Normality test using SPSS: How to check whether data are normally distributed

If data need to be approximately normally distributed, this tutorial shows how to use SPSS to verify this. On a side note: my new project: howtowritecitat....
Statistical analyses often have dependent variables and independent variables and many parametric statistical methods require that the dependent variable is approximately normally distributed for each category of the independent variable.
Let us assume that we have a dependent variable, exam scores, and an independent variable, gender.
In short, we must investigate the following numerical and visual outputs (and the tutorial shows how to do just that):
-The Skewness & kurtosis z-values, which should be somewhere in the span -1.96 to +1.96;
-The Shapiro-Wilk p-value, which should be above 0.05;
-The Histograms, Normal Q-Q plots and Box plots, which should visually indicate that our data are approximately normally distributed.
Remember that your data do not have to be perfectly normally distributed. The main thing is that they are approximately normally distributed, and that you check each category of the independent variable. (In our example, both male and female data.)
Step 1. In the menu of SPSS, click on Analyze, select Descriptive Statistics and Explore.
Step 2. Set exam scores as the dependent variable, and gender as the independent variable.
Step 3. Click on Plots, select "Histogram" (you do not need "Stem-and-leaf") and select "Normality plots with tests" and click on Continue, then OK.
Step 4. Start with skewness and kurtosis. The skewness and kurtosis measures should be as close to zero as possible, in SPSS. In reality, however, data are often skewed and kurtotic. A small departure from zero is therefore no problem, as long as the measures are not too large compare to their standard errors. As a consequence, you must divide the measure by its standard error, and you need to do this by hand, using a calculator. This will give you the z-value, which, as I said, should be somewhere within -1.96 to +1.96. Let us start with the males in our example. To calculate the skewness z-value, divide the skewness measure by its standard error. All z-values in the tutorial video are within ±1.96. We can conclude that the exam score data are a little skewed and kurtotic, for both males and females, but they do not differ significantly from normality.
Step 5. Check the Shapiro-Wilk test statistic. The null hypothesis for this test of normality is that the data are normally distributed. The null hypothesis is rejected if the p-value is below 0.05. In SPSS output, the p-value is labeled "Sig". In our example, the p-values for males and females are above 0.05, so we keep the null hypothesis. The Shapiro-Wilk test thus indicates that our example data are approximately normally distributed.
Step 6. Next, let us look at the graphical figures, for both male and female data. Inspect the histograms visually. They should have the approximate shape of a normal curve. Then, look at the normal Q-Q plot. The dots should be approximately distributed along the line. This indicates that the data are approximately normally distributed. Skip the Detrended Q-Q plots. You do not need them. Finally, look at the box plots. They should be approximately symmetrical.
The video contains references to books and articles.
About writing out the results: I would put it under the sub-heading "Sample characteristics", and the video contains examples of how I would write.
In this tutorial, I show you how to check if a dependent variable is approximately normally distributed for each category of an independent variable. I am assuming that you, eventually, want to use a certain parametric statistical methods to explore and investigate your data. If it turns out that your dependent variable is not approximately normally distributed for each category of the independent variable, it is no problem. In such case, you will have to use non-parametric methods, because they make no assumptions about the distributions.
Good luck with your research.
Text and video (including audio) © Kent Löfgren, Sweden
Here are the references that I discuss in the video (thanks Abdul Syafiq Bahrin for typing them our for me):
Cramer, D. (1998). Fundamental statistics for social research. London: Routledge.
Cramer, D., & Howitt, D. (2004). The SAGE dictionary of statistics. London: SAGE.
Doane, D. P., & Seward, L.E. (2011). Measuring Skewness. Journal of Statistics Education, 19(2), 1-18.
Razali, N. M., & Wah, Y. B. (2011). Power comparisons of Shapiro-Wilk, Kolmogorov-Smirnov, Liliefors and Anderson-Darling test. Journal of Statistical Modeling and Analytics, 2(1), 21-33.
Shapiro, S. S., & Wilk, M. B. (1965). An Analysis of Variance Test for Normality (Complete Samples). Biometrika, 52(3/4), 591-611.

[@number1spot]

Dear Sir, I wanted to let you know that this video of yours is one of the best teaching videos that I came across. The way you explain and visualise the topics is great. Please keep up the good work!

