Hypothesis testing (ALL YOU NEED TO KNOW!)

0:00 Introduction
3:41 Intuition behind hypothesis testing
10:16 Example 1
12:57 Null hypothesis
22:00 Test statistic
28:27 p-valiue
33:38 Confidence intervals
37:46 Significant treatment difference
42:25 Power and Sample size (THE BEST!)
50:47 Example 2

[@chetankumarnaik9293]

The most under-rated(fewer views for an extraordinary content) video on youtube

[@zedstatistics]

Thanks ! Well I don't advertise the channel but feel free to tell all your statistically minded friends :)

[@ispinozist7941]

I hazard a guess that were this video broken into two smaller chunks there would be more views. Some people are intimidated by longer content or have short attention spans. It’s a shame because this content is top class. 👏🏻

[@aniekanetuk3586]

00000000000000000000000000000⁰⁰0

[@narinpratap8790]

Ngl, that first question was hard for me. I had to attentively watch the solution to get a solid understanding of the concept. But then the second question became a breeze for me once I familiarized myself with the underlying statistical ideas. Feel much more confident about my knowledge of Hypothesis Testing now. Thanks for making such high-quality content! Really appreciate it :)

[@ws3727]

great video and illustration. I really like the big map and putting all the details in one long video, very comprehensive and saved my time of finding all short scattered video.

[@amarkavita7197]

kzbin.info/www/bejne/iJyvZJZ9arZ7mKc

[@karishmayadav1391]

One of the best channels ❣️ i enjoy learning from your videos. Thank you so much 🙏😇

[@filter80808]

Delivered casually, while bringing out subtle points very sharply. By far the most lucid explanation I've seen. Thanks for taking the time to make the video and for giving it to the world for free!

[@ado22222]

do you understand his "proof" of why they variance of the T statistics equals to 1 @ 22:58? Would you mind explaining it to me?

[@helengath9032]

⁰

[@amarkavita7197]

kzbin.info/www/bejne/iJyvZJZ9arZ7mKc

[@tonycl568]

No ads. Thanks for doing this👍

[@juliecongress6278]

You actually make me like statistics! I appreciate the explanations with the very understandable examples.

[@amarkavita7197]

kzbin.info/www/bejne/iJyvZJZ9arZ7mKc

[@skylerjohnson9089]

the examples really opened my eyes on statistics, very well done!

[@Ash-zr7yr]

Thank you, your videos have helped change my life!

[@MightyFineMoran]

I can clearly see your ability and understanding of how to present these concepts in a digestible way. You are fantastic at your job :)

[@ethanvirtudazo1657]

Only halfway through this video but this video is really helpful for getting an intuitive understanding of the concepts for hypothesis testing. Thank you!!

[@amarkavita7197]

kzbin.info/www/bejne/iJyvZJZ9arZ7mKc

[@Mymai10Tps]

Amazing videos!!! You have made all the statistics concepts easy to digest and understand! Thanks a lot and please keep it up!!! P.S: just found out that your videos are being used as our lecture recording... WOWWW...

[@giorgialanzarini9164]

You are the best!! Thank you for this video!

[@shavisharma3367]

You're a star. Thank you

[@tassoskat8623]

Thank you very much for this comprehensive and intuitive video on hypothesis testing. I was wondering if we could get this example in code. Maybe in python or another technology or maybe suggest us another video that works on this. Thank you again I feel that this video helped me more than anything in understandying deeply those concepts.

[@ananthanarayanan4100]

This is a brilliant video, thanks👍👍

[@nandiniagarwal9040]

Extremely helpful! Thank you so much!

[@amarkavita7197]

kzbin.info/www/bejne/iJyvZJZ9arZ7mKc

[@derliemonne4883]

This is awesome!

[@lindaren9467]

Many thanks for yet another great video! Now it feels hopeful to me that I can manage this course :).

[@ado22222]

do you understand his "proof" of why they variance of the T statistics equals to 1 @ 22:58? Would you mind explaining it to me?

[@alxndrdg8]

I am bad at statistical methods. you follow an intuitive approach that helps. but i need more examples to understand what those formulae in most books mean and when to use which one. hope you keep making such videos.

