Non-Normal Distribution in Statistics - Skewness and Kurtosis (3-9)

Because many curves, perhaps most curves, are not normal distributions, we need a way to talk about the shape of distributions when they differ from normality. We will learn how to describe curves when the distribution is more spread out or more closely packed together than we would have expected, called kurtosis. And we will learn when a curve is positively or negatively skewed. Stats Cow teaches us a mnemonic for remembering the direction of the skewness: “The Skew is in the Tail.”
This video teaches the following concepts and techniques:
Kurtosis
Skewness
Link to a Google Drive folder with all of the files that I use in the videos including the Bear Handout and datasets. As I add new files, they will appear here, as well.
drive.google.c...
Table of Contents:
00:34 - Kurtosis
02:08 - Negatively Skewed Distributions
02:54 - Positively Skewed Distributions
03:54 - Positively or Negatively Skewed?
05:03 - Bimodal Distributions
07:39 - Standard Normal Curve

[@AlessandroZir]

thanks!! very few videos on this very interesting topic;

[@cantkeepitin]

Great video, but better takeaway would be that the 50% Point is the Median Not the Mean!! Only in rare cases, if the data is 100% symmetric both are identical.

[@alkasankla4488]

Thanks for the video it helped a lot

[@michaelmuvirimi6484]

Thank you for this!

[@ResearchByDesign]

No worries! Glad that it was helpful

[@funubergames2539]

thx for posting! what is the probability you will be within 1 standard deviation of a non normal dist. i know the prob of 1sd in a normal dist is 68%. Do we know what the sd is for a non normal dist?

[@ResearchByDesign]

Good question about non-normality. If the non-normality was due to kurtosis, then the probabilities should not change because the distribution is still symmetrical. If the non-normality was due to skewness, then the answer would depend on the actual shape of the distribution. (Thinking now...) I suspect that although the +1 SD and the -1 SD would be different distances from the mean in a skewed distribution, they would still contain 68% of the scores. I think that the SD is defining the cutoff where you have 68% of scores. The shape of the "container" would change (skewed) but the "capacity" would not. Have to go do some math and see if I am right.

[@funubergames2539]

thx for answering!

[@missy4369]

How can you tell that the graph is abnormal?

[@_Chafia]

Thank you so much for these great courses Doctor ... I have non true bimodal distributed data... i learned from you they must be analysed separatetly and so i did....but i need the source to quote it in my thesis please... i have some question too... do you think we must perform a Shapiro Wilk test after we get a graph showing a non normal distribution just to support the result or is it overtesting... Great Thanks

[@ResearchByDesign]

As for a source, I don't have a citation for you. It's something I was taught many years ago. Feel free to cite my video, if you like. Otherwise, I always credit Andy Field for everything I don't have a citation for...his books are so big that it must be in there somewhere. :o) JK I don't think a Shapiro-Wilk is necessary to "confirm" non-normality unless, perhaps, you were then going to do some kind of transformation. You can get a lot of information from just looking at the histogram. Wish you the best.

[@_Chafia]

Thank you so much Sir.. i'm truly very grateful ... i'm learning a lot from you... good luck and best regards

[@jecintagithiomi4739]

haha loved the cute videos in between

[@peterwestfall6924]

Actually, kurtosis has nothing to do with pointiness or flatness of the peak. You can have an infinitely pointy peak with negative excess kurtosis, and you can have a flat peak with infinite kurtosis. Instead, kurtosis measures the tail heaviness (outlier potential) of the distribution. Data values near the peak contribute very little to kurtosis. It is an unfortunate historical accident (no doubt due largely to both Fisher and Pearson) that people keep repeating the incorrect "peakedness" interpretation. Westfall, P.H. (2014). Kurtosis as Peakedness, 1905 - 2014. R.I.P. The American Statistician, 68, 191-195.

[@ResearchByDesign]

Wow...learn something new every day. I found a link to your article, which I skimmed, and I will read it more fully. This could be worth another video to clarify. Thank you for the "peer review"

[@cantkeepitin]

This is better BUT also not 100% correct, eg. Laplace and Logistic have for large x thw identical exp behavior, but different kurtosis. K is both a mix of tail and peakedness.

[@peterwestfall6924]

There is no mathematical logic that supports the connection of peakedness to kurtosis. The fact that some peaked distributions have high kurtosis is irrelevant, because some flat-topped distributions also have high kurtosis. Also, so infinitely peaked distributions have very low kurtosis.

[@Shalukastylecorner]

sir what is non Gaussian distribution and will it have skewness??pls explain me the answer

[@ResearchByDesign]

"Gaussian" is another term for "normal" distribution (aka bell curve, normal curve, etc). So if your distribution is non-Gaussian, it would be non-normal. That means that it could be skewed, or kurtotic, or both. It does not HAVE to be skewed (could be kurtotic), but a skewed distribution would certainly be non-Gaussian.

[@cantkeepitin]

Uniform data is symmetric, NOT skewed, but non-normal!

[@whiteshadow59]

funny and informative

[@Poojablog123]

Types of non normal distribution...Plz sir reply me..

[@ResearchByDesign]

Not entirely sure what you are asking for...the types of non-normality would include violations of skewness, kurtosis, or being bimodal. Hope that helps.

[@cantkeepitin]

There are hundreds of nonnormal distributions. Two distr can have same skew and kurtosis, but look very different still.