I loved the way you explained how the th quantiles are calculated. I was confused with different formulas other people have used in their videos without telling the underlying concepts. Keep it up!
I looked everywhere to find out why some use i/(n+1) and (i-0.5)/(n+1) . . . . while others use /n and not /(n+1) . . . . thanks for providing a pragmatic clarification of the use of a . . . . I was locked in this whirlpool and you got me out . . . keep well
I have looked at many videos on UA-cam, and yours are the best with many visual concrete examples. Not only Q-Q plot but also other concepts in statistics. Thank you very much.
I was watching your videos on the Hypothesis Testing playlist, and this video was a perfect supplement! Thank you for posting this and explaining all concepts so so intuitively and in a well-motivated manner!
You'd just have to look that up in the standard normal table in the usual ways. I have videos illustrating how to do this ("Finding percentiles using the standard normal table", or something to that effect). There are 2 main types of table, and I have videos for each one.
At 5:10 or so: "We plotted the ith ordered value..." i = 1, 2, 3, 4, ..., 9 (since n = 9). The short version is that there are 9 values, so we split the distribution into 9 + 1 = 10 equal areas.
@ 6:11 ,how did they come up with (i-a)/(n+1-2*a) , where a is a chosen value from 0 to 1/2 ? Would appreciate it for a link to a good, credible explanation. Thanks all.
Thank you very much for your video. In the video, you splitter up the normal curve into 10 areas which is easy to do. How about if we have a sample of size 10 and we want to split up the curve into 11 areas?
It's pretty much the same thing. Choosing 10 equal areas makes for a simpler looking plot, and is a useful simple example, but the overall method stays the same for any sample size. For example, if n = 9 (so we are splitting the curve up into 10 equal areas), to find the appropriate z value to plot the minimum value against, in R we would use the command qt(1/10). If n = 10 (so we are splitting the curve up into 11 equal areas), to find the appropriate z value to plot the minimum value against, in R we would use the command qt(1/11). Cheers.
can you explain why at 6:45 those different formulas are the same? I'm confused...won't they yield different answers? When my teacher did it, he put (i - .375)/(n+.25).
There are different adjustments that have been suggested. They do not lead to the same values of course, but overall they all give a very similar picture.
The values on the x axis are theoretical quantiles of the standard normal distribution. They aren't based on sample data, so they are not z-scores in that sense, but they are z values from the standard normal distribution.
Great video! I only didn't understand how to get the straight line. Which are the first and third quantiles, the smallest and third smallest values of my sample?
could you kindly answer my question? Thank you! Not quite understand why in the strongly right-skewed distribution, the largest values are larger than would be expected, in the right-skewed distribution, there should be less large numbers than small numbers(the probability of the random variable to be small is higher)
It's all a question of how the distribution compares to the normal distribution. Try thinking about it this way: start with a normal distribution, then grab the right tail and pull it out to the right, such that it stretches out and more of the area is contained in the far right tail (then there was when the distribution was normal). Now we've got ourselves a right-skewed distribution. We can shift and scale it such that it has the same mean and variance as the original normal distribution, but there is going to be more area in the right tail. In a typical sample, the largest values we get are going to be greater than would be expected under normality. I hope this helps!
Thanks for your helpful videos!!! QQ plot tells us whether the sample data itself is normally distributed or not, would you mind explaining how do we know whether the sample data come from a normal distribution...?
I'm really not sure what you are asking. The entire point of this video is normal QQ plots, which can help us assess whether the sample data appears to be approximately normal, which, in turn, can suggest whether it's reasonable to think the sample came from a population that is approximately normal. We never know for certain, as we don't know the distribution of the population unless we're simulating. But normal QQ plots can help us make a judgement call on whether the normality assumption is reasonable.
Nowadays we have software that can try different types of distribution functions over our sample. In that case, why do we need Q-Q plots? I mean why not we fit the data to our normal distribution function and visualize it instead of Q-Q plot?
