Statistics 101: Introduction to the Chi-square Test

[@amitbasra5276]

All the generous people who post educational videos on KZbin should get the Nobel Prize. The video that is posted in 2012 is still so fresh in 2019 and is going to help may students and researchers. Thank you.

[@karannchew2534]

Next year: 10th anniversary

[@fatriantobong2097]

true..it makes everything so freshly available to save my freakin time and resources..go to school for some professors who dont kno how to teach

[@magdalenabernach3847]

​

[@hiyalanguages]

in 2023 too ❤

[@chuweichen5677]

watching it in 2024

[@MrEdwardCollins]

Yesterday I wrote an Excel VBA program to parse my last 200 online backgammon matches, consisting of more than 17,000 dice rolls. I wanted to prove the dice rolls generated were not biased. I plan on making the program available to others who play online, so they can analyze their own matches. I've been spending the better part of the day learning about what a chi test is, and how it works, via all of the many website articles and videos available. In my opinion, this video is the best I've looked at so far. (And I've looked at a lot.) THANKS!

[@morganshort8191]

I like the words of encouragement you give in the beginning of each video, I needed the belief in me. By the way, I got my first "A" on stat quiz and your videos were a large part of that, Thank you Brandon.

[@ktreedable]

My new best friend, graphs. Thank you so much for this video!

[@anthonygoldie6961]

I wanted to say thank you for making these great videos I am about to start a Psychology degree and I was highly intimidated by the statistical side of things but your way of explaining things has helped so much THANK YOU

[@nambiarnikhil11]

That was a great video. I like the audio quality and style of teaching. Thank you, Aspiring Data Analyst

[@BrandonFoltz]

You are very welcome Nikhil! I am glad you found it helpful. Keep learning! Best, B.

[@nguyenduclam8652]

Easy to understand, you make complicated things became easier

[@jaspreetbhamra8580]

Hi Brandon!! very helpful video thanks !! But wanted to point this out that we never 'accept' a hypothesis. We only 'reject' or 'do not reject' a hypothesis.

[@TheWholeVein]

Fantastic video. Truly for beginners. Great section at the end on what p-value actually means.

[@galashine7428]

Ok, tomorrow I expect to get a good grade on my exam after watching this video!Thanks a lot Brandon!

[@daohiep2545]

GREAT TEACHER Dr BRANDON FOLTZ

[@geofad2000]

You are such a great teacher

[@Adam-jq1bm]

you're final conclusion is incorrect should be "At the 99% confidence level we are not sure if the die is loaded". The die having a 99% chance of being unloaded makes no sense when previously it was 95% chance of loaded. We can only reject the Null, not accept the alternate.

[@Adam-jq1bm]

Great Videos by the way. Really helps make sense of hypothesis testing. Thanks.

[@gepisar]

Adam Mills yeah, i caught that too. Could we say that we are 95% plus confident that the die IS loaded, but less than 99% sure.

[@tattoostarsxoxo]

Very good presentation! Helped a lot to see examples visually and you explained very well. Was also looking for logistic regressions, multiple regressions, factor analysis, MANOVA, DFAs in your playlists. Hope to see your new videos soon!!

[@laidback4evr]

congrats on 200k subs you deserve it homie

[@msharee9]

Just an excellent explanation I could ever get .. Thanks a ton

[@sameekshamahajan6257]

Is this the same as chi square goodness of fit test? (also psa thank you soo much for making these videos it is helping me tremendously in clearing concepts)

[@drumsandstix128]

A very helpful vid, thank you!

[@mayurputhran344]

Hi Brandon ....your videos are excellent it really helps for freshers...can you guide which videos to refer for "tests of goodness to fit and independence"

[@jmorgan926]

This was perfect for what I needed. Thank you!!!!

[@rexthebruce]

Great video, great presentation -thanks!

