Pearson's chi square test (goodness of fit) | Probability and Statistics | Khan Academy

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Pearson's Chi Square Test (Goodness of Fit)
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The ASA Statement on p-Values: Context, Process, and Purpose www.tandfonline.com/doi/full/10.1080/00031305.2016.1154108 "Failing Grade: 89% of Introduction-to-Psychology Textbooks That Define or Explain Statistical Significance Do So Incorrectly" journals.sagepub.com/doi/10.1177/2515245919858072

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[@pablofernandezesteberena7456]

A clarification for anyone arriving directly at this video like me: the definition of the chi squared statistic for a sample is the sum of (x-E(x))^2/s^2, where s^2 is the variance of the data. When the variable is Poisson-distributed, like in this case, then you are in the particular case where s^2=E(x), as appears in the video

[@LynneLaRochelle]

helpful, thank you!

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When the AP test is in 2 hours and you're finally trying to study 😬

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Statistics is fucking impossible to study for. I've never taken such a dry class in my life

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i study the time im taking the test

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Why do you think it is boring? personally I quite enjoy it.

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I’m actually cramming for a university exam in like 4hrs...

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[@ivancarlson953]

so the p-value would be 0.043293 which is < 0.05 so reject the null hypothesis - same result as using critical values 11.07 < 11.44.

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Over 7 years and this is still very useful :)

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@@TheNotSoOriginal It's all good :) it happens to all of us. Sometimes I have ideas for new technology but then I check online and it already exists :P

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@@TheNotSoOriginal surprised that you replied ! Do you get notifications of all your comments , I mean the ones which are like 3-4 yrs old ?

[@thtprettiichick6920]

Thank you so much! You just taught me how to calculate Chi-squared and my finals are tomorrow. :)

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How was the exam 8 years ago?

[@dasepticeye6741]

@@thewilmarvelfan 12 years?

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[@Firem1nded]

I'm still a bit confused about the conclusion. The calculated value is higher than the critical value. The smaller the P-value, the more significant the result. The smaller the P-value, the higher the cricital value. Thus I'd assume the hypothesis should be accepted, rather than rejected. Otherwise I'd use a P-Value of 0.01 rather than 0.05 and the calculated value would be lower than the critical value and thus be accepted which makes no sense to me.

[@davidnatingga3760]

Realize the following fact. The more the observed data deviates from the expected data, the higher the differences between those values and so a higher Chi-squared value.

[@jacksonsipple]

Yes you would accept the null hypothesis if you had used a P-Value of 0.01. Lower P-value means you need stronger evidence for you to change your default assumption / null hypothesis. There is a greater than 1% chance the owner is right given what you saw. In the video he rejects the owner's distribution because it has a less than 5% chance.

[@jessicamiranda2081]

Thank you!! This example helped me a lot in understanding other purposes of Goodness-of-fit test. Really appreciate it!!

[@EvanZamir]

The Chi-Square distribution is a sum of squares of standard normal variables Zi. What this test is doing is assuming that the squared errors between the observed and expected distributions are distributed ~ Chi-Square. Makes it a bit easier to understand the test when you understand the motivation behind using the Chi-Square distribution.

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What a classic video!!!!.... Understood almost everything in 15 mins

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13 years ago , still holds its title for the best explanation ❤❤

[@mathrageous]

1st year AP Stat teacher loves Khan videos... Thank you Sal :)

[@maziarghorbani]

Perhaps the best chi2 explanation that I have come across. Thanks

[@shantanudas]

Sal, another clear video. However, may be you could have talked a little bit as to why chi-sq is appropriate for this particular type of problem (or similar type) - how would a student know when to select the same distribution for a problem at hand.

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[@Kanzu999]

One thing I don't entirely understand is why do we almost always choose a significance level of 5%? And what exactly would we gain or lose if we make it more or less than 5%? If we make it higher than 5%, doesn't it then make the hypothesis more difficult to accept, since it would require more accuracy to accept it? This would seem to make it more easy to reject a true hypothesis, but at the same time, doesn't it also make it more likely that we won't accept a false hypothesis? Edit: I read that medical experiments have a tendency to choose a significance level of 1%, but wouldn't it be safer to choose a higher significance level, so that a false hypothesis won't be accepted, or did I misunderstand something?

[@kmn1794]

The choice of a significance level will be appropriate, not only to the industry but the precision of available techniques. If your measuring/quantification techniques have an accuracy of micrometres choosing a significance that equates to an accuracy of nanometres is not only inappropriate but impractical.

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[@GooiYingChyi]

Thanks a bunch. It helped me with the homework.

[@tuffy11111]

Thanks for this test. Made it much clearer.

[@jeffclomin883]

Hi ! In the chi square test, each random variable follows a normal distribution N(0,1). However, when you compute the sample chi square statistic, you add terms like ( (Oi - Ei) ** 2 ) / Ei. I don't understand how those terms can be seen as samples from N(0,1)

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Did you finally understand them?

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Wow, that was a very nice example and intro to chi-square! Great job, Sir Khan!

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Awesome. Thank you.