I'm not sure what you are asking. Are you asking why we don't simply plot a histogram and superimpose the appropriate normal curve? We use that type of plot sometimes, but in assessing normality it is generally felt that a normal qq plot is more informative.
jbstatistics Thank you very much for your response. Sorry if my writing was confusing. Statistics in not my field. Yes what I mean is have a histogram but investigate what type of function (or best fit) is appropriate for that. Not just normal. Other fits like Poisson, weibull, Gamma, logarithmic,Johnson binomial,.... Is Q-Q plot also used for those type of distributions as well?
In this video I describe normal qq plots, which for my purposes are the most widely used qq plot. But the idea holds for other distributions as well. We plot the sample values against the appropriate quantiles of a theoretical distribution, and that distribution can be something other than the normal distribution (e.g. exponential, Weibull, gamma). It's a little messier for a theoretical distribution that is discrete, but still works in essentially the same way. (We should be able to figure out whether we're dealing with a distribution that is discrete or continuous by the nature of the problem. For example, we shouldn't be left wondering whether our sample data comes from the Poisson distribution or the normal distribution.)
jbstatistics Thank you for spending time and answering me. I understand now. Is there any book that very briefly gathered all the statistical methods and models and explains when and where we use them without going to mathematical parts of that? My problem is not how to calculate my problem is what model to use. For example if I have small number of samples what method I should use. what if it is discrete . what if it is continuous. what if I want to compare but I do not have normal distribution etc
You, sir, are a gentleman and a scholar.
I loved the way you explained how the th quantiles are calculated. I was confused with different formulas other people have used in their videos without telling the underlying concepts. Keep it up!
You're welcome! I'm glad to hear that you find me clear and concise!
both, very.
I looked everywhere to find out why some use i/(n+1) and (i-0.5)/(n+1) . . . . while others use /n and not /(n+1) . . . . thanks for providing a pragmatic clarification of the use of a . . . . I was locked in this whirlpool and you got me out . . . keep well
This explained it far more clearly than my prof did, Thanks a lot
You are very welcome Ryan. I'm glad you found it helpful.
Really appreciated the simulated values at the end so we could get a visual feel for it. Thanks!
I have looked at many videos on UA-cam, and yours are the best with many visual concrete examples. Not only Q-Q plot but also other concepts in statistics. Thank you very much.
Thanks for the kind words! I'm glad to be of help!
You explained this better than StatQuest with Josh Starmer
Thanks a lot! This was very helpful
I was watching your videos on the Hypothesis Testing playlist, and this video was a perfect supplement! Thank you for posting this and explaining all concepts so so intuitively and in a well-motivated manner!
You are very welcome!
You're welcome. I'm glad you found it useful.
This is the best explanation of QQ plot, period.
Thank you very much.
Great video. I was struggling with qq plots and you made the concept very clear.
I'm glad to be of help!
This is very helpful, you are so much better, more concise, and clear in your way of teaching than my university teacher :)
Thanks
My favorite source for statistics learning! Thanks for the excellent work. It really helps!
I'm very glad to be of help!
You're welcome. And thanks for the compliment!
This was the video that made it sink in. Thanks much!!
Finally, I understood this thing
Şimdi ben de istiyorum 80 80 p
Your video is better than the lecture I'm taking...
Thanks Frâncio! I'm glad you liked it!
Excellent explanation and illustration of QQ plots and distributions.
I had referred many lectures, could understand better than any. Thank you so much
You are very welcome!
You are welcome Susie, I'm glad to be of help!
You're welcome! I'm Glad to be of help!
absolutely amazing!!! loved this video. Big thanks!
You are very welcome!
You are a saviour 🙏 🙌.
You'd just have to look that up in the standard normal table in the usual ways. I have videos illustrating how to do this ("Finding percentiles using the standard normal table", or something to that effect). There are 2 main types of table, and I have videos for each one.
OH MY GOD THANK YOU! 3 minutes it the "Oh!!!!!" moment hit me.
