Type 1 error is worrying too much, while type 2 error is care-free too much.:_) I watched 12 videos of Hypotheses within one day, now I understand them. THANK YOU SO MUCH. I guess I watch them for another 10 times, I can teach this course. Xie Xie.
Brndon! ERROR @ 25:58 3rd line. The sign for mu_0 should be -ve and mu_a should be +ve. So at the end, it should be (mu_a - mu_0)^2, not (mu_0 - mu_a)^2! Please add an erratum! Also make mention of effect size, becuase 'sigma/(mu_0 - mu_a)' is 1/(effect size). Thank you!
Hi Brandon! I'm a med student from Naples, Italy. On 25/02 I'll have my statistics exam, and I have studied entirely from your lessons. You've been such an amazing discovery! YOU're talented and smart, and people believe in you from all over the world! Thank you for everything :)
Thank you very much for your great effort. I think there might a typo for solving n while controlling beta. At 26:00 the difference between µ0 and µa. When u multiplied equation by -1, I think they reverse their position. Anyway your response for clarity
Hail lord Brandon Foltz! The King of Stat-enborough!! You have given a humble peasant like myself immense previously unattainable knowledge and I cannot ask thy majesty for more. LONG LIVE THE KING! but seriously, you have helped me a lot and you are an amazing teacher, so thanks :)
thank you so much for sharing this, Brandon, you can never imagine how a group of chinese students are benefiting from your video, this is alot more helpful than our text book here !!
Hi Brandon, i was always afraid of statistics. I never met a single teacher in my life who would teach so efficiently and clearly. The clarity of topics you provide is awesome. I wish I came across this channel 2-3years back, life would be easy. Thank you so much :)
This is yet another example of Heisenberg's Uncertainty Principle in action. When the means, the hypothesized one and the true one, are close enough, they will be almost indistinguishable by any test because the Type-II error will be huge (meaning small test power) and the sample size would have to be enormous to make the two distributions very narrow, hence distinguishable. But do we really care if the mean is 1 or 1.01? Sometimes yes, sometimes no. It depends on the phenomenon we're trying to investigate. But the standard practice should be (alas, it's not!) to first set on the minimal difference we want to be able to detect and then look for the minimum sample size that would give us enough statistical power to do that (the resolution of the test, I'd call it). So, for instance, if we want to be able to detect a difference of at least 1 between means, and we hypothesize that the true mean is 1, then we would calculate the sample size N so that the power is at least, say, 95% when the mean really is 2 (or 0, for two-sided tests). This power would only increase as the true mean moves further and further away from 1. This is the way to do statistical tests PROPERLY. The current practice, even in well-known journals like Nature, is totally flawed and inadequate, even misleading, but this is due to lack of statistical knowledge of the scientists that carry out tests... Well, mostly, because the truth also is that if you torture your data long enough, it's going to confess ANYTHING and people with a hidden agenda (sadly, especially true for pharma companies) use this principle to convince others about their "miraculous panacea for everything" and make easy money... Long story, though.
In India Parents and Guru (teacher) are worshipped as God, many Indians going through this should be worshipping you! You are our "Revered Global Guru"!!!
thanks a lot Brandon, clearly explained it. one suggestion, if you could point out other video(in desc) that we should check next it would greatly help to follow full statistical course. Thanks a lot again
This is the best series I have come across on hypothesis testing. Thanks a lot for all your efforts in making these videos. I have become you fan! I will surely watch all other playlists you have updated on Statistics.
Best video of the series, Brandon! I especially like your use of animations to explain the effect of standard error on the shape of the distribution. Great job!
I liked all your videos, and am in the process of giving thumbs up to all... the probability of me understanding any Statistics was very very low.. and these videos have changed the game for me!! Best wishes... hope many many more people benefit from your videos!!
Nice explaining, good vidz. However, I would simplify things: set alpha = ß. And calculate µ- alternative on that condition. It will give you a population mean, with given sigma, sufficiently far away from mu zero to make BOTH hypothesis powerfull. If you already know in advance population mean and variance, there's nothing more to know, given the normal distribution.
type 1 and type 2 have a tradeoff. Like mean-variance bias tradeoff exists in linear modeling which leads to optimal or the right fit in regression models.
I feel proud that I not only know when to use the phrase 'accept the null hypothesis', but also understand why! Tremendous video, thanks Brandon! - One question - is the calculation performed here the same as a 'power calculation'? I.e. if you performed these calculations before the study would it be considered power calculation? As power is simply 1-beta I would guess yes
Hi...Brandon! Thanks for the excellent video list. I am wondering that you used "accept Ho" in last slide. Is it typo? Looking forward to hearing from you!