[@amarkavita7197]

kzbin.info/www/bejne/iJyvZJZ9arZ7mKc

[@kingbornguerrier7427]

Thank you so much for this teaching Clear and informative

[@amarkavita7197]

kzbin.info/www/bejne/iJyvZJZ9arZ7mKc

[@carsonl941]

For the power calculation, why is the T1 statistic normalized to the standard error of the null hypothesis, sqrt(V_H0), and not the standard error of the alternative hypothesis sqrt(V_H1), because later on you use 0.1 as the theta_hat and not 0.

[@Siva-Kumar-D]

Thanks for the great lecture. I'm new to statistics, I have a question regarding the test statistic used in this video. is the formula used in this video generalized test statistic or any specific test statistic ? I have read about Z-test , T-test given mean and standard deviation, sample size of population and sample. is power calculation applicable for only when proportion values are given ? It's little confusing for me.

[@amarkavita7197]

kzbin.info/www/bejne/iJyvZJZ9arZ7mKc

[@yulinliu850]

Excellent!

[@m.c.degroffdavis9885]

This is a brilliant video! I love the Zedstatistics series. Query: I learned the 0.05 level of (in)significance was a product of the 95% confidence interval (the other 95% under the curve includes 2 standard errors). Is this wrong?

[@amarkavita7197]

kzbin.info/www/bejne/iJyvZJZ9arZ7mKc

[@jc7671]

For Part (a), I did something slightly different. I calculated the point on the x axis where the H0 curve at the 95% mark. I got 0.058154 (I know spurious accuracy). I then calculated how much of the H1 curve was to the left of 0.58154 (mean 0.1, sd 0.035) and subtracted it from 1. I did it this way so I would understand where 2.8284 had come from.

[@amarkavita7197]

kzbin.info/www/bejne/iJyvZJZ9arZ7mKc

[@rishavdhariwal4782]

i did my problem similar to your process but my 95% mark is coming as 0.11567685 could you help me in how you got your value or what i may be doing wrong( i used excel function of norm.dist with mean of 0 stdev = 0.70711 and then goal seeked my x value) thanks!

[@shuangqili5623]

If my stat teacher can teach 10% as clearly as in this video...

[@solaimansohan9201]

I can feel your pain😥

[@amarkavita7197]

kzbin.info/www/bejne/iJyvZJZ9arZ7mKc

[@SadatQuayiumApu]

A very BIG THANK YOU from Bangladesh

[@ricardoolguinpizarro2863]

Hey there ! Amazing content! Thank you so much. I have a question, how do I calculate the left critical value?

[@amarkavita7197]

kzbin.info/www/bejne/iJyvZJZ9arZ7mKc

[@rahulmohanlall6707]

Excellent video

[@marcos10vb66]

Good stuff!! Thank you

[@uclalse]

I love you! Greetings from Sweden

[@sivasakthi76]

At 39:29, you say confidence interval crosses zero because p=0.58 is greater than 0.05. Could you clarify how to infer it crosses zero if calculated p value is greater than 0.05 ?

[@sagniksanyal1518]

Life saver!

[@HUnatuurkunde]

great ! i like your energy

[@rajasekar7610]

While calculating expected value of T1, why variance of H0 is used instead of variance of H1?

[@Resumeshortly]

Thank you so much, I've been watching the videos on your channel and they've really helped me to develop my intuition into the difference procedures. Although, I still get stuck on the 2-tail test being more stringent than the 1-tail test - so it is harder to show that the mean is not what we think that it is than it is to show that the mean is larger than we think it is... ??? It will take a while to get used to.

[@amarkavita7197]

kzbin.info/www/bejne/iJyvZJZ9arZ7mKc

[@sebon11]

Your way of teaching is AMAZING

[@sashaaries21]

Thank you brother.

[@asad9042]

Bravo! Excellent

[@k1mcheenoodle]

At 1:03:21, did he mean to write .1151 for the cdf (-1.20)?

[@marcustan7236]

Hi, I am just wondering if anyone knows why we used a T- distribution for the hypothesis test but a Z distribution for the confidence interval at 37:36?

