My name is Narayan Rangaraj from the industrial engineering and operations group, operations research group at IIT Bombay and some part of the introductory notes are also due to professor Sabnis from mathematics department. So, you have already seen this idea of confidence intervals which tell you in some precise probabilistic language how likely a parameter likely to be is going to be in a certain interval. So, that is when you are asked to give a range for a given parameter that you are trying to estimate. So, supposing you want to estimate the number of defectives in a total population and based on a sample you have to conclude something you cannot say for sure because the defective phenomenon is probabilistic. So, you can give a range and the larger the range the more likely the parameters likely is going to be in it. So, you can give a very large range, but that is not very useful. So, you want to give a tight range, but which contains the parameter of interest with high probability that is the best that you can do. So, confidence intervals you have already seen, but sometimes you want to ask the reverse question you do not want the the statistician or the experimental investigator or the scientist or the engineer to give a range of values. You have a hypothesis or you have a proposition and the analyst is supposed to either agree or disagree with it. So, you as the user have a have a hypothesis and the the role of the analyst is to either agree or disagree with it. So, the simplest example of course is like a court where a person is either guilty or innocent and some judge or jury has to agree or disagree with that. That is the that is the simplest example of hypothesis testing where the role of the analyst is to give an opinion yes or no not give a range of values and things like that, but give an opinion yes or no. So, on on what statistical basis do we do this? So, that is the topic of hypothesis testing. So, actually the materialist is straight forward it is the first few sections of ROS we will see how far we can go in in this lecture in the next one. So, that is what we will we will do. So, hypothesis testing this is what I plan to do introduction and motivation a notion of significance levels which is a way of saying how confident we are of our hypothesis test. So, when we agree or disagree then with with what probability are we sure of doing that. So, the there is a well known terminology used in hypothesis testing there is type 1 and type 2 errors we will quickly see that and specifically we will we will apply the concept of hypothesis testing to normal populations you know because of the central limit theorem we know that many interesting phenomenon can be assumed to have an appropriately chosen normal distribution. So, testing for means or variances of those normal populations is is one important area in hypothesis testing we will also see it for binomial populations. So, let us quickly start with the introduction. So, given given some data how likely is it that the data has arisen from some hypothesis distribution. So, we will we will answer this question more precisely later on, but this is the type of question. So, for example, if a manufacturer claims that some some parameter has an average value m then do we accept that. So, if somebody says that you know the lifetime of some bulb is so many hours, but you know inherently the the the performance of the bulb is the probabilistic one. So, if we just look at some data how do we accept or or not accept the the manufacturer's claim that the average is indeed so and so. So, as you can imagine if we assume that in this case that the parameter is normally distributed we can draw some random samples and you know it is very unlikely that all the values will be equal to whatever the manufacturer is claiming some of them will be more some will be less. For example, if all of them are less than what he claims then you know we are we are unlikely to believe his his claim. So, some will be more some will be less. So, with what confidence do we accept the manufacturer's claim that the mean is indeed so and so. So, in most in most practical situations there will be some physical meaning to the claim. So, for example, in the in the lifetime claim so if the manufacturer claims that the life of this bulb is 1000 hours then you know if it turns out that the life is actually 1200 hours on average then we are quite happy about it. So, what we are really testing is whether the whether the mean is 1000 hours or more. So, we are ok with you know an increase on one side. So, that is the type of thing which we would like to test through through some data. So, here some quick examples say a medical researcher may want to decide on the basis of some experimental evidence whether coffee drinking increase the risk of cancer in humans. So, this is the type of thing where you know the expert has to give an opinion. So, if there are two kinds of measurement gauges in the market then an engineer may have to decide on the basis of some sample data whether there is any difference between the accuracy of the two. So, this is the type of question that is asked in hypothesis testing which we would like to try to