[@kentlofgren]

Thanks. I do put a lot of time into my best videos so this kind of feedback is really welcome. May I also add that I am a teacher, so rest assure that there are students that benefit from my teaching, hands on, every week ;-)

[@number1spot]

***** Dear Sir, I'm happy if Feedback like this motivates u even more. Do u also have a teaching video on binary logistic Regression or do you have a source where I can learn that task in SPSS? I would very much appreciate it!

[@kentlofgren]

Avteam Innsbruck Sorry, nothing on regression yet, and I do not have a nice link either. Good luck nevertheless.

[@wenyuanliu4602]

hi, Avteam, It is also someone I saw on this topic, thanks Kent!

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yup, i do agree with that

[@carreyoliver1348]

Are you a university lecturer? Well you should be, because this is so easy to understand than reading hundreds of articles/journals to interpret the results i get from SPSS. Any students would be so lucky to have you as their teachers. Thanks this helps me a lot!

[@kelsie.j]

currently writing my thesis for my final year. you've helped me so much. thank you

[@kentlofgren]

Happy to help!

[@ca.elizabeth]

I was stuck with my thesis several times because of being unable to understand a thing in SPSS no matter how many videos, books and "how to's" i run through and FINALLY (!!!) i find the best explanation ever! So now I see that SPSS is actually not so scary and i can tame it :D

[@daisychainsawed]

I have to say that this is THE BEST explanation of normality tests that I have come across (and thats after having looked at a handful of text books, tons of videos and google). The reason I like it is that it actually explains the reasoning for doing normality tests, and more importantly, how to report the results. Excellent! Thanks Kent

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I have been trying to get to grips with SPSS for a year now, and I can honestly say this explanation is the best I have ever had. I have had Lectures, read books, watched videos, gone through handouts numerous times. And I had to comment! Thank you so much! Danielle University Student England

[@kentlofgren]

Danielle Martin Thx Danielle!

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My assignment is due in 8 hours, I've spent 20 hours watching KZbin content, reading Google/reddits etc and I still couldn't understand 20 hours later. I just stumbled across your video and I FINALLY GET IT. YOU HAVE NO IDEA HOW MUCH YOU HELPED ME. THANK YOU. Keep going. And doing what you do. I appreciate you.

[@VirtualSolace]

I'm really amazed by your simplistic yet intriguing explanation. Finally, I learned how to test the normality of data in SPSS. Thank you for making this video.

[@kentlofgren]

Great to hear! I try to make them as simple as possible. The risk, though, is that they become too slooow ;-) However, I learn and improve all the time and the characteristics of my tutorial videos change all the time.

[@kerryb1234]

You are an absolute genius! I am doing epidemiology and biostatistics at uni and our teacher doesnt teach us anything. There are no terms or definitions or even explanations of variables etc. They simply do examples of data, showing graphs and tables and then in class we do examples of SPSS data but I don't understand what it all means, there are no interpretations etc. We have done studies in groups on a simulation database and have a report due this weekend and still they haven't explain how to do run the analysis in SPSS or how to report and interpret the data. So I thank you for being an actual teacher!

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Your explanation is outstanding!! I am new to statistics and I conducted a search on SPSS and your video came up. Seven years later you are right on point! Thank you for this video!!

[@edunomics1970]

One of the most versatile fluent and easy to understand explanation. Thanks a lot for such an easy explanation.

[@mahmoudhosseinnia6257]

Dear Kent Löfgren I really appreciate for your perfect tutorial because I figure out what i couldn't understand in two semester from a professor on SPSS course.

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OMG this is too good, the visuals, narrative and content are very communicative

[@kentlofgren]

Thanks, it means a lot.

[@sonicbouy]

***** Pls make video explaining what is logic of using a F-test which is for F-distribution on on ANOVA when you have assumed that sample comes from normal distribution

[@r12kyyudha]

You have the best pace in explanation and the way you break it down, is just right! Awesome

[@umarfaruq4335]

Dear Sir, Despite the fact that my comment is coming about 5 years late, nonetheless, I feel highly obliged to write it - it is now that I found myself needing such a lecture! The narrative is very clear and simple for anyone to understandard - no unnecessary jargons, not too fast to be frustrating, not too slow to be boring! The graphics and animation is also not overwhelming - its just okay! I hope to come across more of such video lectures that are tailored towards the 'laymen' in statistics.

