Checking normality using skewness, kurtosis, Kolmogorov-Smirnov and Shapiro-Wilk tests

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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.

Опубликовано:

20 авг 2024

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Комментарии : 108

@wajahatalighulam6924 9 месяцев назад

Kind and Soft way of teaching, Thanks Sir

@laylaboroon1579 Год назад

Thank you so much for the great presentation. It was really informative.

@panpanyang8938 4 года назад

easy to follow and very informative explanination

@farzanehtaghaviekrami8154 3 года назад

Thank you for your good explanation.

@user-zf9lp3cb1c Месяц назад

thank you very much Sir..

@sudeshchinthaka9120 2 года назад

Thank you Dr...So much informative and learned lot..

@littilgirl3220 21 день назад

I am ganna try it tommorow ,thank u

@mudasserabbas9260 3 года назад

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

@VahidAryadoust 3 года назад

Please see the following video for a list of references: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Kw5zaxB8Zac.html&

@mudasserabbas9260 3 года назад

@@VahidAryadoust thank you so much

@vainbow4632 5 месяцев назад

@@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.

@ahmedaremu2304 2 месяца назад

Thank you, Prof. I would be glad if you could provide sources for the thresholds.

@crazystatistician 9 месяцев назад

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,

@ahsanqureshi3467 3 года назад

hi, is there a reference identifying Absolute skewness value between -2 and +2. Absolute kurtosis value between -7 and +7 Guidelines?

@VahidAryadoust 3 года назад

Please see this video for more information: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Kw5zaxB8Zac.html

@shubhamjain1334 11 месяцев назад

thank you so much

@DP-xo2gh 3 года назад

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?

@VahidAryadoust 3 года назад

Typically many multivariate analysis textbooks cover such requirements. Please check out Hair et al's volume.

@dsavkay Год назад

THanks! Amazing

@amirhoseinmontazeri2570 4 года назад

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 )

@VahidAryadoust 4 года назад

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

@medinachely 3 года назад

@@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.

@VahidAryadoust 3 года назад

@@medinachely if your sample size is not too small, you can stick with the results of skewness and kurtosis analysis.

@mohamedzeineldin9707 3 года назад

@@VahidAryadoust could you please provide a reference for this .. as i have to mention in my paper why i did that

@VahidAryadoust 3 года назад

@@mohamedzeineldin9707 Please see this book/ chapter 1: www.routledge.com/Quantitative-Data-Analysis-for-Language-Assessment-Volume-I-Fundamental/Aryadoust-Raquel/p/book/9780367671396

@crazystatistician 9 месяцев назад

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?

@user-wj8wb9tn3u 12 дней назад

same my sample size is 300+, and i am so confused about this

@sabrinazazoun3733 3 дня назад

Same here, I have a sample of 20 rats distributed on 4 groups of 5 rats each and found the same problem as you,what to do?

@TODM4XNL 26 дней назад

Thanks for the great video. I have a question: Would you happen to have a reference where I could read about the material your presented in the video?

@OumaymaBarbou 3 месяца назад

Thanxxx a lot !

@vannphk7834 3 года назад

Very helpful, thank you !

@soehartosoeharto8471 4 года назад

thanks for your sharing

@mahirjibril8097 2 года назад

Appreciated for your elaborative video. Just wondering if you citation is available for the assumptions

@Alhamzah_F_Abbas 2 года назад

Very informative session, thank you very much

@bartul5645 9 дней назад

If there were control and experiment groups, should we perform normality tests for parameters one in the control and one in the experiment? If so, that parameter is normally distributed in control and in experiment then can we say it's normally distributed? Or else we should also check if it is normally distributed in general?

@doors22903 2 года назад

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.

@VahidAryadoust 2 года назад

It is an aggregate variable.

@tanzeemaruhi1148 3 года назад

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)?

@VahidAryadoust 3 года назад

It is probably due to the rounding methods used in the two tables.

@user-ho8yj9xo4m 3 года назад

thank you Dr

@yaregaltayelegesse2267 7 месяцев назад

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

@ayeshakhalil1947 Год назад

Is there a reference for these ranges being normal

@kelvinagbakwurujr3349 2 года назад

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?

@VahidAryadoust 2 года назад

The video is only for demonstration. You can use more variables, but in that case, the sample should be larger.

@aqsashabbir1380 2 года назад

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 😊

@VahidAryadoust 2 года назад

For normal data, please use parametric tests.

@aqsashabbir1380 2 года назад

@@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?

@aqsashabbir1380 2 года назад

And i read that for ordinal data apply non.parametric test.... I'm soo much confused about it.