answer. So, you have seen the concept of random variables and independent random variables when you are talking about say about pairs of random variables. So, independence test. So, if you look at data then is there a dependence between a person's blood type and eye color. Suppose this is the experiment or the investigation and some data is collected on these two attributes and our question is someone says that these two things are independent random variables. So, do we say yes or no on the basis of the observed data. So, this is the type of example that I told you that a construction firm has bought a large number of cables and the claim of the manufacturer is that the cables have an average breaking strength of something 7000 psi. So, what this means is that the breaking strength on average is 7000 psi or more. So, do we accept this? So, in each of these cases you know there is a conjecture about the system or the population and we have to decide where to determine this conjecture based on some sample data. So, it is very similar to what you did in construction of confidence interval, but the way the question is posed is slightly different. So, a statistical hypothesis is an assertion of conjecture concerning one or more populations and in the language of hypothesis testing two complementary hypothesis come to mind either the assertion is true or it is false. So, some people use h and h dash h for the assertion is true and h dash for h assertion is false. So, we have two choices either we can reject h dash and conclude that h is strongly supported by the data or we can fail to reject h dash and conclude that h is not strongly supported by the data. So, you know for example, supposing someone claims that I have developed a better vaccine than what is there in the market for some disease. So, you might want to say so where is the evidence of that. So, you look at treatment data for the two vaccines and then you have to conclude whether there is enough evidence to overthrow the existing treatment and whether to accept the new treatment. Now, the data that you have on these things are sample data arising from some inherently probabilistic phenomenon. So, you cannot say for sure, but based on the evidence you would like to you have to say something I mean you cannot just say I do not know. So, in the language of hypothesis testing. So, just to contrast so supposing we put a mathematical proposition as opposed to a statistical proposition. So, mathematical proposition is that effects say some function is of this type some function has a minimum. So, this is either true or false. So, there is no ambiguity about this. So, you can verify this by whatever means, but statistical hypothesis are different in nature. So, statistical hypothesis so people are competing I mean two products are competing and the marketing analyst has made a claim that the proportion of consumers preferring brand A to brand B is 0.4 that is the 40 percent of the consumers prefer brand A. So, this is the hypothesis. Now, you can interpret this in a number of ways. One of the ways is that if you draw a random consumer then that person is likely to prefer brand A to brand B with probability 0.4 or if you pick a large number of people and ask them all which they prefer then about 40 percent of them are likely to say I prefer brand A to brand B. So, this is the hypothesis. So, supposing we actually now start doing this. So, I picked 15 customers and 12 of them are found to prefer brand A to brand B. So, it looks like a large number of them prefer brand A to brand B. So, this hypothesis that 0.4 of them I mean 0.4 fraction prefer brand A to brand B it looks a bit odd because 12 out of 15 prefer brand A to brand B. But from your knowledge of binomial distributions supposing I randomly picked 15 people from the population is it possible that 12 out of them prefer brand A to brand B given that each individual is likely to prefer brand A to brand B with probability 0.4. So, is this possible? So, did you get the question that each customer prefers brand A to brand B with probability 0.4? I got 15 persons in a room and asked them and 12 of them happen to prefer brand A to brand B. So, is this possible? It is certainly possible, but you know you can work out that it is quite unlikely it is certainly possible because you know you can work out the probability that 12 people prefer brand A to brand B given that each one will prefer brand A to brand B with probability 0.4. So, you can actually work it out, but as of now it seems unlikely. So, we would like to say that it is it is highly unlikely that the statistical hypothesis is true. So, we would like to make this conclusion. So, but supposing I say that you know 10 people preferred then you will say that is also unlikely, but certainly more likely than 12 people. What about 8 out of 15 possible? Definitely possible 7 out of 15 very very possible you know. So, at some place we have to draw the line saying that this this looks ok 0.4 seems seems ok. So, of course, exactly 40 percent of the people that you you sampled turned out to like prefer brand A to brand B then you say yeah it looks it looks possible that the the real the real fraction