[@ItaiKafri]

Hey Brandon, I loved this explanation, but have a quick question. I understand the math and the mathematical explanation as for what happens when you change the P value and how it impact the end result. But logically - I'm struggling. You referred to P value as the level of confidence. So when changing the P value from 95% to 99% it's as if I'm looking to find a much more confident answer - or strict as you said. My struggle is that it seems as if I'm 95% confident that I have the loaded die, and 99% confident that I have the fair one. Although you attempted to explain this in the video - I still don't feel that I understand the logical explanation.

[@EagleSlightlyBetter]

It's best to 'reject' or 'fail to reject' the null hypothesis, rather than 'accept' the alternative hypothesis. In the first instance, you might say there is enough evidence at the 95% confidence level to reject the null hypothesis. There is not enough evidence to reject the null hypothesis at the 99% level. In other words, if I only need to be 95% confident, I'll reject the assumption that my die is fair. But if I need to be 99% confident about it (maybe I'm about to accuse a good friend of cheating), I won't throw out the null hypothesis. In the second instance, the stakes are too high and there's more than 1% chance that I could be wrong.

[@manobhavjain6245]

Thanks for the explanation. I had the same doubt as itai, you cleared it :-)

[@raj_grover_chd_usa]

Awesome Tutorial.Is it possible to get the notes on all these topics? I mean the PPTs that you use during the tutorial?

[@kkwok9]

Nice job My respects Sir

[@athomas1108]

Awesome presentation

[@stevebarter5155]

HI Brandon, im quite confused now. I was taught that the p-value is the probability of obtaining the observed statistic, or one more extreme, in favor of the alternative hypothesis. The "alpha" was the threshold at which you would either accept or reject the null. In this you made the p-value, or threshold (confused what is true now), more strict and yet now you accept the null?? How could that be if it already failed the test when it was less strict at 0.05%?

[@villejunttila1425]

I'm a bit confused about one part: In the end, can we really say that we are 99% sure that we have the fair die? Because I thought that the hypothesis test is only about rejecting or not rejecting the null; that if we can't reject the null then all we can really say is that we can't reject it (based on the sample and p-value). There can still be quite a small probability that the observed variance occurred by chance. It's just that that probability isn't small enough for us to base rejecting the null hypothesis on. Basically, the difference between type I and type II errors, as I understand them. Please correct me if I'm wrong :)

[@BrandonFoltz]

Hello! You are correct. I think I addresses this in other comments. I was speaking colloquially there, easy to slip into when making videos on the fly. Unless we control type II error, we either reject or fail to reject the null.

[@sinemkayan2734]

Hi, I am trying to calculate the statistics of "How does CO2 emission correlate with the number of car production? " I know that I should make Goodness of fitnees for each of them but i don't konw how to calculate expected valu. Could you please help me? Thank you sir.

[@explorer9782]

I found sample Proportion and Chi-square test are both for Categorical variables,but when do we use them ?

[@govamurali2309]

Hi Brandon, your videos are amazing..is it possible for you to upload videos on calculus, trigonometry?

[@prawnsauce]

I think the conclusion in the example with a p-value of 0.01 is incorrect. I don't think we can say we accept the null hypothesis with 99% confidence. I think the correct interpretation is that we are unable to reject the null hypothesis but that doesn't mean it is true, and it certainly doesn't mean we can be 99% confident it is true. How can the same data set give us a 95% chance that H1 is true, and a 99% chance that H0 is true? Or have I missed something fundamental here? Please let me know if I am!!

[@davidmcmillan2333]

I was looking to see if someone had made this comment because I thought the same thing. The videos are still great, of course, but I'm in agreement with you that this part is not correct and your phrasing in your interpretation is correct.

[@boonsiangchoo]

I came to the same conclusion as you. It is incorrect to claim that "We are 99% confident that you have the fair die". What you can claim is that "I can't be 99% confident that the die is not fair, but I can be 95% confident that it is not fair". By trying to increase confidence level from 95 to 99%, you need a stricter criteria, which means the result has to be more outrageous to allow such confidence increase.