@VahidAryadoust 2 года назад

@@aqsashabbir1380 That is fine. You can still look into its normality.

@aqsashabbir1380 2 года назад

@@VahidAryadoust thank you so much sir 🙂

@lailanordin835 3 года назад

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?

@VahidAryadoust 3 года назад

Both of them should be reported in your paper.

@lailanordin835 3 года назад

@@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.

@VahidAryadoust 3 года назад

@@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).

@lailanordin835 3 года назад

@@VahidAryadoust thank you so much Dr 😊 I really appreciate it!

@davidbell7361 3 года назад

excellent. Thank you...

@mennatullah2551 2 года назад

Can you please state reference for normality if z range between 3 and -3 it is normal

@VahidAryadoust 2 года назад

Please see Kline 2015 for further information.

@sritama12 3 года назад

Hello Dr, very informative lecture. Could you give some references for the ranges mentioned for the absolute value of skewness and kurtosis? Thanks

@VahidAryadoust 3 года назад

sure, please see Kline (2015) (a book about structural equation modeling).

@sritama12 3 года назад

@@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.

@chuza2003 3 года назад

@@sritama12 Did you find it in 5th edition?

@sritama12 3 года назад

@@chuza2003 No,

@Katrina86 3 года назад

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.

@VahidAryadoust 3 года назад

I would go with the formal tests, i.e., Shapiro-Wilk and Kolmogorov-Smirnov tests.

@Katrina86 3 года назад

@@VahidAryadoust Thank you!

@MoonLight-nc4fi 2 года назад

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

@VahidAryadoust 2 года назад

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.

@gracethong3883 3 года назад

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?

@ericoti4624 2 года назад

very helpfull thank you very much

@unknowninvictus2520 2 года назад

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!

@VahidAryadoust 2 года назад

Check out Andy Field's book.

@unknowninvictus2520 2 года назад

@@VahidAryadoust Thank you!

@Cxcxco89 2 года назад

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

@VahidAryadoust 2 года назад

That is a decision to be made by the analyst. To me, skewness and kurtosis rules will be fine.

@Cxcxco89 2 года назад

@@VahidAryadoust Thanks again

@henokasfaw8254 2 года назад

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?

@VahidAryadoust 2 года назад

I would go with the Z scores.

@asbinanceasbinance1473 3 года назад

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!

@VahidAryadoust 3 года назад

Please see Kline (2015), a volume on structural equation modeling.

@asbinanceasbinance1473 3 года назад

@@VahidAryadoust Thank you very much for your answer and for the source. This is a great help. Best regards.

@solomon5955 3 года назад

what is the reason beyond for Shapiro-Wilk didn't achieve, but the histogram PP plot and other results are well??

@VahidAryadoust 3 года назад

SW is a formal statistical test. I would suggest using skewness and kurtosis for examining normality.

@fondueeundof3351 Год назад

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?

@VahidAryadoust Год назад

There are different ways to estimate skewness & Kurtosis. One should consult the literature to choose the best.

@mariasusanoliveratorres4295 3 года назад

Hello, If I have a sample of 301 participants, is it consider unreliable? or it does not change that much. thank you.

@VahidAryadoust 3 года назад

No, the sample seems to be fine (depending on the number of your variables.).

@rayboat119 Год назад

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?

@VahidAryadoust Год назад

Do not use ML method of parameter estimation.

@rayboat119 Год назад

Thank you. Your videos are super helpful.

@0127550443 2 года назад

HI, I'm having 300 respondents in my research, is the Kolmogorov-Smrinov test suitable for to determine the normality of the samples?

@VahidAryadoust 2 года назад

I suggest using skewness and kurtosis the way discussed in the video.

@0127550443 2 года назад

@@VahidAryadoust Alright，thank you

@afnanaboras7649 4 года назад

how ca I calculate the Z range please?

@kailiangtiew3577 3 года назад

The Z value can be get from your computed statistics of skewness and Kurtosis value divide by standard errors.

@szekhiongfam5958 Год назад

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 😊

@VahidAryadoust Год назад

I'd go with the skewness and kurtosis values.

@szekhiongfam5958 Год назад

@@VahidAryadoust Thank you☺️

@danielcanoy5803 Год назад

Hi, Dr. Can we run a normality test for Likert Scale data? Or Likerts are already understood as not normally distributed?

@VahidAryadoust Год назад

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.

@danielcanoy5803 Год назад

@@VahidAryadoust Thanks, Dr.!

@danielcanoy5803 Год назад

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?

@VahidAryadoust Год назад

@@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.