is 0.4, but if I got something too low. So, if I if I got 0 people out of 15 prefering brand A to brand B then you would be suspicious of the statement that 0.4 is the fraction. If I got 15 on 15 you would be suspicious, but somewhere in the in the middle you would you would be ok with it. So, what is that middle region where you would be ok with it? So, that that is the type of question that we will we will ask in. So, for example, here if the true probability which we do not know, but that is the claim in this case that is the claim made by somebody if if the true probability is 0.4 then the probability of observing 12 or more successes in 15 trials is 0.002 it is from that binomial calculation each one. So, it is like tossing a coin 15 times the probability of heads is 0.4 and I got 12 heads out of 15. So, what is the probability of that? So, you can work it out right I hope you can work it out. So, if you think about it you can. So, it is physically possible. So, it is not impossible. So, I cannot reject the hypothesis totally, but it is highly unlikely. So, the the way that the statistician would like to pose his conclusion is to give a level of significance. So, so before that similar language for an example which I will follow through now using some numerical value. So, for example, supposing the cure rate for a given disease using standard medication 60 percent, then a new drug is anticipated which somebody says has better medication properties than the standard one. Now, the new drug is to be tried on a sample of 20 patients and the number cured x in the 20 is to be recorded. So, this is the way we will we will go about the investigation to see whether the new drug is indeed more effective than the old drug. So, supposing 12 out of those 20 turned out to be ok, then you know it is it is about the same as the old drug. So, we want something significantly better than that. So, is there substantial evidence that the new drug has higher cure rate than the standard medication? So, society is generally conservative and you know we require strong evidence to overthrow status quo. So, generally people are comfortable wherever they are or they have got used to it. So, to overthrow something which is established you require strong evidence because one thing is it has a cost to go over to a new thing. So, you do not want to do it just very casually you want enough evidence that something is really better otherwise it is not worth it. So, this is a conservative way of putting it I am not saying that we should be that way, but sometimes it appears like that. So, now here the relevant hypothesis is that the new drug is better than the standard medication that is the p the success rate of the new drug is greater than 0.6 and the reverse of that is it is not better than the than the standard medication p is less than or equal to 0.6. So, this is the language used in hypothesis testing there is something called the null hypothesis and something called the alternative hypothesis. I will try to find out why this term null and alternative use why null hypothesis, but that is the it is usually used for the status quo that you are where you are and the opposite of that is the alternative hypothesis. So, of the complementary statements concerning the unknown state of nature in this case the effectiveness of the new drug one is called the null hypothesis the other is called the alternative hypothesis.  So, we accept both the possibilities initially and then we want evidence regarding one of them and the way it is posed is that one of them is taken as the null hypothesis and you look if there is enough evidence to overturn the null hypothesis or to reject the null hypothesis. You can as well do it the other way around, but the implications are slightly different in terms of your perception and the way people look at it. For example, in a court of law you can assume the person is innocent and it is up to the prosecution to prove that the person is guilty. So, if there is not enough evidence then you say that I have no evidence to say that the person is guilty. So, I continue to believe that he is innocent. You can say you can start the proceedings the other way around the person assumed to be guilty and it is the duty of the defense to prove that or to overturn that assumption. You cannot prove anything in this statistical thing you can only give enough evidence to believe one way or another because from the type of example that we have seen we cannot be absolutely sure. So, even if for example, even in the even if the new drug is indeed has a success rate of 80 percent. If I draw a sample of 20 people by bad luck I may I may just pick a lot of people who did not respond to the treatment even though the average I mean the probability of responding is 80 percent. I may by bad luck I may pick you know out of 20 people 15 people did not respond to the treatment that can happen with a very low probability it can happen. So, the data shows that you know the sample proportion is only 0.25 whereas, the real proportion is 0.8 that can happen. So, if I look at that data then I will be I will not be accepting the hypothesis that the new drug is better. So, I will have