Quantile-Quantile Plots (QQ plots), Clearly Explained!!!

Quantile-Quantile (QQ) plots are used to determine if data can be approximated by a statistical distribution. For example, you might collect some data and wonder if it is normally distributed. A QQ plot will help you answer that question. You can also use QQ plots to compare to different datasets that you collected to determine if their distributions are comparable. This video shows you how to do both things.
NOTE: The data in this video are measures of gene expression. If "gene expression" doesn't mean anything to you, just imagine that the data represents how tall a bunch of people are, or how much they weigh. Then consider the y-axis to be the height or weight of the people, and the x-axis just represents all of the data you collected on a single day. In this case, all of the data were collected on the same day, so they form a single column.
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Corrections:
4:35 The Uniform Distribution has one extra quantile
5:30 I should have said that Quartiles divide the data into 4 parts.
#statquest #quantile #qqplot

[@statquest]

Support StatQuest by buying my book The StatQuest Illustrated Guide to Machine Learning or a Study Guide or Merch!!! statquest.org/statquest-store/

[@maindepth8830]

that intro alone, made me forget my hate for statistics and instantly fall in love with it

[@statquest]

Hooray!

[@timonveurink6335]

Haven't seen the video yet, but that intro earned you a subscription

[@angiemycine6509]

It made me think that the whole video was going to be a song lol. Very interesting nonethless

[@marioadiez]

I'am not suscribed for the plots, but for the music!

[@setsu2221]

That intro hit me hard xD

[@kittyxing]

Thanks sooooooo much! This is the only video I found explained the details of generating QQ plot and also make the concept so clear and easy to understand!

[@statquest]

Thank you very much! :)

[@robertopizziol7459]

I was waiting for the "BAAM" all video long, got just a couple of great "HOORAY!". Thank you for the awesome channel Josh!

[@statquest]

You made me laugh. :)

[@kevon217]

Couldn’t have asked for more clear explanation, thanks!

[@statquest]

Glad to help!

[@aashishshrivastav9531]

🤔🤔🤔🤔🤔 well I thought that q-q plot was difficult but thanks to you I got it now. thanks and keep it up!!!

[@alisalehi4980]

I really appreciate from your very easy way explanation. I faced with so difficult and rough terminologies that I could not even understand the meaning of them.

[@pradiptithakur3655]

Awesome video. Explained so clearly. Really helped me a lot!

[@statquest]

Hooray! :)

[@Clarin3t1]

You had my like at the beginning with the jingle. Thanks for explaining this so well!!

[@statquest]

Glad you liked it!

[@robertb-l5422]

Very well explained, thanks so much

[@dominicj7977]

Can you do a video on normality tests like shapiro wilk and anderson darling? If not anytime soon, can you share link to some good materials?

[@user-ii5ch8nw6s]

It's so clear! Thanks a lot for your video.

[@hebaebrahem7893]

Your videos are cool and concise , thank you .

[@robertocannella1881]

Thanks for all the videos! Great music BTW. Also I'm looking forward to rockin' my new SQ hoodie!

[@statquest]

TRIPLE BAM! Thank you for your support!

[@sirisudweeks9334]

very nicely explained. it was a tricky concept until this video! thanks!

[@statquest]

Hooray! I'm glad the video helped. :)

[@kusocm]

Best intro song, it can be used as a 'mnemonic' for what QQ plots are used for =)

[@josevaldes7493]

Triple BAMM! Serious man your channel is pure art. Thanks

[@statquest]

Thank you!

[@tymothylim6550]

Thank you for the video! It was short and easy to understand :)

[@statquest]

Thanks! :)

[@guillemvia6813]

Awesomely explained! Good job!

[@statquest]

Thank you! :)

[@ThuyPham-yu7cw]

wow, now I can clearly understand it ! thanks alot !

[@statquest]

Hooray!!! :)

[@matavalamuttej841]

You made it very clear man !!! Great doing

[@statquest]

Glad to hear that!

[@gianlucalepiscopia3123]

This is very very cool, more likely to learn on KZbin than in a classroom. Grazie

[@statquest]

Glad it was helpful!

[@navatagames]

Nice video. Explained everything in just under 7 mins. Awesome. 😄👍👍

[@statquest]

bam!