[@amarkavita7197]

kzbin.info/www/bejne/iJyvZJZ9arZ7mKc

[@gamebm]

17:27 For both cases, to evaluate the variance of p Var(p)=Var(N)/N_t^2, one needs the variance of N, Var(N), the latter can be evaluated using E(N)=p(d/dp)(p+q)^Nt and E(N(N-1))=d^2(d^2/dp^2)(p+q)^Nt, where q=1-p, and p=p_0 or p_1 and Nt is the number of total samples, such as n_0 and n_1. I kinda think the derivation is omitted in the video (is there a more straightforward way to see it?) so write it down here a side note.

[@mahbubulhasan4672]

Are you using Prezi making these videos? Or May I know what tool u used to make your videos? TIA

[@anindadatta164]

Very well explained in the video. The method of hypothesis testing curve would work well in case of binary events, as the variances of null and alternate hypothesis curves have been calculated using the binomial distribution formulas. How to draw the hyposethis curves when the event outcome is more than binary, say three or more possibile outcome?

[@amarkavita7197]

kzbin.info/www/bejne/iJyvZJZ9arZ7mKc

[@GregThatcher]

Thanks!

[@madsboyd-madsen3463]

How does the sample difference go on to +/- infinity, when P0 and P1 are both probabilities ? (around 20:30)

[@bhavyaasharma7504]

Hi, firstly of all thanks from the bottom of my heart for this video. Secondly, why we can't have sameness in our alternative hypothesis? The distribution of difference at 16:18 would just have a higher number as a mean and the decreasing differences on the both sides. Where beyond a critical value the sameness should exist?

[@akramkhan4414]

Thank you!

[@ado22222]

do you understand his "proof" of why they variance of the T statistics equals to 1 @ 22:58? Would you mind explaining it to me?

[@dineafkir5184]

Great videos Zed. Thanks. Should the Alternative hypothesis for the tail-biased example not be H_a not equal to 0.5 cause it can be larger or less than 0.5

[@dineafkir5184]

OH yes onetailed and twotailed and hence alternative can be larger than... og not equal to... :-) Thanks mate

[@amarkavita7197]

kzbin.info/www/bejne/iJyvZJZ9arZ7mKc

[@lvlycreator92]

You will make a really good cricket commentator. You got that voice 😀 But pls don’t quit making tutorials. Thank you for very clearly explained videos.

[@vijayendrasdm]

Hi great video, At 4.55 mins, a graph pops out. Please correct if I am wrong, no way you will be able to see a plot like what you show if you were to toss A coin 100 times . are you implying tossing 1 coin 100 times and repeating this experiment N no of times ?

[@ado22222]

@ 22:58 why on earth the variance divided by the variance squared should be equal to 1??

[@divyanshgupta4894]

During the prediction of sampling statistic distribution, why the number of observation for p1 and p0 is different (i.e. n1 and n0) since if we are finding θ, the number of observations for the proportion of positive outcomes for both non-operative and operative should be same.....?

[@Dhruvbala]

At 22:57, why is the standard error just sqrt(var(theta)) and not sqrt(var(theta)/n)?

[@irfanshakeer1373]

As always, amazing it is. On the first example, while standardizing the normal distributions, the test statistic which was used was "T". Why isn't it Z statistic? (I'm just a beginner here, sorry for the question)

[@JohnSmith-ok9sn]

Sample size was large enough for a z-statistic to be used, instead of the t-statistic. T-statistic is for very small samples/observations. Z-statistic is for large samples/observations. (*Usually, more than 30 observations - use the Z-statistic; less than that - T-statistic. )

[@Chandrajith100]

Less than 30 sample we use T statistics and for samples above 30 we use Z score!!!

[@raoulroberts2024]

Excellent video as usual. One edit, if I may, at 31:19, it should be p

[@ado22222]

@ 22:58 why on earth the variance divided by the variance squared should be equal to 1??

[@amarkavita7197]

kzbin.info/www/bejne/iJyvZJZ9arZ7mKc

[@raphsaxbee2130]

Thank you sir!! - raph

[@asutoshghanto3419]

how do you make slides?

[@amirrezamousavi6195]

in Example 1 we have binomial distribution which the variance should be np(1-p).