made a mistake that that can happen. So, in hypothesis testing we will make mistakes the only thing is we want to put a probabilistic bound on those mistakes. So, as I said the choice of what to call the null hypothesis and what to call the alternate hypothesis is the matter of convention. So, in in courts of law often the null hypothesis is the person is innocent and the alternative hypothesis which can be accepted only with enough evidence to overturn the null hypothesis otherwise you say that the null hypothesis cannot be rejected is that ok. So, that is you know innocent until proven guilty that is the way many courts operate. So, for example, the consequences of wrongly rejecting the null hypothesis that means if you wrongly convict somebody that is a very bad thing I mean that is what we feel. So, supposing you I mean this is a matter of opinion and convention between between us. So, supposing I say that I wrongly convict somebody and punish then you know later on we find out that actually we had made a mistake that is one type of error which we can make. The other type of error which we can make is we wrongly conclude the person is innocent and do not punish actually the person is guilty, but we do not punish that is also mistake, but we may say that the first mistake is a more serious one because an innocent person was punished. So, for example, in extreme cases supposing you know you hang a person who is innocent then there is no way of even compensating that mistake or you know if you impose a severe penalty then you know there is no way of retrieving that that loss. Whereas, the other way round that is somebody who should have gone to jail or who should have been hanged as per the laws of the country was not hanged that is also a blot on the justice system, but that is a less serious error is that ok. So, there is a difference between the two types of mistakes. So, depending on which one we view as more serious we we appropriately define the null hypothesis in the alternative hypothesis. So, the convention is that wrongly overturning the null hypothesis is a more serious error than wrongly accepting the null hypothesis ok. So, that is where this type 1 and type 2 error come in which we will we will talk about. So, choice of so, the null hypothesis is called H naught and the alternative hypothesis is called H 1. So, I told you that either H and H dash or H naught and H 1. So, in this terminology when an investigation is aimed at establishing an assertion with substantive support obtained from the sample the negation of that assertion is taken as the null hypothesis the assertion is taken as the alternative. So, when you want to make a new claim then that is put as the alternative status quo is often the null hypothesis. So, before claiming that a statement is valid adequate evidence must be produced to support it. So, if I if I want to establish that a person is is likely to be guilty then I have to give adequate evidence for it otherwise you say that you you will stick with the null hypothesis. So, the null hypothesis should be regarded as true and should be rejected only when the data strongly testify against it ok. So, this is what I said that. So, in a sense the the purpose of the hearing is to see whether there is enough evidence to establish the guilt ok. If there is not enough evidence then you do not conclude that he is guilty you do not you do not actually prove that the person is innocent or something that is not the purpose of the the trial the purpose of the trial is to see if there is enough evidence to convict ok. So, technically I suppose you should you should conclude at the end of a trial that he was found not guilty you do not say he was found innocent or something you say he was found not guilty that is there is no evidence to conclude that he is guilty. So, therefore, he is not guilty at the moment the other way round. So, if you start with assuming that he is guilty and then you try to say that he is innocent then you conclude that the person is innocent. So, this is just a question of language, but you can see the way the the consequence that I that I have said. So, I believe in in in Scotland or something they have this this third verdict of not proven. So, you know you say that there is not enough evidence to conclude that the person is guilty and in some cases there is not enough evidence the other way also that is if you start to the assumption that guilty there is not enough evidence to prove that the person is innocent also. So, you sort of leave the person in in limbo in sort of in between and say that not proven and that can also be very damaging I mean that is it is like it depends on on on how society views these things. So, at least in the old days the Scottish courts used to you give this verdict of not proven that is we sort of we tend to believe that the person may be guilty, but we do not have enough evidence of it, but we do not have strong evidence that the person is actually innocent also. So, we leave it somewhere in between. So, I think in India and many other places we we we declare the person not guilty that is it or we convict. So, now coming back to this more more tangible problem. So, supposing