[@eskausimon]

The best video on normality tests because unlike most others that that tell you to use skewness, kurtosis, histogram, blah blah, you explain step by step how to carry out a normality test, how to interpret the outcomes and how to report findings. Thanks a great deal Kent.

[@kentlofgren]

Thank you, that's very kind of you to say.

[@yonelamaziko287]

You explain slowly and clearly enough for my brain to understand, I am currently searching for more of your videos on statistics because you just might be my saving grace.

[@kentlofgren]

Thank you. Lying in my sofa, chilling with the tablet. Always nice w. positive feedback.

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Now this is one example for excellent structured video. Provide aims , explanations etc. Wish my lecturers knew how to explain like this. Thank you!

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one of the best video i have ever seen, and the best thing what i found in this video is the explanation is in a scientific way with number of references

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Have watched too many videos but in this video I have found all the necessary details and you made it in a way so that anyone can understand it. Thank you sir!

[@kentlofgren]

Thanks and welcome!

[@lihamena2780]

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Best explanation and the pace is so great for non-statistical person. You gave me more than I expected. Well-done.

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Sir, even now this video continues to guide students. We are thankful

[@kentlofgren]

It's my pleasure

[@miscelleneoustubes]

Easy and best among hundreds I have watched! Great thanks sir.

[@haroldasraz]

Thank you Kent for a very clear explanation of normality exploration on SPSS. This video is applicable for JASP users too.

[@kshipramoghe3361]

Great way to learn...Thanks a lot for the slow and steady explanation with complete clarity.

[@louisacharlotte1]

I agree, thank you :)

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thank you for so nicely explaining the normality test. I was in search of this explanation for the last many months and found your video. I will watch the rest of your videos so that I could understand my research data. I love learning biostatistics but found no one in my area to help me. Finally found your video. I wish you were my teacher.

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Now this is what you call statistics/SPSS for dummies! So helpful. Thanks.

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Been looking for days for some decent explanation. Thank you very much for this one, simply explained with details, extremely helpful.

[@marcooliveri5172]

Thank you very much for your lesson, it is the clearest and most helpful on KZbin!

[@PapaKinemeAndMyKineme]

Coming from a statistician like me, this is a great instructional video for Normality checks.

[@kentlofgren]

+Jimmy Bayrante (Joyce) Thx Jimmy, appreciate your feedback. I put a lot of time into this one. On a side-note, I can also tell you that I had to check how to pronounce some of the terms (e.g. kurtotic) before recording :-)

[@PapaKinemeAndMyKineme]

+Kent Löfgren hahaha! no worries. everything is perfect in the video. thank u so much

[@szshikamaru6557]

+Kent Löfgren Thanks for the great video. But what if one gender's Shapiro-Wilk test score is below 0.05? what do we do then? Thanks

[@maytalili2347]

amazing, my head mixed up and couldn't understand my professor's discussion. thanks for this. you saved me in my statistics subject👍👍👍👍👍

[@kentlofgren]

Excellent!

[@markrukavina8770]

Great video and incredibly helpful. The narrative and visuals were very thorough and delivered at a pace that made it very easy to pick up the concepts and procedures. Also, as someone who tends to struggle with statistics, I appreciate you explaining everything and not assuming a baseline of knowledge. Thanks so much!

[@kentlofgren]

Glad you enjoyed it!

[@adiladil78]

Easily, the best video on KZbin on this topic. Thanks for the great upload.

[@hasviniypadmanathan6047]

Dear Sir, Thank you so much for the lesson and sharing. This was the only videos I could understand after watching and reading few books. Thank you again sir. I hope you have a nice day.

[@hasviniypadmanathan6047]

I am novice and beginner in statistics and your video really helped

[@kentlofgren]

You are most welcome! Glad that it helped.

[@ritusam1]

one of the best Statistics video I ever watched. Thank you Sir.

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Thank you very much sir for this great video. The way you teach is easy to understand and for the first time in my life as PG student I know now how to analyse data normality. Keep up the good work sir!

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This the best explanation I have found on KZbin on normality tests.

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Dear Kent, This is the best video tutorial I have watched related to SPSS stuff. (I have watched quite a few) Thank you for this

[@m4dnus]

the word "each" on 38. sec saved my life thank you :)

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Your explanation has helped me in completing my thesis. Thank you very much. God bless your work.

[@kentlofgren]

Good luck with the viva!

