Chi-squared Test for Independence! Extensive video!

0:44 Introduction
3:18 FULL EXAMPLE
5:05 Finding the expected distribution
9:42 The null and alternate hypothesis
10:40 Test statistic
11:08 Degrees of freedom
16:15 Decision rule and calculating the critical value
18:27 The conclusion

Video for chi-squared goodness of fit test:

Video for chi-squared distribution (history and derivation):

[prateeksharma]

this channel is like a masterchef serving the most complex dishes with a flavour that everybody can enjoy without overshadowing the authentic taste.

[randall.chamberlain]

Mate, you are the only one who ties the knots all along the conceptual backgrounds which bring about the methods blindly used by most of us. Superb. Couldn't help but subscribe and comment here. Keep at it. This channel is pure gold.

[zedstatistics]

Re-uploaded with corrected formula. Thanks Henna for spotting it!

[elenaguzman]

I love! Love! the way you explain things! Thank you so much for your amazing teaching abilities - you definitely have a gift.

[karannchew]

Chi Sq Test of Independence
Ho: X and Y are independent.
So, if chi sq is low, delta is low, distribution of x (e.g. social media number of user) does not change with y (gender), x and y are independent, reject Ho.

Chi Sq is lower than the critical value. So, I can't say gender influence choice of app. But I can't say gender does not influence the choice either.

Therefore we can't say Gender and App Preference are dependent.
We can't say gender influences app preference.

However, 19:06, we also can't conclude that Gender and App Preference are independent.
We can't say gender does not influence app preference.

19:16 There's not enough evidence that one is guilty. But it doesn't mean he is proven innocent.

[dharuns]

Great explanation. Wanted to clarify an info on the video. In the end you say Chi square test has rejected the null hypothesis which means not enough evidence to suggest that they are dependent. Shouldn't it be " not enough to suggest that they are independent" cause that is the H0.

[kintapetonia]

thank you for your clear and in depth explanation, I've watched the other recommended videos as well. it helps a lot with my understanding. and now I know it's [kai] square not [chee} hahahaha

[nithyajacob]

Such a good video...thank you very much

[daniyaniazics]

Finally understand what is degree of freedom 😍🤩

[aimanali]

Greatt explanation. 👏👏

Though i am still confused about some things. 😢

But your videos are way too understandable

[PunmasterSTP]

Thanks for another extensively awesome video!

Also, X/Twitter > Facebook, Instagram and TikTok...

[hemantdas]

Hi Justin! Can we not take null hypothesis as ho: social media preference is Not independent of sex. How do you decide which one is h0. Please explain.

[Matibonilla]

Thank you! So clear! I just have a question... If your example DID reach a significance level... What should i do to know wich group is the most far away from the expected frecuency? For example, can you say something like: The Tiktok gruop differs the most from de Facebook group?. Ty!! Great videos, keep up at it! Greetings from Argentina

[Competent]

Videos like this informative have only 28k views while videos on tiktok have millions and millions of likes. Thats the irony😬

[karannchew]

There's not enough evidence to suggest they are dependent.
They are not dependent, based on the given data.
They don't affect each other, based on the given data.

BUT
There are not necessarily independent. Because we need a more rigorous test and more data to draw such conclusion.


There's not enough evidence that he is guilty.
Not enough proof that he is guilty.
BUT he us not necessarily innocent. Need much more proof and different criteria to conclude he is innocent.

[HERO]

Seriously, I would pay college tuition to you instead of some incapable professors.

[adityanjsg]

I hate Equations.. Only a person longing for true understanding will tell that!