the existing cure rate is 60 percent that is the probability of cure is 0.6. So, randomly selected person from the population will react successfully to the new medication with 60 percent probability. So, supposing 20 patients were selected at random and the new drug was administered with proper procedures. So, x is the number cured. So, now based on the value of x can we conclude that the new drug is better than the old one. So, that is the statement. So, actually let p be the cure rate of the new drug. So, what we want to see is supposing p is the actual the success rate of the new drug you know could we have got this x from from that p then you know we will take a we will take a call on this. So, in view of the guidelines of our hypothesis testing paradigm or the language of hypothesis testing or the framework of hypothesis testing p is less than or equal to new 6 p p is less than or equal to 0.6 is the hypothesis that the new drug is not better. We actually want to come out to the evidence that the new drug is better otherwise the old drug is there it is already there in the marketplace there is nothing substantially better to change over. So, let x denote the number of cures out of 20 in the trial that I have conducted. So, x can take on value 0, 1, 2 up to 20. So, I can say something like this I will if 15 if 15 people out of 20 respond to the new drug then I will actually assert the new drug is better than the old drug. Old drug had success rate 60 percent. So, this one has better than that and if it is 14 or less then I will I will not change over. So, here my I will conduct a test. So, the sample size is in this case 20 and I will test I mean I will record the number of successes and that is x and for a given p the number x is a random variable for a given p depending on the outcome of that random variable measurement I will I will decide whether to accept or reject the claim. So, such a number such a random variable x is called a test statistic. So, remember that you know I have to specify this procedure up front I have to say that on this basis I will accept or reject the test. So, the test is the new cure is administered to 20 people and I will measure the number of successes that is a random variable depending on the value of that random variable in this case one random variable I will I will have a region where I will accept the hypothesis the alternate hypothesis or I will accept the null hypothesis I mean basically either reject the null hypothesis or accept the null hypothesis that is the way it is it is put. So, that that random variable which we define is called the test statistic. So, now, coming to the type the two types of errors that I spoke about the decision which is reached by a test it could be wrong. So, this is the first thing that you know every statistician or every data analyst or every probabilist or scientist dealing with random phenomenon has to accept and internalize that we could be wrong. So, you know unlike a deterministic phenomenon where you are either right or wrong probably. So, in making a statistical statement we could be right or wrong we are only trying to put some concrete quantitative bound on on our errors. So, as I said you could make a mistake. So, the question is what type of mistake and what is the likelihood of that mistake and how much confidence do we have in our assertion? We can run away from the whole thing and say because I am not sure I would not say anything, but that often is not possible. So, we have to make a statement. So, for example, in the light bulb example supposing we are buying equipment for this I can say that you know I will test each and every piece of equipment till its failure and then only I will buy it then you know I will be left with nothing to use. So, I will get a lot of 1000 light bulbs I will select 10 of them and I will find out what is their lifetime till destruction and on that basis I will accept or reject the hypothesis regarding the entire sample. So, that seems more practical because you know. So, this is this is often the basis for quality control through inspection right. So, supposing I have to certify that some material that I have purchased is of the desired quality I cannot sample the entire lot I have to sample a part of it and on that basis I have to either accept or reject a lot which claims to come with a certain quality. So, this is in fact a very practical thing which is which is done you know day in and day out. So, lot of survey sampling. So, your TRP ratings in advertising, your customs inspection procedures, your audit principles, quality control on shop floors in manufacturing environments, quality certification for any attribute it is based on these principles of you know sampling and coming to some conclusion based on that. So, what is being talked about here is actually very tangible and concrete in an uncertain world right. So, the two types of errors is are as follows one is that the null hypothesis is true, but the test says that it should be rejected. So, we wrongly reject the null hypothesis. So, this is called type 1 error. So, this is a sort of the more serious one. So, tests are often designed to control this type 1 