosis between -2 and +2 are considered acceptable in order to prove normal univariate distribution.
You can also go for various test for Normality check like shapiro wilk test, Kolmogorov smirnov test or even by plotting QQ plot.
3 Recommendations
28th Sep, 2017
Salam Jassim Hmood
Al Muthanna University
2 Recommendations
28th Sep, 2017
Iqbal Thonse Hawaldar
The Kingdom University
Some says for skewness (−1,1) (−1,1) and (−2,2) (−2,2) for kurtosis is an acceptable range for being normally distributed. Some says (−1.96,1.96) (−1.96,1.96) for skewness is an acceptable range. so better go for various normality test like SWT, KST or even by plotting QQ plot.
3 Recommendations
1st Oct, 2017
Noraani Mustapha
University of Malaysia, Kelantan
the range is between -2 to +2.
3rd Oct, 2017
Nicholas Kirwan Donaldson
King's College Hospital NHS Foundation Trust
I agree with Mohsin Altaf's answer. Skewness is a measure of (a)symmetry and kurtosis is a measure of peak-ness (how high the central peak is). It is good practice to keep in mind the expected values of these two statistics for a normal distribution so that you can guide your judgement: skewness about zero and kurtosis about 3.  I find the following link very informative:
1 Recommendation
3rd Oct, 2017
Nicholas Kirwan Donaldson
King's College Hospital NHS Foundation Trust
1 Recommendation
10th Oct, 2017
Presidency College
For good structural equation modeling analysis I recommend the value should between +1 and -1.
1 Recommendation
12th Oct, 2017
Peter H Westfall
Texas Tech University
Just to clarify: Contrary to what many sources state (incorrectly), kurtosis is most definitely NOT a measure of "peakedness" of a distribution. Rather, it is a measure of the outlier character of data or a distribution, as compared to that of a normal distribution. See here for a clear explanation: https://en.wikipedia.org/wiki/Talk:Kurtosis#Why_kurtosis_should_not_be_interpreted_as_.22peakedness.22
1 Recommendation
9th Nov, 2017
Panayiotis Theodossiou
Cyprus University of Technology
Fit the data using a flexible parametric distribution such as the skewed generalized t (SGT) or the skewed generalized error distribution (SGED) and use a log-likelihood ratio to test the null hypothesis of normality of the data. Simple kurtosis and skewness statistics, including the BJ test may give misleading results because of outliers.
1 Recommendation
This is the best site, explaining all SATAT analysis in detailed:
2 Recommendations
26th Nov, 2017
Arvinder-Singh HS
Clinical Research Centre
The standard which is fiollowed is skewness between -1 and +1
Kurtosis between -3 and +3.
1 Recommendation
26th Dec, 2017
Romer Castillo
Batangas State University
A normally distributed data has both skewness and kurtosis equal to zero. It is near-normal if skewness and kurtosis both ranges from -1 to 1. Values outside that range may still be "acceptable".
1 Recommendation
11th Jan, 2018
University of Jordan
for skewness, it is prefered not to exceed one; less than .20 is excellent,
4 Recommendations
16th Jan, 2018
Qais Almaamari
Gulf University
Hi Dear
According to George and Mallery (2016), the arithmetic mean is a good descriptor if the Skewness value obtained is within ±2.0 cut-off point. Byrne (2016), set the cut-off point For Kurtosis, which is less than 7 to be acceptable.
Best Regards
Almaamari
8 Recommendations
22nd Jan, 2018
Michael Christoph Thrun
Philipps University of Marburg
I would approach the problem visually and exploratively because in my experience every statstical descriptor or test requires mathematical prerequisites or model-assumptions.
Use QQ-plot to compare to Gaussian or ABC-plot to measure Skewness.
Michael, J. R. (1983). The stabilized probability plot. Biometrika, 70(1), 11-17.
Ultsch, A., & Lötsch, J. (2015). Computed ABC Analysis for Rational Selection of Most Informative Variables in Multivariate Data. PloS one, 10(6), e0129767. doi:10.1371/journal.pone.0129767
The R language provides the relevant implementations. Write to me, if you require package names.
4 Recommendations
13th Feb, 2018
Wilfred van den Brand
Open Universiteit Nederland
Most sources cited here are books, I would like to add the article of Ryu (2011). Following this article the cut off point is -2 / +2.
Ryu, E. (2011). Effects of skewness and kurtosis on normal-theory based maximum likelihood test statistic in multilevel structural equation modeling. Behavior Research Methods, 43(4), 1066-1074.