Thank you, sir. You saved me again.
Very Nice and well explained in simple terms..thank you..!!
Thank you so much for this video. Explains Q-Q plotting very well.
At 5:10 or so: "We plotted the ith ordered value..."
i = 1, 2, 3, 4, ..., 9 (since n = 9).
The short version is that there are 9 values, so we split the distribution into 9 + 1 = 10 equal areas.
this is great. Now i can understand what R is doing! :)
Really nice introduction, and very informative
It was a very helpful video on q-q plot! Thanks a lot.
So concise and clear. Thank you.
+Audilia S You are very welcome!
Thank you so much! Clear and comprehensive!
great video. really helps in building intuition.
Perfectly explained!
@ 6:11 ,how did they come up with (i-a)/(n+1-2*a) , where a is a chosen value from 0 to 1/2 ? Would appreciate it for a link to a good, credible explanation. Thanks all.
You're welcome!
Thank you very much. You are my lifesaver!
Make sense, very clear. Thank you.
Very nicely explained!
thanks for clear and perfect explaination. Good work
You are very welcome!
thank you very much for this quick and clear explanation. It is fantastic.
You are very welcome. Thanks so much for the compliment!
YES! I have also been watching this series! Very well-explained!
James A. Chen Thanks James. I'm glad to be of help.
Very well explained. Thank you!
Thanks for such a great tutorial, the best one that I catched so far. It would be nice to post the R codes somewhere in your website.
so touching for an excellent video
thank you sir ! amazing experience
Fantastic explanation, thank you
You are very welcome, and thanks for the compliment!
Excellent! Excellent! Excellent!!!
Really good explanation!
Thank you very much. It is a very clear explanation!
This is a very good explanation. Thanks.
great video, cant find similar videos elsewhere
This is really helpful, thanks a lot!
You literally saved me !!
Glad to be of help!
Very well presented! Thanks a lot :)
Super useful, thanks 👍
excellent description
Awesome work!
Thanks!
Thank you very much for your video. In the video, you splitter up the normal curve into 10 areas which is easy to do. How about if we have a sample of size 10 and we want to split up the curve into 11 areas?
It's pretty much the same thing. Choosing 10 equal areas makes for a simpler looking plot, and is a useful simple example, but the overall method stays the same for any sample size. For example, if n = 9 (so we are splitting the curve up into 10 equal areas), to find the appropriate z value to plot the minimum value against, in R we would use the command qt(1/10). If n = 10 (so we are splitting the curve up into 11 equal areas), to find the appropriate z value to plot the minimum value against, in R we would use the command qt(1/11). Cheers.
jbstatistics Great. Understood now. your Chanel is the best. I appreciate your help.
Helped a lot, thanks!
Incredibly good!
Ohhhhhhhhhhhhhhhhhh！ I got this! yeah! finally!
Thank you so much for this.
can you explain why at 6:45 those different formulas are the same? I'm confused...won't they yield different answers? When my teacher did it, he put (i - .375)/(n+.25).
There are different adjustments that have been suggested. They do not lead to the same values of course, but overall they all give a very similar picture.
What a great video. Superb job! Subscribed!
Frâncio Rodriguesbn Jr is a CT yes you y me for the rest of
4:42 on the x axis, the values range from -1 to +1. Are they z score?
The values on the x axis are theoretical quantiles of the standard normal distribution. They aren't based on sample data, so they are not z-scores in that sense, but they are z values from the standard normal distribution.
@@jbstatistics How do you get these theoretical values or Z values that you plot as x-axis?
Great video! I only didn't understand how to get the straight line. Which are the first and third quantiles, the smallest and third smallest values of my sample?
You're the greatest!
Thanks Fyodor!
It helps a lot! Thank you so much!
I'm glad to be of help!
Seriously. Much appreciated.
Can you please give some references for the function you used to approximate the quantiles? The (i-a)/(n+1 -2a) formula? Where does it come from?
very helpful. thank you
Thanks!