error. The other type of error is actually that the null hypothesis should be rejected, but the test the random outcome of the test says that we should accept it continue to accept it. So, that is also a mistake. So, that is called type 2 error. So, is that what type 1 and type 2 error. So, here is the sort of summary. So, on the columns are the real state of nature that is H naught is true or H naught is false, which we do not know, but those are the two possibilities. Our actions are on the rows either do not reject H naught or reject H naught. So, if H naught is true and we do not reject H naught then that is the correct thing to do, but if H naught is true, but we reject H naught then then we can commit a wrong which is of type 1. So, that is called type 1 error and if H naught is false and we, but we do not reject it then that is also wrong that is called type 2 error and H naught is false and it reject H naught that is correct. So, this is the guideline for in a sense defining what is H naught and H 1 in the first place as I said it could be done either way. So, generally speaking falsely rejecting H naught that means, type 1 error is viewed as a more serious consequence than failing to reject H naught when H 1 is true. So, is that ok that is the. So, in the in the legal analogy falsely convicting somebody who is actually innocent is considered a more serious error than declaring a guilty person innocent by mistake ok. So, that is the. So, to put some probabilities to it probability of type 1 error is the probability of rejection of H naught when H naught is actually true. So, that is called alpha and probability of type 2 error is the probability of not rejecting H naught when H 1 is actually true. That means alternate is actually true, but we do not reject the null. So, that is called beta. So, generally we put some bounds on alpha and then try to get the best beta possible you know we do not want alpha to be more than something because you know that is you know consequence that we do not want to bear. So, for example, we may say the probability of type 1 error should be no more than 5 percent or something like that. So, a test of the null hypothesis is a course of action specifying the set of values of the random variable test statistic x for which H naught is to be rejected. So, for example, in our testing for a new new treatment H naught was that the probabilities less than or equal to 0.6. So, we will we will reject it if x is the high value out of 20 if let us say 15 are successful then it seems likely that you know the value of the value of p is in fact more than 0.6. So, we will reject the null hypothesis and accept it. So, we may say we can say the following for example, that we will reject the null hypothesis if x is 15 or higher. So, that is a possible test that we say. So, in a given implementation of this test we take a sample of size 20 draw I mean test I mean see the outcome of the treatment on those 20 randomly chosen persons record the number x which is the number of successes if the number is more than 15 we reject the null hypothesis. So, this is our proposed test. So, we would like to see. So, the random variable whose value serves to determine the action is called the test statistic and the region of values the range of values for which the null hypothesis is rejected is called the rejection region of the test. So, that is just the language used. So, for the example if the null hypothesis is the probability of success is 0.6 or less and the null alternate is that the treatment is in fact, better than the existing one which is 0.6. So, the alternate hypothesis h 1 is that p is greater than 0.6 we could propose that h naught is rejected if x is greater than or equal to 15 and h naught is not rejected if x is less than or equal to 14. So, this is the possible test. So, x is actually a known probabilistic random variable. So, it follows a binomial distribution with n equal to 20 and p the probability of success of an individual trial. So, what is the what is the type 1 error? So, the type 1 error is the probability of rejecting h naught when h naught is true. So, that means that. So, supposing p is 0.6 then what is the chance that I get 15 successes? What is the chance that I get 16 successes or more? In that case I will be actually rejecting the hypothesis that the null hypothesis. So, summation from 15 to 20 for p equal to 0.6 I choose k sample I mean I can get k successes out of 20. So, p raise to k and 1 minus p raise to 20 minus k. So, those are the failures. So, that quantity is the type 1 error is that ok. So, supposing p is 0.6 that means the treatment is not really not really better than that that is a maximum that the null hypothesis is true. So, supposing the treatment is 0.6 but by chance I get 15 or more successes then I will say that actually the success rate of the new treatment is better than 0.6 and I will overturn null hypothesis in error. So, let me restate actually the success rate of the new treatment is only 0.6. So, roughly speaking 12 out of 20 should be responding favorable to the treatment, but by chance I got lucky and I mean lucky or whatever I by chance I got 15 or 16 or up to 20 successes. In