Checking normality using skewness, kurtosis, Kolmogorov-Smirnov and Shapiro-Wilk tests
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- Опубліковано 24 лют 2020
- In this video, I will explain how to use SPSS to evaluate check for normality using skewness, kurtosis, Kolmogorov-Smirnov and Shapiro-Wilk tests.
Please also check the following video for further information:
• Normality, Skewness, K...
The criteria that I will explain are as follows:
1. Skewness & Kurtosis
Samples below 50: use the z value. -1.96 and +1.96 (Z scores for kurtosis and skewness are computed by dividing the skewness and kurtosis by their SE)
Samples between 50 and 300: use a more liberal z range. -3.29 and +3.29
Larger samples:
Absolute skewness value between -2 and +2.
Absolute kurtosis value between -7 and +7
2. Kolmogorov-Smirnov test AND Shapiro-Wilk test
Use with samples below 300
For samples larger than 300, they may be unreliable.
Data used in this video were derived from Core 3 Research Programme: A Quantitative Study of Learning and Teaching in Singapore Classrooms, the property of the National Institute of Education, Nanyang Technological University, Singapore.
Thank you so much for the great presentation. It was really informative.
Thank you for your good explanation.
Thank you Dr...So much informative and learned lot..
easy to follow and very informative explanination
Very helpful, thank you !
Very informative session, thank you very much
Kind and Soft way of teaching, Thanks Sir
thank you very much Sir..
thanks for your sharing
THanks! Amazing
thank you Dr
thank you so much
Thanxxx a lot !
excellent. Thank you...
very helpfull thank you very much
Appreciated for your elaborative video. Just wondering if you citation is available for the assumptions
Thank you, Prof. I would be glad if you could provide sources for the thresholds.
Thank you for this wonderful video, I would really appreciate it if you can provide any reference for skewness value between -2 and +2. Absolute kurtosis value between -7 and +7 Guidelines. thankyou
Please see the following video for a list of references: ua-cam.com/video/Kw5zaxB8Zac/v-deo.html&
@@VahidAryadoust thank you so much
@@VahidAryadoust The exponential distribution has an excess kurtosis of 6 and a skewness of 2. Those bounds on the skewness and kurtosis for large samples here are so ridiculously wide that one would call almost any distribution normal using them.
Thank you for your presentation. Could you please provide a citation for recommending z range of -3.29 - 3.29 for samples between 50-300?
Typically many multivariate analysis textbooks cover such requirements. Please check out Hair et al's volume.
Thank you for the informative helpful video, Doctor! If I may ask few questions, are the four variables that you used in this video aggregate or mean of each representing indicators? For example, the variable "comprehession" is aggregate or mean of indicators "qrc1r, qrc2r, qrc3r, and so on" I see in the video? Would appreciate your response, thank you.
It is an aggregate variable.
Hi Dr. Vahid,
Thank you very much for this useful video!
I have 2 questions about normality:
1. When we are calculating the skewness and kurtosis values or performing the Kolmogorov and Shapiro-Wilk tests, should we do these tests with the mean of the variables or items of each scale?
2. Should we also look at the histogram to decide whether our data is normally distributed, apart from these tests and skewness and kurtosis values?
Cheers,
Hi Dr. Vahid. I have a question
about the descriptive stats in your paper ( gender and academic major bias in peer assessment of oral presentations). For the scoring criteria scores, did you run the analyses on raw scores? How many raters rated each student’s performance?
In my case, each student has been rated twice by 2 different raters using an analytical rubric. Do you have any suggestion for running this type of desc stats? Do I put all the scores in spas? Thanks a lot
You should run agreement analysis or inter-rater reliability first. If these look fine, then average the scores and compute kurtosis, skewness etc of the average scores. Videos on rater agreement analysis etc are available in this channel.
if i evaluate normality using skewness for 30 variables, all 29 variables are distributed within normal range except one variable is not skew normally. Can I choose parametric test for these 30 variables since all 30 variables are consider as one factor?