4 Recommendations
3rd Apr, 2018
University of Münster
Dear Everyone,
I am having an awkward situation with my data. If I look at the histogram, z-values criteria(only 5% to have greater values greater than 1.96 etc), skewness is in between -1 and 1, all these criterion are fulfilled. But the normality KS test and Shapiro values are significant. I have tried the transformation but still it is not working. Can someone tell me can i argue with respect to histograms and these z values criteria that my data is normal?
1 Recommendation
3rd Apr, 2018
Wilfred van den Brand
Open Universiteit Nederland
In many situations the KS and Shapiro-Wilk tests are too sensitive. In my opinion the best you can do is avoid them and use the histograms and skewness values to underpin normality.
4 Recommendations
3rd Apr, 2018
University of Münster
Actually, I have to run the Multivariate regression. For that the first assumption is the normality and second is the homogeneity. Lets say my data is normal on the basis of histograms and skewness values. But I am also getting the homogeneity "Levenes test" significant.
I have three different products and a variable performance that contains the values for all these 3 products. When I choose "Multivariate" and select Homogeneity test then it gives me significant result and also the Box value is significant. I have tried to use transformed option (Cube, square, Log etc) but the problem is that if i square the values then it gets right for one product but gets wrong for the other product. I dont know what to do in this situation?
Thanks
1 Recommendation
12th Apr, 2018
Muneeb Faiq
NYU Langone Medical Center
I just came across the following site. Please have a look. May be there is some use.
1 Recommendation
16th Apr, 2018
Noraani Mustapha
University of Malaysia, Kelantan
Normally..the range is -1.96 thru +1.96. This is the range of normal distribution or dispersion distance from 0 to both continuum
3 Recommendations
16th Apr, 2018
Khalid Al-Salhie
University of Basrah
1 Recommendation
12th May, 2018
Mohsin Hassan Alvi
Pakistan Institute of Living and Learning
What I understand about Skewness is..
Distribution of Data Left Side = Positive Values
Distribution of Data Right Side = Negative Values
1. Value = < -1 or >1 (Highly Skewed)
2. Value = between -1 and -0.5 or 1 and 0.5 (Moderate Skewed)
3. Value = between -0.5 and 0.5 (Distribution is Symmetric)
2 Recommendations
30th May, 2018
Jerry Miller
Texas Children's Hospital
Another one is the w/s-test for normality. Used to determine the significance of the difference of a frequency distribution based on a given sample and a normal frequency distribution. Can be computed by hand.
Found in 100 Statistical Tests, 3rd Edition, by Gopal K. Kanji, 2006. Sage: London.
1 Recommendation
5th Jun, 2018
Jeevan Jyoti
University of Jammu
there are varied views about. stringent limits are +1 To -1 whereas liberal authors recommend +3 to -3.
Further p value of Kolmogorov-Smirnov should be insignificant.
2 Recommendations
22nd Jun, 2018
Paul Louangrath
Bangkok University
KURTOSIS: Considered not normal if exceeds 3
SKEWNESS: To conclude normal or not, calculate D'Agostino K square test equivalent to chi sq. df = 2 or about 5.999. If K sq. > 5.999 or > 6.0, then the skew characterizes a non-normally distributed data.
1 Recommendation
10th Aug, 2018
Clem Wang
CarePredict
It's all very well to say use X as a cut off for some number. But, you are taking your data and boiling it down to one number. Just as with the boiling method of cooking, you can lose the flavor of what's really there.
I recommend making a Q-Q plot to see if something isn't lurking in your data that gets lost by making these calculations. It's also possible the QQ plot will suggest that you haven't really collected enough data.
2 Recommendations
10th Aug, 2018
Janet Hanson
Azusa Pacific University
Clem,
Could you describe your methods for the QQ plot? Thank you for sharing. I agree other statistical methods are useful and can reveal underlying characteristics of the data worthy of consideration for drawing valid conclusion.
Janet
1 Recommendation
10th Aug, 2018
Clem Wang
CarePredict
Janet Hanson - If the data is perfectly normal, the dots should (in theory) all fall on the QQ Plot line but due to chance the last few bits on the ends probably won't.
On the other hand, if there's a hint of an S or C shape, where the ends gently swaying away from the QQ Plot line, then something else may be going on even though statistically your Skewness and Kurtosis cut off numbers say you probably have a normal distribution. In that case, you may want to get more data (if time and resources allow) to see if anything interesting is happening with the "Outliers".
What I'm seeing in some data I'm analyzing, is that there's a gradual deviation from the normal distribution depending on a gradual loss of functionality. It's fsirly subtle but I wouldn't have noticed it if I just relied on numeric values or a histogram Plot. With a series of QQ Plots, it's clear that something is awry.
I hope that helps.