that case I would wrongly conclude that the treatment has an effectiveness of more than 0.6 based on this test. So, the chance of that happening. So, my test definition is that x if x is greater or equal to 15 out of a sample of 20 reject the null hypothesis. So, I could reject the null hypothesis wrongly which means I put p equal to 0.6 compute this binomial expression and if this quantity tells us that the probability of making an error of type 1 is that ok. So, you can just think about it and say that this will be some quantity between 0 and 1. Hopefully this quantity should not be too large that means then you know if this quantity is you know 0.25 or something then you know there is a 25 percent chance that I am making a mistake of type 1 which is which is a bit uncomfortable. So, normally the language uses that you put a level of significance. So, significance level for a hypothesis test is a bound on the type 1 error that you want to commit ok. So, it the concept is quite simple, but the way it is put is that significance level alpha is the bound you would like to put on type 1 error for a test namely the probability of wrongly rejecting the null hypothesis when in fact, it is true. So, let us just look at probability p equal to 0.3, 0.4, 0.5, 0.6. So, if p is in fact, 0.3 then you know we are very unlikely to get more than 15 successes I mean up to 3 decimal points it is 0, but you know with p equal to 0.6 we actually can get 15 or more successes just by chance with a 12.5, 12.6 percent chance. So, if we design a test saying I will conclude that p less than or equal to 0.6 is not true if I get 15 or more successes then 12.6 percent of the time even with 0.6 probability of success I will actually get 15 or more successes. So, I will be making a mistake of type 1 12.6 percent of the time. So, if we are ok with that then we can go ahead with that test. So, do you see the issue involved in designing the test. So, in a hypothesis testing the task of the analyst is to design the test. So, here the design of the test is that let say I have funds to conduct tests on 20 people. So, the sample size is given to you let us say. So, now I have to say what is my acceptance region and rejection region. So, what is the number of people whose successes I will conclude as rejection region for the null hypothesis and the complement of that will be the acceptance region ok. So, there is a rejection region what is the probability that I will be rejecting in error you know by mistake. So, that is alpha which is the type 1 error which if the true probability is 0.6 then the test that we will get 15 or more successes with 0.6 binomial probability is actually not insignificant it is 12.6 percent. So, it is like saying that the I am asked to give a recommendation whether the new drug is better or not and actually the new drug is just as effective as the existing thing which is 0.6 based on this test I will overturn the existing treatment and go for the newer treatment hoping that it is better and I will be wrong 12.6 percent of the time I mean if this if this activity is done repeatedly. So, that means in error I will be changing my system and you know revamping everything and my norms and my standards and I will do that 12.6 percent of the time. So, that is maybe too much of a I mean if you are uncomfortable with that then we will say let us not go with 15 or above let us tighten it up and say 16 or above or 17 and above. So, that is the type of decision we may say or we may say we need a larger sample size because you know the larger the sample the more accurately I can pin it down. So, I hope you got the flavor of it you have to sit and work it out it is the underlying mathematics or the underlying statistical computations are actually quite straight forward in this case it is just a binomial probability computation. Of course, for a large sample size and when n p is small you can do a normal approximation to the binomial and you know use all the things that you have learned so far. The only new thing is what is the question what is the application of the principle. So, the language of hypothesis testing has to be understood that there is a there is a thing called the null hypothesis there is a thing called the alternate hypothesis. There is a test statistic which is a random variable defined by us depending on the value of the random variable there is a rejection region there is an acceptance region and there is a chance of committing an error of rejecting the null hypothesis by mistake when it is actually true and that error is called type 1 error and the maximum level of that type 1 error is called the level of significance of the test and so test has to be designed with that in mind. So, this is the summary of what I have said so far any questions from your side. So, in this case the level of significance is 0.126 that means there is a 12.6 percent chance of making a type 1 error. So, normally you know we would like to say beforehand what should be our type 1 error. So, we can set it in advance and then design the test accordingly. So, we may say we want to make only a 1 percent error or 5 percent error or 10 percent error of type 1 and so for example, 