[@dlisetteb]

actually it is palatal pronounced, something like 'he' square, since it was taken from modern greek

[@johnotumba8427]

how did you calculate observed value please

[@tomscott3]

well done

[@priyadarshiniraghavendra1725]

thank you so much !!!!!! you are my god.

[@ismatandika]

Great. Please what's the link for the next video?

[@ZanyProductionz]

why does a chi square test stat being greater than the critical value mean that there is a dependency between the variables?

[@DoFlamingo_1P]

Awesome👌✌

[@mazharsoufi5270]

You're amazing! thanks a lot

[@mazharsoufi5270]

Brandon I am a medical resident doing research now, what do I need to know as far as statics, is there a link for basics tests.. things.. excel sheet use.. I can't recall the basics from ed school. is there a simple book u'd recommend? thanks boss

[@MysticMD]

Thank You!

[@sharon246787]

Graphs are my friends! wow

[@Mooreeezy]

So if I lose in Mario kart more than random chance should allow, does that mean the computer was cheating all along?

[@jollyjokress3852]

so in this case 99% confidence doesn't mean your 99% confident that it's the fair die? I mean, the confidence should actually decrease with a larger non-rejection area, logically...

[@Nilpferdschaf]

I think your second conclusion is slightly wrong. You said we can be 99% sure that the die is fair. I think it should say "We CAN NOT be 99% sure the die is loaded" which is not quite the same. We are only >1% sure the die is fair.

[@seancullin9440]

You cant tell me you're 95% confident its loaded in one example 99% confident its fair in another. Just like if the critical value is 15.07 and you get 15.05 then you're 99% confident that its fair however if you get 15.09 you're 99% confident its loaded? That just doesn't make sense logically. I understand variation changing the critical value however how can you account for such a small amount of a variation swinging your conclusion so drastically?

[@bodhach]

I agree with you ! The more strict with 99% doesn't make sense to me either.

[@christopherhenry7787]

I didn't think you could accept the null hypothesis? You can only fail to reject the null hypothesis.

[@BrandonFoltz]

Hello! Yes, I have addressed this in other comments. When doing these off-the-cuff sometimes these things happen. Just a flub. Thanks!

[@christopherhenry7787]

@@BrandonFoltz thank you for the reply. totally understand. I just wanted to make sure I wasn't misinterpreting it. I definitely learn a ton from your videos

[@AbuAl7sn1]

9:00

[@MikkoHaavisto1]

ATTENTION EVERYONE There is a mistake in the video. 33:24 The test is just saying that "we can't be 99% confident that the die is loaded". It doesn't say "we can be 99% confident that the die is fair". This wouldn't make any sense, since we already are 95% confident that the dice IS loaded from the previous test.

[@williamhass9747]

You are mostly correct. Never accept the null hypothesis. Only fail to reject.

[@BrandonFoltz]

Oh thank you! I appreciate your comment. But it is YOU that are awesome. :) Making the effort and taking the time to come on here and learn and grow is what is AWESOME. I have two videos on One-way ANOVA in Playlist 13. If you go to my channel page and click on "Playlists" you should see it there. I have a two-part video on Two-Way "Block" ANOVA under development and hope to have at least Part 1 uploaded this weekend. I've just been crazy busy. All the very best Sini! - B

[@lmiller1413]

That is so encouraging!

[@ddigwell]

I've read and re-read the chapter in my text book on the Chi Square Test three times before I decided to KZbin it. You Sir, are my Stats hero.

[@adityachandra5287]

Hi Brandon, your videos on stats are truly amazing. Do you have videos on Data Analysis?

[@BrandonFoltz]

+Aditya chandra What about Data Analysis are you looking for?

[@adityachandra5287]

+Brandon Foltz Decision tree, cluster analysis, Naive Bayes. Other aspects required for data analysis..

[@121var]

+Brandon Foltz Do you have videos on Multiple hypothesis testing ?