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Thank you so much, It was by far the finest SPSS explanation I've ever seen. very easy to understand.

[@kentlofgren]

You're very welcome!

[@blackredJazz]

Life saver! Explained it better than my lecturer!

[@danijela-denyvelickovic8494]

Dear teacher thank you. All best from Montenegro-Serbia.

[@kentlofgren]

Yes, one category may have data that are non-normal and you can correct that (transforming data) if you want to use parametric tests (t-test or ANOVA for example). I would google for square root transformation (abbreviated SQRT in SPSS). Best of luck with your research and paper.

[@archikajohari505]

Dear Sir This is the first video of yours I have watched and wanted to let you know that this one video itself has made me search for your other related videos. Your way of teaching is great. I have a query here. you said that if one category has a non-normal data we can opt for transforming the data. Is transforming data applicable in a case where one of the four levels of independent variables is not normally distributed? Of the four levels of an independent variable, one is not normally distributed. Can I go for parametric tests or should I opt for transforming that particular data of independent variable?? Please help.

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The best video on the Internet so far. 100/100 recommended!

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I agree with Avteam Innsbruck. I like the way you organize the material and your voice is very soothing. Kindest, Robin

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Thank you sir.... This video has saved people around the world... :P

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NOW is a perfect time to watch this video because it helps me with my current project. Thank you Mr. Kent Lofgren. I just found this video is helpful.

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Your explanation is very clear for an amateur , amazing work👍👍👍

[@kentlofgren]

Glad you liked it

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I am in 2023, so glad to hear your lecture. Please keep posting the video, its extremely so helpful for me. Now, I know how to exclude my data for the further test. I got very clear explanations. Hope you always happy and health. and ofc I looking forward your video on statistic topics. Please make video about Manova test. Thank you

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Respected Sir, You just saved my day sir, I am glad to come across a channel like yours's whose primary motive is to teach in the simplest way possible with detailed information. kindly keep us showering with such great videos.

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Wow, thanks a lot for this excellent video! This is the first time I see someone explaining it so well and even providing sources and reporting tips. Awesome!

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This is one among the best video on normality test..It's so clear and simple to understand with easier way.. Thankyou so much Sir 🙏

[@kentlofgren]

You are most welcome

[@Lensonthethames]

Superb explanation - thank you. Something incredibly difficult made simple. Appreciate the how to write up statistical methods (ignoring z values) and even how to reference it with the final reminder that it is for parametric analysis (eg t-test). You make stats fun at last!

[@adventurewitheve8606]

Thank you VERY much! It is the first time when i understand statistics!

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Thank you very much for explaining so clearly! Wonderful pace of speech and amount of information (not more or less) for my brain to take on statistics. This way of using speech together with text and visuals helped me understand!

[@theamolaksingh]

Very much thank you Kent Lofgren for explaining with patience.

[@kikawarichardcliff5286]

I must say that this video is one of the best. Clear, precise and informative.

[@_Anonymous_9]

That was honestly the best SPSS tutorial I have ever watched... would love to see some more on regression, T-tests etc in detail if you ever get a chance.

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Man, this was by far the best video on this topic so far! Thanks for sharing your knowledge!!!!!!

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Very well organized and with a nice flow..Kudos to you,sir!

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Thank you sir! your voice is so calm and soothing!

[@kentlofgren]

So nice of you, thx.

[@eloiseburbridge103]

This is the best educational video I have ever seen by far. Currently carrying out preliminary tests of normality on my data and it was a huge help. Thank you so much!

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the only video which clearly told how to calculate Z value...thanks...

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Clear explanation and interpretation. Very helpful for non-statisticians like me.

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very clear, good pace and simple instructions and explanations. Thank you for helping me navigate my way through statistics.

[@kentlofgren]

Giorgia Wa Thanks for your kind words. I just released a new video, about survey data: kzbin.info/www/bejne/g36qYn6IhZ51hpI Good luck with your work/studies!

[@tracithomas5427]

Thank you for an excellent tutorial. You are a fantastic teacher and I wish you much success in all you do.

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Thank you for this! This taught me in few minutes what I have been struggling to figure out for a day now. I didn't even know I will have to interpret the result

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Your presentation is excellent. Additionally, you should consider narrating certain types of documentaries, as your voice has a David Attenborough quality. Very good.

[@kentlofgren]

That's kind of you, thank you very much.