[@sdsa007]

@13.58... I'm doing a retrospective on our experimental design choices....... we got a result on one side.... why did we get a t-statistic on the right-side? because we set out parameter estimate as p1-p0... if we set our parameter estimate as p0-p1 we would have got the t-statistic on the other side of the tail-end.... More importantly, It occurred to me that p1 and p0 are defined as positive outcomes (asking is there a sig difference in one therapy having more positive-outcome than the other?), but if we did negative outcomes instead (asking is there a sig difference in one therapy having more negative-outcome than the other?), I suspect we would still be able to reject the null hypothesis, but we would be working with a different normal distribution and then depending on how we setup our parameter estimate we would get a t-statistic on one end or the other.... BUT both questions should lead to the same conclusion.... self-consistent with each other... I don't know if its worth doing twice the work... but it might give confidence that the therapies have normal distribution.... which would reinforce the self-consistency, thus the validity of the test.

[@hyperbolicandivote]

Great teaching! But at 17:05 variance and Linear Algebra are associated. What is the connection?

[@amarkavita7197]

kzbin.info/www/bejne/iJyvZJZ9arZ7mKc

[@gregattac5458]

Where exactely does that formula for the variance come from? In your other video on variance and standard deviation it is a totally different formula :(

[@kushalvora7682]

If you're talking about the surgery example in the beginning then it comes from binomial distribution. Learn about central limit theorem and binomial distribution you will easily understand it.

[@ajaxaj8470]

@@kushalvora7682 @18:10 Why the variance of the theta is p*(1-p)/(1/n1+1/n0)? variance for binomial distribution is p*(1-p)*n right????

[@PlanBCZ]

@@ajaxaj8470 Because each patient has Bernoulli distribution => variance for one patient is p(1-p) and you have n patients so you divide it by n :).

[@julianavarela4936]

A savior

[@dustiinde4216]

Thank you! can I ask you which software you are using to show your slides. I know that zooming can be done using Ms. Powerpoint, however not all possible.

[@artemkonnov8570]

Looks like Prezi to me

[@avaolsen1339]

At the 28:23 mark, I am confused by the conclusion :'...operative patients did better than the physio only patients'. This is a two tailed sample test. H1: p1 p2. So, if H0 is rejected, it can only approved that p1 p2. We can not refer that p1> p2. Please clarify. Thanks!

[@amarkavita7197]

kzbin.info/www/bejne/iJyvZJZ9arZ7mKc

[@ajaxaj8470]

@18:10 Why the variance of the theta is p*(1-p)/(1/n1+1/n0)? variance for binomial distribution is p*(1-p)*n right????

[@vslaykovsky]

I'd guess that binomial distribution is a distribution of sums of outcomes. And here we are talking about proportions.

[@yuxuantian1182]

p0 is the probability of the positive outcome of the operated group, it is actually a **Bernoulli** distribution with the outcome being YES (with probability p0) or NO (1-p0). The variance of Bernoulli distributions is p*(1-p), and because it is a **sampled** distribution, the variance needs to be divided by n.

[@jingyuwang9635]

I am still confused about the variance linear algebra . is there anyone can help to explain a bit?

[@luisrodrigueziii7316]

Hello sir. Why does theta have to equal "p1-p0=0" ? If they both subtract to give 0, then why can't one say: "p1=po"? Are different formulas used between these two ways to describe the null hypothesis?

[@sophie8400]

Can someone explain why the standard error is just the root of the variance? I thought it was the standard deviation divided by the squareroot of theobservations. Or is this somehow the same?

[@stevey7997]

I wondered that as well at first. But I think the reason is that here we care about the standard error of an estimator for which we already calculated the variance, which includes the number of observations. The formula you are referring to is the standard error for a mean estimator where you only know the variance (or standard deviation for that matter) of a sample, not the estimator. I hope what I'm saying is clear and I also hope the reasoning I came up with is correct...

[@carlostolosa6530]

at 25:54 why you chose to use pooled proportion BUT at 35:25 you did not use pooled proportion? I used θ ÷ sqrt(p1q1/n1 + p0q0/n0) as my test statistic which leads me to t=2.009868 is that okay as well?