[@harshalshinde227]

can u plz do a video on Paramteric Vs Non parametric test. Also , on non-parametric test like Mc Nemar, Fisher Exact , Blandman Goldman analysis, Cronback alpha etc. The SPSS software has chart which gives the listing of the different groups. Also, please add biostatistical concepts to it like odds ratio etc. Also, last but not the least an alogorithm how to apply which test when we have certain situtaion and data.

[@pratikmehta1246]

Can you accept the null hypothesis? It should ideally be fail to reject at 99% and reject the null at 95% right?

[@frankpeetershome]

I agree with you. Fail tot reject the null hypothesis at the 99 percent confidence level is how I would phrase the conclusion. I guess you van never accept H0...

[@samuelalarco7496]

I thought that you should never accept the null hypothesis You just fail to reject it. At least that is what our professor keeps repeating over and over and over again.

[@Babiroo321]

"I'm not going to explain it EITHER" lol. PS. LOVE your videos. They are a godsend plus you have a lovely way about you.

[@zorbasg1001]

You are my hero. You are god of Statistics! New School of teaching. University should take notice of your way of teaching. 7 stars!

[@zoldyck_uwu]

@Brandon , At 34:14 , The slide says "We must accept Ho" but isn't it "We fail to reject Ho" instead ? Is there any specific reason why you mentioned to accept it ?

[@BrandonFoltz]

It was just a slip in the moment while recording sorry! Unless Type II error is controlled, it's Fail to Reject.

[@juditmolnarsansum6476]

Hi Brandon, thanks for these videos, they are really good. I am not sure that you are still online (alive) because I could not see you to answer recent questions but hope all is good with you. I do not understand one thing (at least) about your explanation regarding the chi-square: You said in one video that chi-square =(n-1)s2[meaning:squared]/sigma2[meaning:squared] and then you used this formula: chi-square=sum[(O-E)2[meaning:squared]/E]. (Sorry for the typos.) So I have no idea where these formulas came from and how they can be equal? If you are out there, could you please give me an explanation? Thanks.

[@rafael_l0321]

I've been watching all the playlists and they are great. This video has the first statement that I disagree with. When you use p = 0.01 you say that you are 99% confident that the die is fair. This seems wrong to me, because when you increase the nonrejection region, you should only say that you increase confidence if the chi² value is outside the nonrejection region. If that were not the case, we could call any die fair by using an arbitrarily high nonrejection region that includes higher values of chi² and say that we are 99.999999% sure that the die is fair. Does that make sense? Thank you very much for the videos.

[@MikkoHaavisto1]

I think you are correct. The test is just saying that "we can't be 99% confident that the die is loaded". It doesn't say "we can be 99% confident that the die is fair". This wouldn't make any sense, since we already are 95% confident that the dice IS loaded from the previous test.

[@ycbarton]

Yeah, I'm confused as well. with the same dice result, we say it is NOT fair with 95% confidence yet we say it is fair with 99% confidence?

[@sposada2000]

Your explanations are very clear. I really appreciate your quality explanations

[@liranzaidman1610]

Hi Brandon In the case where in 95% we reject and in 99% we accept, what would we the "right" answer in real life?

[@volkerdellwo242]

Great videos on this channel!! One question to this one: Did you actually "change the p-value"? Or did you not rather change the alpha-level?

[@xiaoli3249]

I like his video a lot. I think once the data is set, p-value is determined, we change alpha-level to decide to reject Ho or not.

[@jXevyer]

I'm always excited when I realize you have video for one of the topics that I am going over in class. As soon as I saw this one, I thought, "thank, God! I'm going to understand this part." LOL... Thank you for your help.