Thank you for the video. But I am not sure if the controlling of type 2 is feasible in real since if we redo the experiment in 36 samples, the hypothetical mean changes, thus the two sides of the equation which used for the seek of n is unbalanced again. thus we will get a different n. Am i understand right?
Awesome video! Just one question: the "mainstream" sample size formula is n= (1.96)^2*sigma/E^2...The denominator matches perfectly, however the only difference I see from the formula you came to is the 1.96 squared. Im trying to see how this relates to your (za+zb)^2 factor. Could you help me make the relationship.
@ 15:17 you have both an alpha level of .01 written to the left of the curve, and then to the right of the curve you write that any sample with n =25 with a mean value of more than 3.699 would result in rejection of the null hypothesis if sigma and alfa remain the same, but here you have written that alfa is .05. This confused me a bit - shouldn't it be 0.01?
Dear Sir: First of all, thank you very much for the great video! I have a question: your video does not include an example of proportion. In your example, the standard error (sigma) of the NULL distribution and the alternative distribution is the same. How about the case of proportion? Let's say the NULL distribution mean is 0.5(i.e. 50%), the alternative distribution mean is 0.7(i.e. 70%). Now the standard error of NULL distribution is sqrt(p*q)=sqrt(0.5*0.5)=0.5; the standard error of alternative distribution is sqrt(0.7*0.3)=0.458. From there, we can still figure out the appropriate n sample size for a specific beta. Am I correct?
Does it mean that we cannot control type II error rate based on sample size if we don't know the population standard deviation (sigma)? Or do we have to use sample standard deviation (s) that we gathered on the first study to estimate the "optimal" sample size, then redo all the experiment using the "optimal" sample size?
Hi Everyone, how would this work when we have proportions like 50% and 60% and like the population is equally divided? and there are two independent categories and we are calculating or trying to calculate the n and power for an increase of let's say from 50 to 60 in one of the categories. with let's say an alpha of 0.05. How would one find a common alpha/beta/n/power?? 1000 equally divided into 500 and 500 for example for both categories... In this case we do not exactly have the standard deviation... we can get the standard error with sqrt(p(1-p)/n ) but how does one go about this problem?
Just a quick question ... So would we only control the Type II error if we were testing our from the perspective of the alternative hypothesis ? What I'm actually asking is : in practical situations, when would we want to control the Type II error ?
Hi there. When would we want to control the Type-II error? The short answer is: ALWAYS. This is how professional hypothesis testing should be carried out. And to preempt your question: Yes, it's possible to control the Type-II error but not in the way most people would like to think about it. To control this error for a continuum of alternative hypotheses, you have to first decide on the resolution of the test, that is, what kind of differences you want to be able to distinguish between... Do you really care if there is a difference of .01 between what you think is true and what really is true? This is the resolution of the test. The smaller the resolution, the more data you'll have to gather to be able to distinguish between what's true and what you think is true. But it's POSSIBLE. And you can construct tests with any power you desire for all alternatives you care about... and I mean "all alternatives you care about AT THE SAME TIME.", to be absolutely clear. It's not that hard if you notice that the power function is increasing as the means are getting further away from each other...
Hi Brandon. Thanks for the great explanation. I don't understand why having a sample mean at point B would result in an incorrect Rejection (Type I Error). Isn't it falling in the rejection region?
Taking alpha = 0.01 means that 99 percent of the sample means are inside our interval but there are 1 percent of the samples which have the mean that corresponds to the same population mean. So, B point is that extreme sample which is a part of sample means but luckily we are incorrectly rejected the null hypothesis in a true sense because the two population samples are extremely far away. if they had been closer than indeed we can see that type 2 error decreases as alpha increases and vice versa. Let me know if you understood or not? thank you.
I think if we choose immediate integer ,type II error would be controlled exactly at 5% and if we choose sample size greater than 36 it will decrease type II error rate further as alternative population mean moves away from the hypothesized mean.
I think controlling type 2 error is impossible since we cannot choose one point of mu alternative. This means that we ALWAYS cannot say that we accept the null hypothesis. Am I right?
Controlling Type-II error is possible but not in the way most people would think about it. Since the error is different for any particular alternative, what you have to do is to first set on the resolution of the test (what is the smallest difference in means you want to be able to detect with a given power) and then calculate the minimum sample size to achieve the power you want. Say, for instance, that you think the mean is 0 and want to be able to detect a difference of at least 1 with a power of 99%. What you then do is calculate N for your alternative of 1 so that your test has the stated power. If the difference is even greater than 1, your test will have a guaranteed power of 99% anyway... This is how you control it.
Thanks for the video. I have a small correction. At time 19:48 you have z_beta = -1.645 but at at 28:02 you have z_beta = +1.645. I think the latter is correct.
I'd recommend you consider updating/improving/remaking this video. It's long, dense, and difficult to understand. Some different approaches may help certain folks understand the concepts.