[@navatagames]

@@statquest bam indeed. 😁

[@piotrszocik7775]

Great explanation, have a nice day :)

[@padraiggluck5633]

Really excellent presentation, Josh. ⭐️

[@statquest]

Thank you! :)

[@km2052]

thanks , awesone , this is useful in measuring gene expression effect

[@MeWatchingYouTubeVideos]

How helpful! Thanks a lot for your amazing videos

[@statquest]

Thanks!

[@joaovasconcelos5360]

Your videos are awesome, thank you so much!

[@statquest]

Glad you like them!

[@ehsans2135]

so clear, so good , so nuce thank you , Josh

[@statquest]

Thanks!

[@urjaswitayadav3188]

Thanks for the great explanation as always! So QQ is just a way to plot and visualize the similarity of two distributions? Are there any other scenarios when these can be used? Thanks!!

[@TheAbhimait]

QQ is mostly used to check tail conditions. Density plots and cumulative plots are the best way to check distribution symmetry.

[@jorenmaes498]

I just noticed when you said "please subscribe" at the end of the video, the subscribe button lit up:)

[@statquest]

bam! :)

[@heplaysguitar1090]

Explained like a pro. Tripple BAM!!!

[@statquest]

Thank you! :)

[@thechickendiet]

very clear with great examples!

[@statquest]

Thanks!

[@aj_actuarial_ca]

Thanks a lot for the wonderful explanation!

[@statquest]

Thank you!

[@response2u]

Legendary explanation! Fantastic!

[@statquest]

Thank you!

[@julesd3115]

Awesome video - thank you SO much for saving my sanity.

[@statquest]

Thanks!

[@alanpdrv]

Thanks for this! Finally I understand

[@statquest]

Hooray!

[@wanhope3660]

Sweet, its not that difficult to grasp anymore! Thanks

[@Shred427]

such an awesome video, thanks!

[@statquest]

Glad you liked it!

[@Danielbassist13]

phenomenal explanation and really cool intro music man!

[@statquest]

Thanks!

[@joerich10]

is there a statistical test we can do to determine how far away the dots are allowed to deviate, rather than just eyeballing it? Or is eyeballing good enough? I.e. a stat test that could say 'the chance of these 2 distributions being the same is less than X%

[@statquest]

The "K-S Test" is what you want. However, it is very strict and tends to reject the null too easily. It's one of the few statistical tests where a large p-value (suggesting no difference) is more convincing than a small one. en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test

[@kissapeles]

@@statquest How were the lines drawn? Least Squares? Maybe doing R^2 calculations can provide an idea? Still trying to grasp my statistics a bit better :( :)

[@biancafeitoza4030]

Thank you for your help! Greetings from Brazil.

[@statquest]

Muito obrigado! :)

[@sarrae100]

How beautiful and simple is that explaination 🥳

[@statquest]

Thank you!

[@richardbarton9076]

This was super helpful!

[@statquest]

Thank you! :)

[@user-or7ji5hv8y]

great video. a video on the intuition on why q-q plot works might be interesting.

[@statquest]

I'll keep that in mind.

[@arneoosterlinck7590]

Great explanation, thanks!

[@statquest]

Thank you! :)

[@vineetkaur1667]

Very well explained !

[@statquest]

thank you!

[@asmaulhosnanisha4657]

I could have better grades if i had faculties like you...thank you Josh!!

[@statquest]

Thanks!

[@bingxinyan8103]

Helpful and easy to undderstand.

[@statquest]

Thanks!

[@user-id1rf6gt6h]

Helped a lot! Thank you :D

[@statquest]

Hooray! :)

[@hanhan2360]

QBUS?

[@geogeo14000]

And again, thank you for another amazing video ! A little question : most of the points have to fit in the straight line for the data to be considered as normally distributed and at 4:15 you said it is not the case. Althought the intersection points are really close to the line, it does not matter, most of the point have to be strictly ON the line, right ? The fact that other intersection points are close or far from the line does not give any relevant information ?

[@statquest]

I'm not sure I understand your question. For more details on how to interpret QQ-plots, see: stats.stackexchange.com/questions/101274/how-to-interpret-a-qq-plot

[@geogeo14000]

@@statquest ok thank you !

[@schiu867]

It helps a lot. Thanks!

[@statquest]

Glad it helped!

[@alecvan7143]

Best intro by far so far

[@statquest]

Hooray!!!! :)

[@12copablo]

Hoorray! Thx for the video :)

[@statquest]

BAM! :)

[@tallwaters9708]

Thanks for the videos, if you're still looking for ideas how about k-l divergence?

