Describing Distributions with Skewness, Kurtosis, Modality, & z-Scores Business Statistics (Week 6A)
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- Опубликовано: 21 авг 2024
- The normal curve is the most important distribution in statistics. When distributions differ from normality, we describe them with kurtosis (leptokurtic, platykurtic, mesokurtic), with skewness (positive or negative), and with modality (unimodal, bimodal, multimodal). In addition to those visual cues, we can also use z-scores to show the relative location of scores in the distribution. We meet Pafnuty Chebyshev and Antonio as we learn why we need z-scores. We also cover the empirical rule. Dr. Daniel shows you how to create z-scores in Excel. All examples use the DogToys2.xlsx (link below)
Lecture date: Tuesday, February 16, 2021
Missouri State University
Snow day - lecture recorded at home office
Statistics Instructors: you are free to link to this video and the playlist for your seated or online statistics course or for other educational purposes.
Edited in Camtasia 2020
Visual and audio content from DigitalJuice.com
Music:
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Link to a Google Drive folder with any files that I use in the videos including spreadsheets, the Bear Handout, and the DogToys2.xlsx dataset. As I add new files, they will appear here, as well.
drive.google.c...
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I love this video!
This is brilliant! Many thanks for explaining with such awesome example.
You're very welcome! Glad that it was helpful
Hello, nice and important subject , with a very wonderful winter snowing day
Many thanks!
Actually, kurtosis does not measure peakedness or flatness at all. Rather, it measures tails (outliers) only. The logic is simple: Kurtosis is the average of the z-values, each taken to the fourth power. Outliers (where the z value is far far zero) contribute greatly, while the data near the mean (where the z-value is near zero) contribute virtually nothing. So you can have a flat-topped distribution with very large kurtosis, and you can have a peaked distribution with very low kurtosis. Here are some examples: stats.stackexchange.com/a/483215/102879
See also the current Wikipedia page, and in particular,
en.wikipedia.org/wiki/Talk:Kurtosis#Why_kurtosis_should_not_be_interpreted_as_%22peakedness%22
Dr. Westfall - thank you so much for this comment. While it is never fun to be called out on incorrect conclusions, it is part of correcting mistakes and part of science. I downloaded your article on Peakedness R.I.P. from The American Statistician. I think this may be worthy of a new video...certainly worth exploring whether all those things I was told about "peakedness" in my education were off track, or not. Really appreciate learning about this!
@@ResearchByDesign Yes, it was strange this this mistake persisted for so long. It probably has to do with the fact that famous people like RA Fisher just kept repeating it, without thinking about it. But there is actually no logic to claim "larger kurtosis implies more peakedness" and "smaller kurtosis implies more flatness." Instead there are only examples where such occur. But generalizing from such examples is like saying, "Well, I know all bears are mammals, so it must be the case that all mammals are bears!" There are plenty of non-bear mammals, and there are plenty of non-peaked distributions with high kurtosis, and there are plenty of peaked distributions with low kurtosis. If you do develop and more materials on this topic, I will gladly review them.
the video image is too poor, you need to fix it more
Got a new series in the works with much better quality. You will see it rolling out after the new year. Cheers