[@anahitaghanad5954]

Thank you so much for the great teaching method.

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I thank you very much for your precious contribution to shared knowledge. Clear, simple and effective. I wish you the best.

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Well explained, with all the knowledge you need and you kept it short!

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Thank you very much Kent! It is possible that your tutorial will save my exam.

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Excellent tutorial. For beginners, it gives a very good explanation. Please get the maximum benefit by watching this video.

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What a fantastic method of lecturing? You're great!

[@berto591]

best video on how to check normality i've found

[@yourlocalowl.]

Kent Löfgren thanks for such a clear explanation of data normality test

[@simonpeterlokomo403]

This was absolutely helpful for a novice in stats like myself, cheers and keep up the good work!

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Sir , i am so glad that i had found such a good video regarding normality tests .. Thank you so much sir . Too easy to understand :)

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This a great tutorial. Clear and well paced and well explained. Thanks

[@Charlie-co4ry]

Very clear and concise; I particularly like how you've included a sample writing. Thanks.

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thankyou so much for making this video, i'm currently working on my bachelor degree thesis, and kinda lost for a week now and i'm running out of time, since my supervisor isn't around, but this video really helpful. thankyou. -lilian, Malaysia

[@abdulsyafiqbahrin5768]

Thank you for sharing your knowledge. Its easy for me to understand the general idea about normality test calculation.

[@abdulsyafiqbahrin5768]

For those who lazy to type the references given: Cramer, D. (1998). Fundamental statistics for social research. London: Routledge. Cramer, D., & Howitt, D. (2004). The SAGE dictionary of statistics. London: SAGE. Doane, D. P., & Seward, L.E. (2011). Measuring Skewness. Journal of Statistics Education, 19(2), 1-18. Razali, N. M., & Wah, Y. B. (2011). Power comparisons of Shapiro-Wilk, Kolmogorov-Smirnov, Liliefors and Anderson-Darling test. Journal of Statistical Modeling and Analytics, 2(1), 21-33. Shapiro, S. S., & Wilk, M. B. (1965). An Analysis of Variance Test for Normality (Complete Samples). Biometrika, 52(3/4), 591-611.

[@MrLunadecancer]

hahaha thats why i was looking in coments!

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It's really awesome the way you explain it sistematically and understandable..good job Sir

[@kentlofgren]

Thank you. I often create tutorial videos so that I can learn the topic myself. All the best!

[@user-qp2ll6zc5j]

Thank you very much, Kent Lofgren. The explanation was brilliant!

[@EvelienMaes]

Dear Kent Löfgren, thank you so much for this video. It is so clear, so helpful, and the best that I have seen here on youtube. Thanks to you I finally know what to do and how to proceed with my thesis. Ánd how to write it down (I really appreciated that part of the video!). You are an EXCELLENT teacher! Thank you thank you thank you!

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Bravo!!!! The way of explaining the required topic is tremendous....sir......thanks for the video.....it really helped

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Kent - thanks for taking the time to post your video. It's clarified my thoughts for my SPSS all nighter.

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Thank you very much Kent! Your video's very helped me with my first lab report!!!!

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Thank you so much sir.... This video is very useful for me... Your way of explanation is too good...

[@kentlofgren]

So nice of you!

[@gtiz5]

Thank you for the clarity in your explanations! Excellent video - great pace and tone of instruction, including the practicality thereof.

[@ponmathiparamanandam1335]

BEST VIDEO TO LEARN NORMALITY CHECK

[@siobhanbeatrice4813]

Great video. Great conceptual translation. Thank you very much!!!

[@georgewaldkirch3604]

Thank you for such a concise and effective explanation.

[@JEKareem16]

Thanks a ton for this video, I was looking high and low for explanation on normality tests using skewness kurtosis values, as the other normality tests weren't positive. Excellent explanation and reporting style. Very grateful to Kent.

[@zowsk4527]

Great video, saved me from really struggling with my dissertation data analysis! Thanks for the reference list too as I needed to reference how and why I carried out these tests!

[@dr.santhakumarijetty9452]

Best teaching way.. I liked your analysis.

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one of the best video i ever watched, thank you for sharing knowledge

[@Angelopianolessons]

Sir, really thankful for this wonderful video. I have been going through many videos but this has all in one and so well explained. Thank you very much for all the efforts taken and may you be blessed with more strength to serve the people. God bless you