[@jameswhitaker4357]

Not gonna lie, stats is my super weak spot. You've helped me a lot in my Data Models course and interpreting my results. +1

[@statquest]

Happy to help!

[@jameswhitaker4357]

@@statquest Thank you! I'm just kicking myself for not taking more stats courses at this point!

[@statquest]

@@jameswhitaker4357 My stats courses were all pretty terrible, so you never really know what you're going to get. I had to teach myself statistics, and these videos are how I taught myself.

[@jameswhitaker4357]

@@statquest That's what I'm going through right now! I've been using your videos and a "Intro to Statistical Learning with Applications in R" textbook which has helped a lot. I think when I saw terms like "heteroscedasticity" or the crazy formulas I would get scared and put off the studying, until I took a course that required knowing it LOL. And luckily most of these statistical tests and concepts are now pretty easy to perform in programming. Cheers!

[@statquest]

@@jameswhitaker4357 I actually wrote a little about heteroscedasticity. Maybe I should record it.

[@Shuffellove]

i love statquest!

[@statquest]

Hooray! :)

[@vlakrunn]

You simply saved my life

[@statquest]

Bam!

[@user-hv9wx5kd9u]

Best Explanation ever!!! 🎉🎉🎉

[@statquest]

Thanks!

[@user-wx4vf5gj2f]

Thanks for saving my life

[@statquest]

Hooray! :)

[@Atomflinga]

What's the approach for determining which distribution has the best fit for the data? Would the r-squared of the data against the straight line be a suitable measure for how well the distribution describes the data?

[@statquest]

This is a good question, and, to be honest, I'm not sure what the answer is. I like your idea, but it may oversimplify the problem. i.e. you could get a high R^squared value, but still have some real obvious problems if you looked at it visually.

[@alexgimeno170]

Understand it now - thank you!

[@statquest]

Hooray! :)

[@averkij]

Thank you, Josh.

[@statquest]

Thanks! :)

[@ananyaagarwal7108]

Hi Josh, Amazing Video there :) Just want to understand the intuition behind the working of QQ plots ? Is it the fact that quantiles of every normal distribution are just scaled up values of a standard normal distribution and that is why we expect a straight line ?

[@statquest]

Pretty much

[@ananyaagarwal7108]

@@statquest Thanks for the response ;) Would really appreciate if you could make something on the same or share some content that could explain the intuition behind QQ Plots.

[@alifia276]

Thank you! Awesome explanation

[@statquest]

Thank you! :)

[@bharathkumar5870]

i have a doubt...why to use this method,instead just plot the points and see if it forms a bell curve....correct me

[@statquest]

@@bharathkumar5870 I'm not sure I understand your question. Are you asking, "why don't we just create a histogram with the data and see if the histogram looks like a normal distribution"? If so, histograms can be very tricky in terms of selecting the correct bin size. In contrast, with a q-q plot we don't have to worry about optimizing a bin size or anything else.

[@bharathkumar5870]

@@statquest thank you sir ..u cleared my doubt. Different bins give different distributions😀

[@lashlarue7924]

It's a party time with Josh Starmer and his quantiles! 😆🤘 Party on, Wayne!

[@statquest]

:)

[@maple49027]

Thanks for this wonderful explanation! I'm curious if we can tell anything about the slope in a QQ plot? Does the slope always equal 1 when the data follows a certain distribution?

[@statquest]

As long as the x and y-axes are normalized to quantiles, then the slope should be 1 if the data follows a certain distribution. However, usually the x and y-axes are in the original units, and this means that the actual slope isn't super important. What is important is that the points form a straight line.

[@maple49027]

@@statquest Thanks!!

[@FlopMeister71]

Hi, I understand how the quantile points are plotted wrt observed vs theoretical distributions, what I don't understand is what determines the slope of the straight line. While this is fairly intutitive for a normal distribution, for say the Weibull distribution I am unclear how the slope of the striaght line is used to determine whether the observed vs theoretical quantiles are a good fit for a given distribution. Any ideas?

[@ngocnguyen9517]

I came here for the same question and left with no answer LOL

[@mikii2755]

This video vas quite helpful

[@BossCock17]

du hast zerfetzt bro, danke

[@statquest]

Bitte!!!