[@harryfeng4199]

did u manage to figure out y, im confused on that as well

[@carlostolosa6530]

@@harryfeng4199 nope. 😅

[@carlostolosa6530]

@@harryfeng4199 i forgot how to do statistics nowadays 😂 but i think i got it when reviewing it today because of your reply. Note that at 25:54 we assume Null Hyp: p1-p2=0 but when calculating confidence interval, we have p1-p2≠0 instead. e.i. p1-p2=0.14 in that case, we dont use pooled proportions since at 35:54 we dont assume p1=p2 anymore unlike in Null Hyp at 25:54

[@harryfeng4199]

@@carlostolosa6530 thxxx!

[@Paivren]

I think there is an error at around 26:00. You are inserting p-hat (i.e. the proportions measured in your sample) for the "true" proportions p given by the 0-hypotheses. Shouldn't the resulting t be t-distributed instead of normal-distributed?

[@Maymona93]

Thank uuuuuu

[@CoCo-mw6cs]

at 6:51, isn't the true probability should be close to 0.08? cause the y axis is probability.

[@skg2109]

Great video but I was expecting a t-test in the first example. Why is it a normal distribution?

[@swapnilparekh7738]

clt

[@qingli1799]

Why the variance of the theta is p*(1-p)/(1/n1+1/n0)? I checked the variance for binomial distribution is p*(1-p)*n. Thank you

[@ajaxaj8470]

I had same doubt as welll. Did you get it?

[@vslaykovsky]

I'd guess that binomial distribution is a distribution of sums of outcomes. And here we are talking about proportions.

[@georgemathai8659]

Any thoughts on why it would be wrong to approach this as a chi square test for independence (i.e. recovery being independent of treatment)?

[@TomerBenDavid]

Which software creates this bubbly presentation?

[@ES-qe1nh]

prezi

[@whetstoneguy6717]

At video 58 minutes why do you not divide by n-1 or 400-1=399 instead of 400. This is an important concept I do not understand. One never knows the true variance and only knows the same variance. Therefore I would expect the denominator to be 399 to reflect n-1. Respectfully submitted--WhetstoneGuy

[@mohammedamayri2237]

"We are attracted to it because it's nice and round" lol I don't feel that the choice of words here was totally innocent.

[@woldetinsaemekonnen3866]

It is clear thanks but to defined hypothesis again teacher

[@whetstoneguy6717]

Mr. Justin Z--video 18.0: Why is V(P1-P0) the sum of V(P1) + V(P0) and not the difference of V(P1) + V(P0)

[@carlostolosa6530]

factor -1 out from V(-P0) as (-1)²

[@user-jw8sq2vx9s]

good

[@stephensonal4082]

Was it coincidence that the critical value was 1.96 and rejection was at 1.99 a difference of 0.03 and alpha 0.05 was p value 0.047?

[@essexbaz]

I understood what you were saying until the test statistic formula.

[@trocks2113]

Nice Video!!! But from 59:22 here, I am starting to confusing...

[@LucaVincent]

same i have no clue from that exact point

[@RedFeather11]

variance calculation shouldn't be V(p1)-V(p0) ?

[@afuturemodern]

no variance adds

[@ivybelieves8071]

⭐️⭐️⭐️⭐️⭐️

[@George-lt6jy]

i like to be very sure in my tests so my alpha is 0.0420

[@Imsulit28]

fucking good video

[@noemisandoval9967]

I have never been more confused in my life

[@parthmaheshwari1899]

Why SE is multiplied with z in CI calculation kzbin.info/www/bejne/bnuslpKZr5ukfaM

[@yuzhenliang3414]

21:00 I may say 0.05 is 5% that is the two-sigma limitation, a lot of standards use two-sigma limitation.

[@drachenschlachter6946]

H1 is wrong at the beginning....

[@kneazleje]

trying so hard to understand :(

[@ignacio560]

First!

[@amits310874]

I am sure that several persons might have completed PhD after watching your videos (including me) likely to submit within next two months

[@DarkKnightLives]

Did anyone notice, Justin is probably color blind!! @47:26

[@maazkhan9972]

example is really tough for beginners...try choosing a simple example instead of a complex one....

[@violett9581]

Oh my god, I am so stupid