Hi, my sample is 500. Another question arises regarding my skewness and kurtosis values, which suggest that my data is normally distributed. However, the results from the Shapiro-Wilk and Kolmogorov tests, along with histograms and Q-Q Plots, indicate that the data is not normally distributed. Which set of results should I trust?
Hello sir, I liked it very much but could you please mention a source for the explanation you have given in relation to kolmogove and Shapiro-wilk tests so that we can cite. I faced the same problem because my data is large which is 600
hi, is there a reference identifying Absolute skewness value between -2 and +2. Absolute kurtosis value between -7 and +7 Guidelines?
Please see this video for more information: ua-cam.com/video/Kw5zaxB8Zac/v-deo.html
Dear Professor, thank you for a good lecture. I would like to ask if I have a small sample (less than 50 cases) and Shapiro-Wilk and Kolmogorov-Smirnov tests show that distribution is normal, however when I inspect the histogram it looks like not normal distribution of the variable. What should I conclude from this? Thank you in advance.
I would go with the formal tests, i.e., Shapiro-Wilk and Kolmogorov-Smirnov tests.
@@VahidAryadoust Thank you!
Is there a reference for these ranges being normal
Thank you for the video. Do you have a reference for the skewness and kurtosis value ranges for larger samples? Where do these ranges come from? Thanx a lot!
Please see Kline (2015), a volume on structural equation modeling.
@@VahidAryadoust Thank you very much for your answer and for the source. This is a great help. Best regards.
thanks for your great and useful video. I have a question:
can you reference those 4 criteria, please?
(i mean criteria about skewness, kurtosis and sample size for Kolmogorov-Smirnov and Shapiro-Wilk tests )
Hi, if you mean reference textbooks, you can look here:
www.routledge.com/Quantitative-Data-Analysis-for-Language-Assessment-Volume-I-Fundamental/Aryadoust-Raquel/p/book/9781138733121
@@VahidAryadoust I have the same situation with my data. The histogram, skewness and curtosis are in the normal distribution. But the KS test results is .000 of Sig. I'm reading the book you recommended, but I can't find in the discussion of KS and large sample. What is the chapter that discuss this. I need it to report in my paper.
@@medinachely if your sample size is not too small, you can stick with the results of skewness and kurtosis analysis.
@@VahidAryadoust could you please provide a reference for this .. as i have to mention in my paper why i did that
@@mohamedzeineldin9707 Please see this book/ chapter 1:
www.routledge.com/Quantitative-Data-Analysis-for-Language-Assessment-Volume-I-Fundamental/Aryadoust-Raquel/p/book/9780367671396
Hi Dr. Thank you so much for sharing this. I have a question:
Do we need both absolute skewness and kurtosis value or only one of them?
Both of them should be reported in your paper.
@@VahidAryadoustI'm sorry, maybe my question is not clear. To consider the data is normal, both absolute value should follow the value given? For example, the data show that absolute skewness is between +2 to -2, but not the absolute kurtosis value. So the data is consider to be normal distributed? Thank you in advanced Dr.
@@lailanordin835 Yes, both the indices (skewness and Kurtosis) should follow the constraint tenable. Note that Kline (2015) has a more liberal range for Kurtosis: -7 to +7, whereas skewness has a more stringent range in normal data (-2 to +2).
@@VahidAryadoust thank you so much Dr 😊 I really appreciate it!
Thank you for this presentation sir. But I want to ask, why did you use only four variables in the "Dependent List" column when we have other variables in the data?
The video is only for demonstration. You can use more variables, but in that case, the sample should be larger.
Thank you for sharing professor, would you suggest to use the kurtosis/skeweness rule of thumb in order to check the normality distribution of a likert scale on 5 points? I know there is debate on the possibility to approximate the distribution of this kind of scale to normality
That is a decision to be made by the analyst. To me, skewness and kurtosis rules will be fine.