[@81-jdowlwp]

@@statquest quick question to 2:04 in your video: if we have 15 data points and we divide the dataset into 15 quantiles, then shouldn't the smallest quantile be 0.06666 so around 0.07? because in your video you are saying that it is 0.7, which would mean, that 70% of all data is covered by just one datapoint. Thank you for your video :)

[@wenweipeng7056]

Do I need to matter the exact size size or probability when dividing the contribution? Or just need to only make sure the sizes are equal?

[@statquest]

Just equal sizes.

[@brayanmurillo4427]

thanks for the explanation, can you clarify this please?: if we have 15 quantiles, then I thought you should plot 14 red lines in the normal distribution and the 15th line should reside in +infinite. and a little question: is the straight line generated by linear regression?

[@statquest]

Plotting a line at infinity would be hard to do and you can fit the line with regression.

[@apoostle]

Thanks! It helps.

[@statquest]

Wow!!! Thank you very much for your support! BAM! :)

[@snehasampath3486]

Hello, the video was amazing and I was able to get an idea of QQ plots. I do have a question though. How do we draw the normal distribution and uniform distribution? Is it just random?

[@statquest]

The normal and uniform distributions are well defined by equations. So we just plug numbers into them to get the values out.

[@robderon]

precious help, thank you

[@statquest]

Thanks!

[@MasterMan2015]

Step 3 is not very clear. How do you put the lines on the normal distribution. How do you start putting the lines ? and How about the distance between each two lines ?

[@statquest]

The quantiles for the normal distribution divide it so that the area under the curve between two lines is equal for all of the divisions. Since the normal distribution isn't as tall on the edges, there is more space between lines then in the middle, where the distribution is tall. Thus, the spacing between lines makes the area under the curve between the middle two lines is the same as the area under the curve between lines on the edges.

[@MasterMan2015]

Thanks! It is easy to see that in the case of Uniform distribution. How about the starting point ? I think it's randomly that you started by -1.5 but I can start from -2 or -1 or ..

[@statquest]

The starting point is defined by the need for each unit between lines to have the same exact area under the curve. To understand what this means, imagine you had to divide a normal distribution with a single line so that 50% of the area under the curve was on the left side of the line and 50% of the area under the curve was on the right side of the line. Where would you draw that line? Well, there is only one choice - right down the middle of the normal curve. If you drew it anywhere else, there would either be more area under the curve on the left side or the right side. Now imagine you had to divide the area under the curve into 4 equal amounts. Again, there is is only one option - you put a line in middle, and then you put another line so that the area under the curve on the left side is divided in half and then a third line so that the area under the curve on the left side is divided in half. Any other locations for those lines will result in the areas under the curve not being equal to each other. Thus, in this example, we have no choice about where to put the lines - they have to be put in the one configuration that makes the area under the curve between every pair of lines equal.

[@MasterMan2015]

Perfect! got it!

[@statquest]

Hooray!!! :)

[@nutellaturtle2931]

How would you tell skewness from looking at the QQ plot? For example if some of the data points fell below the straight line (representative of a normal distribution) does that indicate positive/negative skew? Cheers :)

[@nutellaturtle2931]

Ah, is it correct to say that, roughly, if at the beginning the majority of points were consistently/mostly above the line since the beginning then you'd say the data is positively skewed, and conversely, if most points laid below the line since initially then the data is negatively skewed?

[@statquest]

Here's a link that explains how to interpret qq-plots: stats.stackexchange.com/questions/101274/how-to-interpret-a-qq-plot

[@outerplanetexplorer1711]

Little confused by the scales for the axis of a q-q plot (I think I'm overthinking the fitting of the straight line part) What if my sample contains values strictly between 100 - 200 (normally distributed) and I want to check this distribution against the normal distribution. My interpretation of the video is that a q-q plot should return values that fit perfectly on y = x. However because of the scale of my data, surely this isn't true. Rather is it that we can say that they will fit some line y = x + C(arbitrary constant)? Not even sure if I'm right about this haha... Is this the latter the correct interpretation? And in a hands on context we run a regression on a Q-Q plot to confirm this sort of thing?

[@statquest]

You are correct that the line will not always by y = x, but depends on the values for the different distributions. So y = ax + c is a more "general" line that the data should be on - the important thing is that they data are on a line, any line, if so, then you can use quantile normalization (or z-scale normalization, depending on the distribution) to compare the two samples. For example, I could compare two normal distributions with very different means, one with mean = 4 and the other with mean = 400 (here's the R code): data1

[@outerplanetexplorer1711]

Thank you! And as others have said, you're truly a phenomenal teacher!