4 Recommendations
13th Aug, 2018
Erling Rognli
Akershus universitetssykehus
When the normality of your data is in question, it might be worthwhile to look into robust estimators. This is a very readable introduction:
Field, A. P., & Wilcox, R. R. (2017). Robust statistical methods: A primer for clinical psychology and experimental psychopathology researchers. Behaviour Research and Therapy, 98, 19-38, doi:10.1016/j.brat.2017.05.013.
3 Recommendations
30th Aug, 2018
Ataul Karim Patwary
University of Malaysia, Kelantan
Thank you Dr Naeem Aslam . I have learned a lot by reading the above answers.
Thank you Dr Janet Hanson for detailed explanation.
1 Recommendation
30th Aug, 2018
Saif Hosam Raheem
Good information
12 Recommendations
5th Sep, 2018
Dr. Saroj Kumar Rana
Postgraduate Institute of Medical Education and Research Chandigarh
Normally between -1 to +1
6th Sep, 2018
Dhritikesh Chakrabarty
Handique Girls' College
A normal distribution is symmetric.and mesokurtic.
Hence for a normal distribution, skewness is 0 and kurtosis is 3.
There is no any interval value for the skewness as well as for kurtosis of a normal distribution.
2 Recommendations
22nd Oct, 2018
University Of Kufa College of Science
Normally distributed data: 2>kurtosis>-2
22nd Oct, 2018
Salam Jassim Hmood
Al Muthanna University
Lies between + 2 & -2
23rd Oct, 2018
Aamna Khan
National University of Sciences and Technology
According to George & Mallery (2016), the value of kurtosis with a value of skewness between +2 is acceptable. For reference
George, D., & Mallery, P. (2016). IBM SPSS Statistics 23 Step by Step: A Simple Guide and Reference (13th ed.). New York: Routledge.
1 Recommendation
23rd Oct, 2018
Jeevan Jyoti
University of Jammu
though a normally distributed data has zero skewness, which means maximum observations are lying in the centre. Similarly the value of kurtosis fora normally distributed data is 3. But in reality we hardly get completely normal data, so some deviations are permissible. Hair et al. (2012) have prescribed + 1to -1 for the same.
23rd Oct, 2018
Symbiosis International University
To me its a question of perspectives. For a quantitative finance researcher a K>3 is welcome as that indicates a FAT Tail. He will be more interested to get such a value. Whereas a consumer behaviour researcher would love to observe K either lower than or equal to 3 for obvious reasons. Kurtosis values thus are perspective based and heuristics cannot be developed easily.
3 Recommendations
23rd Oct, 2018
Robert Trevethan
Independent author and researcher
I have been observing the above posts with interest, particularly because I think that determining satisfactory skewness and kurtosis is probably more complex than indicated by the typically used rules of thumb.
The following article by H. Y. Kim (2013) indicates, for example, that sample size can influence how researchers should use and interpret skewness and kurtosis (e.g., with small samples, easily obtained z values should be used) and that different stats packages might provide different information concerning kurtosis. Here is the URL:
The following YouTube presentation is clear and thoughtful:
I would be happy for people to react to the information in these sources.
Robt.
23rd Oct, 2018
Aamna Khan
National University of Sciences and Technology
+2 and -2 is acceptable range. In previous answer - was missed out.
4 Recommendations
23rd Oct, 2018
Robert Trevethan
Independent author and researcher
Thanks for responding, Aamna. I should have been more explicit. By "rules of thumb" I was referring to the notion that skewness or kurtosis values that lie in the range of -2 to +2 are satisfactory. I think this isn't always the case, and might be so only for samples greater than 300 or so.
I was recently examining some data (N = 200) in which skewness and kurtosis were less than |1|, but the histograms clearly indicated the data were quite skewed and leptokurtic. At first, I couldn't work out why there was a discrepancy between what the histograms and the descriptive stats were telling me.
It was only when doing what Kim (I provided the reference above) recommends that I was able to obtain the statistics for skewness and kurtosis that matched up with what the histograms looked like. In essence, Kim recommends dividing the skewness and kurtosis output from SPSS by the relevant standard errors (also provided by SPSS) to obtain a z value if numbers in the sample are less than 300. It's a little more complex than that, but easy to understand from Kim's article, which is open access.
I hope that's helpful, but please feel free (anyone) to come back. Communication is the beauty of ResearchGate.
Robt.
1 Recommendation
23rd Oct, 2018
Jessica E S Hoskins
University of California, Los Angeles
I believe the reason you are getting two general answers to this question is that different programs produce different values for kurtosis. I believe SPSS subtracts 3 (the kurtosis value for a normal distribution) so that negative values represent platykurtic and positive values reflect leptokurtic. In SPSS if you are unsure you can use the standard error to determine whether your value differs significantly from normal.
3 Recommendations

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