[@1directionluver123]

Hahaha same happens with me

[@daegudude1048]

Big thanks from South Korea Brandon, it really helped me understanding general understanding of Chi-square test! But just a quick thing that I don't really understand, you mentioned that raising the strictness(p-value), we all of sudden 99% confident that it is fair die. So we don't reject null hypothesis. I get it theoretically because Chi-square critical value of 99% confidence level, it is 15.09 so our x^2 isn't above the Chi-square critical value. But if you think more rationally...Actual data hasn't changed but how could you 95% sure that it was loaded die but now 99% confident that it is a fair die???? how was this possible? Just doesn't make sense rationally.

[@bodhach]

Great video except the last part where you are confused when you reduced the p value. Here by reducing p value you are being more stricter and increasing your confidence limit to 99%. So your critical threshold must decrease s. Excel 2016 agrees with me. DM me if you have questions.

[@orlandowan5847]

A diagram would REALLY help the point being made at the end of the video when the selected confidence level is arbitrarily changed for the same observed data to reverse the decision about the hypothesis.

[@Luutzen007]

The problem example shows indeed, choosing hypotheses makes no sense. This changing world is GRADUAL, and you can only compare probabiities (X2 P-values) Just calculate problem X2 probability (P > cumulative value. Excel: =CHISQ.DIST.RT(x2,df)). And that's ALL you got and use this P-value in your conclusion. Decreasing significance makes the hypothesis statement insignificant. :D

[@NikkiThapa]

You really know how students' brain function.. Thank you for this tutorial.. God bless..

[@davitbitsadze316]

Thank you man, at last I found someone explaining it in a very comprehensive way.

[@MuhammedShiharMZaid]

According to the CHI Square formula, the denominator was supposed to be the Hypothesized variance right? and here it seems like the expected value is taken as the denominator. Will somebody clarify this?

[@tamannas5538]

One of the best and most helpful explanations I've found for this topic on the internet!

[@winstonloke2860]

Very educational, except the first section on the graphs doesnt really talk about chi square. Not complaining though :)

[@ycbarton]

why in the example of "fair die and loaded die", you are using the terminology of "p-value" instead of "significance level"?

[@YabiKidibu]

Thank you so much Mr. Foltz. I am taking a Research course at Embry-Riddle Aeronautical University, and your lessons have been very helpful

[@jeroenverbong4884]

So, the die has a 95% chance to be not fair. But maybe, the chance of the die being loaded is even smaller than the chance of being fair. Shouldn't that be calculated too?

[@carey7858]

Do you have Mann u Whitney / Wilcoxon signed rank test/ or Kruskal Wallis test you have basically taught me my whole stats class because you are an awesome teacher but I can't find these nonparametric tests or anything comparing parametric to non parametric

[@michaelpappas3857]

totally agree with review below! Excellent explanation! Thank you!

[@winstonloke2860]

can chi square be used on a "non frequency" and instead quantitative data set? if it can't, is there a statistical test that does that?

[@juicer111]

Yeah I have a question about the chee square test!

[@drmuhammadtariq2071]

Male prefer coeducation than females. Which test i should apply

[@xsli2876]

We are 95% confident that this is a loaded die, but we are not 99% confident about it.

[@conlin314]

This is excellent, but I have a problem with "I am 95% sure this die is loaded" and "I am 99% sure this die is fair." I am sure you are aware of the problem. I wonder if there is a different way to say the second conclusion. I took college Stat 50 years ago and this is a REALLY good series.

[@dennisfelippa2353]

The statament in the video is wrong. The hypotheses are incorrectly enunciated, which leads to a wrong statement even though the math is right. The correct enunciations are: 1) "we can affirm the dice is not loaded". 2) The other must be the complement which is "We can not affirm that the dice is not loaded". So the right statement are: We're are 95% confident that the dice is not lodaded We're not 99% confident that the dice is not lodaded

[@darlove2513]

Hi there. Brandon, you say: "It helps us understand the relationship between two categorical variables..." Well, that might very well be true but the confusion is that your test with the die does not fall into this category of tests! Please see the comments below and notice how much some people are confused. And rightly so. This is because your test with the die really tests what amounts to a uniform distribution of the outcome. There are no categorical variables here, only a distribution. Testing if the distribution is uniform is the same as testing if the die is fair - that should be easy to understand. However, your test has no connection with "two categorical variables." Please try to either change your test accordingly or explain the difference between what you're doing on the slides and what you mean by "relationship between two categorical variables." That should help people understand...