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Good luck students taking the AP statistics tmr! Pray for me guys

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hopefully the complete problem will be stated.. thank you

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Thank you got an exam in 2hrs

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well explained and clear and easy to understand. thank you xx

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Thank you very much.....excellent explanation

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Well explained,,,,thank you sir

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[@pkittali]

Please correct if I am wrong but it will be a two tailed tests and the P value to consider would be for 0.975% (12.83). So as 11.44 is within 12.83, we would accept the hypothesis.

[@ABESW0RLD]

That's what I thought too, have you found an answer to this?

[@eXcelMathS]

yup i agree it should be a two tailed tests because the alternative hypothesis is H1 = not correct.

[@moen5313]

Chi square only has 1 tail for all those seeing this comment.. so the P value remains 5% as the video, and the null hypotheses therefore remains rejected as the video shows the solving.

[@eXcelMathS]

the concept of chi square can only do 1 tail test is incorrect because chi square goodness of fit can do 2 tail test as well. It all depends on how you state your hypothesis.

[@moen5313]

@@eXcelMathS Hey you might be right, this exercise didn't really apply well to my bio-statistics course, I had to see two different outcomes for each exposure for my exercises in the Chi-square, but it's the same concept, so you may certainly be right about the 2-tail testing

[@techtata3504]

@neoaeonian well, it is actually correct, because chi^2= Sum [ (Observed-Expected)^2 / Expected ] Note that the denominator is not squared.

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Very nice, thank you for explaining this

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Wow you explained this so well, I actually got it! Thank you :)

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Fantastic video. I teach Stats & forgot how to do this. Great refresher

[@wahhmann123]

what is the explanation of when the number of sample goes up with same probability and pattern, the resulting hypothesis changes from accepting H0 to rejecting H0?

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*subscribes as a thank you for cutting some of the unending stress I am exuding from my stats final in 5 hours* *nervous smile*

[@fearlesspeanut6868]

Thanks for the video, this just explains how to, but is there a video on why the difference between observed and expected follows Chi-squared test? And also does the expected distri (e.g. normal vs binomal vs possion) matter? what is the proof for that?

[@GoobNoob]

This cleared a few points up. Good video from Khan.

[@winthover]

Thanks a lot for the explanation. What would happen if the random variables were not independent? Would it still follow Chi square distribution? How would it affect the degree of freedom?

[@eXcelMathS]

i suppose usually for simplicity sake we always assume random variables are independent

[@erikerik3750]

Great explanation and sample. Just what I was looking for. Thanks.

[@fattyfetz]

@CogitoErgoCogitoSum this test is a non-parametric statistical test therefore you would use it when you cannot obtain the population parameters μ and σ

[@dara9837]

why does the X² test divides to the expected value and not the variance?

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thank you soo much for uploading....amazing explanation...so much clarity

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ik its been a decade but thank you so much, hypothesis tests in general confuse me a lot

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REALLY WELL EXPLAINED KHAN ACADEMY - WELL DONE

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Turns out I actually do get Chi-Square Test after watching this. Thank YOU so much!

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AP STATS exam today, thanks alot!

[@delcapslock100]

So you would use this Chi Square goodness of fit test to determine whether a set of data came from a particular distribution?

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Update your TI OS. The formula should be under STAT > TESTS > D: GOF-Test

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Saved. My. Life.

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Thanks for this video...I read the 1st couple of page in my Elementary Statistics book and was sooooooooo confused. You made this so clear! The only thing was your df (degrees of freedom)...I thought this was supposed to be number of columns minus one x number of rows minus one.

[@klat285]

Thank you. Thank you. Thank you!

[@GabiRav]

Very good explanation. . Is it not better using a spreadsheet?

[@donnyz89]

its not a random graph... he doesn't go into the probabilitstic proof of how a chi-sq distribution is dervied and the validity of it but I'm sure you can find it if you dig. But the probability is the p(finding the data, given the suggested frequencies). i.e. how likely is it to find the observed data IF the suggested distribution is TRUE. If that likelihood is very small (

[@ivancarlson953]

This example assumes that the confidence level is 95% and an alpha of 0.05 or (1 - .95), that is the risk of making a Type 1 error (a false positive - rejecting the null hypothesis when it shouldn't have been rejected). As the vid shows, the chi-square statistic of 11.44 > critical value of 11.07, so we reject the null hypothesis and accept the alternative hypothesis. We get the same result by looking at p of 0.04 < alpha of 0.05. Imagine the example used a confidence level of 99% instead of 95%, we'd have an alpha of 0.01 instead of 0.05. With an alpha of 0.01, the chi-square statistic would still be 11.44, but it would < a new critical value of 15.09, so we could fail to reject the null hypothesis. Again, we would get the same result by looking at p of 0.04 > alpha of 0.01.

[@2828jordan]

I feel this initial presumption is wrong. Null Hypotheses should always start with "negative".

[@Nandine2]

Hey can you do some videos on error propagation to go with your statistics videos? thanks

[@marciroxas7653]

Thank you for that Sir.

[@Prija1234]

Awesome explanation