[@jalbertomendivil]

I know it may sound dumb but i just got it when i understood that theoretical quantiles were the quantiles of a normal standard distribution or Z-value.

[@statquest]

bam! :)

[@anaswahid8520]

Sir I have been facing problem in ggplot2 package in R programming now a days Could you please help?

[@gayathrikurada3315]

Hi Josh, can we use percentiles in place of quantiles to plot QQ plot ? If so, in case of percentiles we can only have upto hundred percentile no matter how big our data is then how to have a definitive answer whether or not the 2 datasets have similar distributions as mention in the video at 6:30 ?

[@statquest]

The terms "quantiles" and "percentiles" are often used interchangeably, and in this case you can swap out quantiles for percentiles. And you can have as many percentiles as you want - however, the largest percentile is always 100. For example, you could have the 0.5 percentile, or the 1.23 percentile.

[@gayathrikurada3315]

@@statquest Thanks Josh.

[@urjaswitayadav3188]

I have another question: does shape of a QQ plot also has some information? Like difference in the beginning or at the end, or overall shift of the values.

[@urjaswitayadav3188]

Thank you!

[@Dekike2]

Hi!!! Great video!!!! It was very helpful to understand Q-Q Plots!!!! But just one question, how do you calculate the quantiles for your dataset?? I mean, the first observation of your dataset is 0.6, but I don't understand why, since the first observation leaves 0 observations on one of its sides. Should the quantile be 0? In the video where you explain how to calculate quantiles, you explained that the quantile for each observation is calculated dividing the number of observations that this value leaves below between the total number of observations... So, for the first point... 0/15 = 0. Why 0.6??

[@statquest]

I think I see the confusion here. The x and y-axes on the QQ-plot (on the right side) are labeled "Normal Quantiles" and "Data Quantiles". This is a little misleading - what we are plotting are the values at each quantile, not the quantile name itself. So if the first quantile is called "quantile 0", but it represents -1.5 in the normal distribution and 0.6 in the data, then we draw a dot at -1.5, 0.6 to represent the first quantile. Does that make sense?

[@Dekike2]

@@statquest Perfectly. I understood this after watching some more videos. I would suggest you to clarify this if you make a new version!! As I already told you, congratulations for your videos and of course, your quick reply!! You explain really well, and the videos are perfect (easy to follow and to understand). I'm doing my Ph.D and it is really helpful people like you. Thanks a lot.

[@Fan-fb4tz]

@@statquest Thank you very much for all your videos! They help me a lot. Just a follow-up question on this: how can we decide where to start as smallest quantile value in the theoretical distribution? Like you mentioned, "quantile 0" value in the sample distribution is 0.6, but how can it represent -1.5 in the normal distribution? My confusion is normal distribution doesn't technically have "quantile 0" value because it's infinity on the both tails.

[@statquest]

@@Fan-fb4tz On the left side the first quantile is defined for the first point of 15 data points, meaning that 1/15 of the data is equal to or less than that point. Thus, we find the corresponding point on the normal curve such that 1/15th of the area under the curve is to the left of it.

[@yangyu5525]

@@statquest strictly speaking, the 15 lines(15 data points) divide the whole data into 16 equal groups or parts，So corresponding to normal distribution should be divided into 16 bins so that every bin has the same probability of 1/16 ,right?

[@pankajverma3842]

what a nice lecture!

[@statquest]

Thanks! :)

[@sumayyakamal8857]

THANK YOU!!!!!!

[@statquest]

Thanks!

[@dioic13]

Nice lecture, but how do u identify boundary conditions, like - 1.5, for normal distribution?

[@statquest]

This is explained at the very start of the video at 0:38. We have 15 data points, so our data have 15 quantiles. We then divide the normal distribution into 15 quantiles. Each quantile should have an equal probability - thus, with the normal distribution, the quantiles on the edge are relatively far apart, to compensate for the relatively low probability of observing a value out there. In the middle of the curve, the quantiles are close together since there is a higher probability of observing a value there. Since each quantile has to have the same probability, then there is only one way to configure the 15 lines that we draw. If that last part doesn't make sense, then just imagine we only had one quantile - so we needed to divide the normal distribution into two equal parts. Where would we put the line? Well, there's no choice involved here because there is only one location for that line - right in the middle. Similarly, when we have to divide the normal distribution into 15 equal parts, there isn't a choice about where to put the lines, there is only one option.