Why did you choose Z=-3 and Z=3. Is there a formua to choose Zmin and Zmax
Excellent!
it's very good and very simple explane!
Thanks!
could you kindly answer my question? Thank you! Not quite understand why in the strongly right-skewed distribution, the largest values are larger than would be expected, in the right-skewed distribution, there should be less large numbers than small numbers(the probability of the random variable to be small is higher)
It's all a question of how the distribution compares to the normal distribution. Try thinking about it this way: start with a normal distribution, then grab the right tail and pull it out to the right, such that it stretches out and more of the area is contained in the far right tail (then there was when the distribution was normal). Now we've got ourselves a right-skewed distribution. We can shift and scale it such that it has the same mean and variance as the original normal distribution, but there is going to be more area in the right tail. In a typical sample, the largest values we get are going to be greater than would be expected under normality. I hope this helps!
very clear thank you sir !!!!! I am studying in university as a year 3 student and sometime I see this in my course material
Thanks for your helpful videos!!! QQ plot tells us whether the sample data itself is normally distributed or not, would you mind explaining how do we know whether the sample data come from a normal distribution...?
I'm really not sure what you are asking. The entire point of this video is normal QQ plots, which can help us assess whether the sample data appears to be approximately normal, which, in turn, can suggest whether it's reasonable to think the sample came from a population that is approximately normal. We never know for certain, as we don't know the distribution of the population unless we're simulating. But normal QQ plots can help us make a judgement call on whether the normality assumption is reasonable.
Thank you so much for your reply, that was exactly what I wanted to ask. Apologise for my unclear explanation ..@@jbstatistics
Thank you !
good job... pretty clear
why is it -3 to 3 on the horizontal axis
Nowadays we have software that can try different types of distribution functions over our sample. In that case, why do we need Q-Q plots? I mean why not we fit the data to our normal distribution function and visualize it instead of Q-Q plot?
I'm not sure what you are asking. Are you asking why we don't simply plot a histogram and superimpose the appropriate normal curve? We use that type of plot sometimes, but in assessing normality it is generally felt that a normal qq plot is more informative.
jbstatistics Thank you very much for your response. Sorry if my writing was confusing. Statistics in not my field. Yes what I mean is have a histogram but investigate what type of function (or best fit) is appropriate for that. Not just normal. Other fits like Poisson, weibull, Gamma, logarithmic,Johnson binomial,....
Is Q-Q plot also used for those type of distributions as well?
In this video I describe normal qq plots, which for my purposes are the most widely used qq plot. But the idea holds for other distributions as well. We plot the sample values against the appropriate quantiles of a theoretical distribution, and that distribution can be something other than the normal distribution (e.g. exponential, Weibull, gamma). It's a little messier for a theoretical distribution that is discrete, but still works in essentially the same way. (We should be able to figure out whether we're dealing with a distribution that is discrete or continuous by the nature of the problem. For example, we shouldn't be left wondering whether our sample data comes from the Poisson distribution or the normal distribution.)
jbstatistics Thank you for spending time and answering me. I understand now. Is there any book that very briefly gathered all the statistical methods and models and explains when and where we use them without going to mathematical parts of that? My problem is not how to calculate my problem is what model to use. For example if I have small number of samples what method I should use. what if it is discrete . what if it is continuous. what if I want to compare but I do not have normal distribution etc
How do you find the z values from a normal distribution chart? I have a problem that say x= 0.8, i=.10, z = -1.28? How do I get that from the table?
thanks great video
Thanks but how can we use "standard normal table"?
This table is scary 😿
how did you get .1 under the curve?
great video
thanks a lot!
+Juan Salazar You are welcome!
pretty darn straight line XD
When n = 9, i/(n+1) = 0.1, 0.2, 0.3, ...
great one
Thank you.
You are very welcome!
well explained
Superb
so in i the observe value?
Finally!
Try to give presentation on outlier test in statistics. Single Grubb test, multiple grubb test etc ......