@@VahidAryadoust Thanks again
Hello Dr, very informative lecture. Could you give some references for the ranges mentioned for the absolute value of skewness and kurtosis? Thanks
sure, please see Kline (2015) (a book about structural equation modeling).
@@VahidAryadoust Thank you Dr Aryadoust. I have the third edition of the book, where Kurtosis cut off is mentioned as +3to -3. And skewness as +.5 to -.5. I will check the particular edition.
@@sritama12 Did you find it in 5th edition?
@@chuza2003 No,
Hi, why are some of the skewness and kurtosis values different for the first table (from where you found z value) and the second table ( the more detailed one)?
It is probably due to the rounding methods used in the two tables.
My sample size is 180. All the Z scores are below 3.29(except one). But the Kolmogorov-Smirnov and Shapiro-Wilk tests showed the data is not normally distributed(significance less than 0.05). Should I consider it as normally distributed or not?
I would go with the Z scores.
what is the reason beyond for Shapiro-Wilk didn't achieve, but the histogram PP plot and other results are well??
SW is a formal statistical test. I would suggest using skewness and kurtosis for examining normality.
Hello, I have a question, Where could I find the (statistical) theory of this video. More precisely what literature was used for the values and sample sizes for the criteria of skewness and kurtosis. Many thanks!
Check out Andy Field's book.
@@VahidAryadoust Thank you!
Hi doctor, can I ask for my data with sample size of 50 patients, the skewness and kurtosis test is within normal range, however the SW test was not normally distributed, may i know which one to follow, thank you 😊
I'd go with the skewness and kurtosis values.
@@VahidAryadoust Thank you☺️
Hello, If I have a sample of 301 participants, is it consider unreliable? or it does not change that much. thank you.
No, the sample seems to be fine (depending on the number of your variables.).
How can I check for normality using skewness and kurtosis estimators that already assume the underlying distribution to be normal? Isn't that going in circles?
There are different ways to estimate skewness & Kurtosis. One should consult the literature to choose the best.
how ca I calculate the Z range please?
The Z value can be get from your computed statistics of skewness and Kurtosis value divide by standard errors.
Thank you for the presentation. I want to conduct an SEM, but it seems my data is not normally distributed ... can I proceed with the analysis?
Do not use ML method of parameter estimation.
Thank you. Your videos are super helpful.
Can you please state reference for normality if z range between 3 and -3 it is normal
Please see Kline 2015 for further information.
HI, I'm having 300 respondents in my research, is the Kolmogorov-Smrinov test suitable for to determine the normality of the samples?
I suggest using skewness and kurtosis the way discussed in the video.
@@VahidAryadoust Alright，thank you
Hello Dr.
My sample size is less than 300 so (- 3.29 +3.29) range i used.. But if i perform other styles to check normality, then my data is considered not normal distributed.
Please guide me if my data is normal then which test i slected paramtric or non.pramatric? Thnk u in advance 😊
For normal data, please use parametric tests.
@@VahidAryadoust thank you sir for guiding me.. One more thing is that my data is normaly distributed and apply parametric test but my data is ordinal because i use likert scale data in questionneir..... Then what can i do?
And i read that for ordinal data apply non.parametric test.... I'm soo much confused about it.
@@aqsashabbir1380 That is fine. You can still look into its normality.
@@VahidAryadoust thank you so much sir 🙂
Hi, Dr. Can we run a normality test for Likert Scale data? Or Likerts are already understood as not normally distributed?
There are two schools of thought:1) yes, you can (this is practically the dominant school of thought) 2) no, since Likert scales are not normally distributed.
@@VahidAryadoust Thanks, Dr.!
Another question, Dr., what if the results of the Confirmatory Factor Analysis' CFI, TLI, RMSEA, SMNR were below the significant values, what should a researcher do next?
@@danielcanoy5803 Look at modification indices, to find out how to improve the fit of the model. For example, you might be prompted to identify the worst (the lowest) path coefficients and remove the path; re-run the analysis iteratively till you arrive at a better model.