[@tawkameyu]

It just saved me, the person who did this => you're the best

[@statquest]

Thank you! :)

[@user-bz8nm6eb6g]

Thank you!!!

[@statquest]

bam!

[@MusafirHoonYaro]

Mr. Starmer: I am trying to understand the values 0.6, 1.1, 1.9 etc. that you have for the points on the y-axis. Are these the "raw" or "observed" data or are these numbers derived from some calculation? And, these points have a corresponding values on the x-axis (-1.5, -1.2, -0.89 etc.). I am totally lost as to how these values were derived. I am trying to understand this video in the context of linear regression where I have seen "sample quantiles" plotted on y-axis against "theoretical quantiles" on y-axis but it is not clear as to how these values have been derived? I apologize if my question doesn't make sense - I am not sure as to how to word the question purely because of my ignorance of the topic. Thank you for any direction you may give.

[@statquest]

Those are raw measurement values. The corresponding x-axis values come from asking a computer program (like 'R', or even excel) to give us the quantiles.

[@praveenchalampalem4038]

You are really Awesome!!!

[@statquest]

Thanks! :)

[@bin4ry_d3struct0r]

I always wondered how statisticians choose a distribution to which to fit the data when eyeballing it is insufficient. Now I know the answer: QQ-plots. Thank you for this!

[@statquest]

bam! :)

[@Azazello1482]

Hi, thanks for these videos! I'm confused by the logic of what happens at 1:20, when you split the data using 15 lines that occur at the points themselves. Wouldn't the intuitive thing to do be to cut the _space_ so each point resides in its own piece, rather than to use the data (i.e., the demarcations) as the cut points? In other words, you need only 14 lines to slice this data space into portions that each contain a single point. When this is then repeated on the standard normal distribution curve, wouldn't we then want to slice that curve into n equal pieces using n-1 cuts (not make n cuts resulting in n+1 equal pieces)? Edit to add one more question. I feel like I mostly get it, but I'm fuzzy on the intuition that underpins why this all works. Is it enough for the line to be straight, or must it also be at a 45-degree angle? I see how we're graphically connecting the data to the standard normal distribution, but I'm not certain as to what the intuitive connection is. It feels like it has something to do with calculus---that we're trying to compare the rates of change between quantiles for both our data and the data in a known distribution to ensure that they are constant and in lockstep.

[@statquest]

We put the lines on the points, because those are the known values we are working with. And the line only needs to be straight - the angle doesn't matter because it's a function of the scale that the data are on.

[@raghavgaur8901]

Hi Josh,I wanted to know that how did you choose the 4 data points from the original set by observing the another set of datpoints containing only 4 data points.

[@statquest]

Can you tell me what part of the video (time and seconds) you are talking about?

[@fkhan4504]

Crytal clear explanation

[@statquest]

Thanks! :)

[@bobo0612]

Thank you

[@statquest]

Thanks!

[@Yambaization]

5:30 I am confused... I thought that quartiles are three (not four) values, which divide the dataset into four equal numbers of data points. In your example you say that four data points are quartiles? 🤔

[@statquest]

Oops. That's a mistake. Quartiles divide the data into 4 parts.

[@Cozmaus]

Actuary studies is something else bro

[@statquest]

Noted!

[@pratapseshachalam2859]

very nice video. What's the difference between normal and uniform distribution? I thought both are same

[@statquest]

Normal Distribution: en.wikipedia.org/wiki/Normal_distribution Uniform Distribution: en.wikipedia.org/wiki/Uniform_distribution_(continuous)

[@adhiyamaanpon4168]

hey joh one doubt... i read one article stating inorder to check whether a dataset is changing over periodic intervals(similar to stock market dataset but in this case we don't know whether it changes or not),so to find out they will split the data into parts(previous week data will be treated as test data and week before the previous week will be considered as train data..now they have mentioned we will plot QQ plot between these 2 datasets to find if they are similar or not..if they are similar we can understand dataset hasn't changed over period of time... My doubt is till now i have seen qqplot for a single variable only...but how this concept can be extended to entire dataset??

[@statquest]

I guess you could do it separately for each variable in the dataset.