[@cherzhang8015]

i am also the one who is confused at this point.

[@drsagie10]

Hi, I was confused on the examples on min 27:30 regarding the observed. If you only ask the person to toss the die 100x how did he/she get 111, 102, and 124?

[@VK-sp4gv]

The die is tossed 100×6 = 600 times total.

[@myleftshoe9]

I took 3 stats classes in my undergrad and grad work knowing that I would never need to "Do" stats, but only understand the very basics later in my career. Huh! 30+ years later I have to do stats. Thank you for your videos. I have gone through Chi Squared video #1 twice. Now I am working on Video 2. If I have a basic question, can I include it here? For example, when I increase my Confidence from 95% to 99.9% shouldn't my P value go up? I used Excel formula =chisq.inv(0.05,3) with result 0.710723. But =chisq.inv(.001,3) resulted in 0.090804

[@bikidas5029]

Particularly when we should use chi square test

[@jenniferobrien8603]

The PROBABILITY of me passing my stats class was before watching your videos was slim to none. I was near my BREAKDOWN POINT. You sir, are not your AVEAGE Joe, I MEAN, the biggest COMPLEMENT I can give you is that my CONFIDENCE LEVEL has been TRANSFORMATIONAL and POSITIVE. Thank you very MUch!

[@gazaueli]

Such a bummer I just now discovered your channel a week before my stats final! This is by far the clearest and most concise explanation of the Chi-Square test I have found. Thank you!

[@mauriciodavidperez4709]

Hej! A lot of thanks for these videos. I just noticed that the text in the slide in minute 19:00 says: "I need you to be 95% in your conclusion" 95% what? Maybe that can be improved. Thanks again for your wonderful work!!

[@ebenezertawia1374]

I like this tutorial, is very comprehensive

[@davidkashu4215]

guys that last part wasn't so clear but if it helps try this when chi-square value is greater than the critical chi-square value you reject the null hypothesis and if it is less than do not reject the null hypothesis...compare only on bases of the null hypothesis! goodluck

[@Xionkid]

If your H1 is that the die is not fair (≠), than should you not do a two-tailed test? If you say it's equal or grater that, you ask if the die gives an equal or better result than a regular die. Just asking for clarity.

[@MuhammedShiharMZaid]

Can somebody pls - explain why the Variance (O-E) squared was divided by "100" and what does it represent in this instance?

[@shr90602]

Hi. Thank you for your videos. They are great. I have a question. I can see where we can get an expected value for the dice since they are have only six sides, but how could we get an expected value for your first example with freshman, sophomores, juniors, etc. Where would we get an expected value there? Maybe an expected value would be just the average over time? Thanks

[@yvette3278]

you did a great job of explaining this and it really helped me

[@trevorchernoff1462]

I am a tad confused. It says that chi-squared observes two categories. In this example it looked at 6 sides of a die (was that 6 categories?) or are the two categories the expected and observed?

[@harshalshinde227]

categories here are fair and unfair die and the numbers 1,2,3 etc are the counts/frequencies.

[@jwv4114]

You are getting me through my stats class! THANK YOU!!!

[@boranboynuk]

Shouldn't it be more like "we are %95 sure that the die is loaded" and "we can't be %99 sure that the die is loaded"? Anyway great and helpful video, thanks

[@jayatinevatia4291]

Hi Brandon.. Thank you so much..your videos are really really helpful in understanding the basics....not sure if you have your videos on Factor Analysis including Exploratory, Principal Component analysis...If yes..Pls let me know...if not can you pls explain these topics even...? Thanks

[@niagaracanadagooners2111]

Does Playlist 12 on Chi -square have more videos? if so how many? could you please help with the links?