0.05 level of significance means that the chance of type 1 error is no more than 5 percent. So, I am willing to live with you know 5 percent of the people being hanged by mistake or whatever we are trying to. The type 2 error is the probability of not rejecting H naught when H 1 is true which is a similar binomial computation which we can compute for this one for different values of p is that ok. So, it is again in this case it is say p is 0.8 actually it is much better than 0.6 ok, but by bad luck we get only 12 successes out of 20 or even less. So, in the way we have defined our test for any value of p greater than 0.6 we could still get 14 or fewer successes. I mean we could definitely get 14 or fewer successes with some probability what is that probability that is type 2 error. That means, actually the value of p is say 0.7 or any value like that which is more than 0.6, but our test says you got 14 or fewer successes. So, do not do not over turn the null hypothesis even though actually it should have been. So, that also is there. So, type 2 error is also there that we could continue to accept the null hypothesis and it is in fact false. So, that type 2 error also can be computed. So, any given test will have a type 1 error and a type 2 error. So, you have to sort of balance out these things is that ok. So, normally the first criterion for designing a test is a bound on type 1 error and that is called the level of significance. So, that is the first thing then if we have any leeway in defining the test either by increasing the sample size or by redefining the number of successes or whatever we are trying to measure then we can try for putting a bound on type 2 error ok. Normally, we if we have only one parameter in the test statistic one random variable in the test statistic. For example, the sample size is given and we just have to decide what is our threshold value for accepting or rejecting that is the only thing in our control. Then all we can do is put a bound on type 1 error and say that this is a level significance test for level of significance for this test. And we can say that there is a resulting type 2 error we cannot do anything about it, but we have control the type 1 error is that ok. So, in this example for a given x I mean for a given level like 15 for a given p you can you can compute the type 2 error and you have to live with that that is it. There is another term used called the power of a test which is 1 minus type 2 probability of type 2 error. This is another term that is used which is the probability that the test will reject H naught when H 1 is actually true. And it is in this sense that the that means we are doing the right thing we are doing the right thing in rejecting H naught when H 1 is actually true. So, that is called the power of the test. So, the the one of those four boxes. So, H 1 is actually true and we actually reject H naught. So, this bottom right entry in in this table of four that H naught is false that means H 1 is true and we reject H naught. So, that probability of that of that happening is is called the power of the test. So, it is 1 minus given H naught is false two things can happen either we reject H naught or we do not reject H naught. The probability that we reject H naught is called type 2 error beta 1 minus that is called the power of the test. So, we would look for a test with high power. So, this is the same thing this is what I said earlier. So, in our example for for different values of p we can we can talk of the power of the test. So, for example, p equal to 0.8 the power of the test is 0.804 for p equal to 0.9 the power of the test is 0.989 that means for for p equal to 0.8 the test will rightly throughout the null hypothesis it should because the the probability is actually greater than 0.6. In fact, it is 0.8 it should throughout the null hypothesis it will do that 80 percent of the time at p equal to 0.9 which is significantly more than 0.6 it will throughout the null hypothesis 0.989 percent of the time this particular test which is rejecting the null hypothesis and x is greater than or equal to 15. So, every test will have some power. So, you know we can we can define different rejection regions we can say I will I will throw out the null hypothesis null hypothesis p is less than or equal to 0.6 that is the null hypothesis I will throw it out when my test statistic is greater than 15 or 18 or 14. So, each each rejection region will will have different power I mean will different will have different type 1 and type 2 errors different power also. So, we just have to select the right one. So, to follow up you can you can just read chapter 8 of of the text book and of course, these. So, the material is very standard. So, unless you put pen to paper and try to just follow the examples given in the book there are enough solved examples in the book and you know one or two of these problems will be taken up for tutorial sessions. So, the the material is very standard. So, only you have to just get familiar with the terminology of this this this topic which is actually a fairly useful one. I mean it is a it is got an interesting history of how how people have tried to formalize uncertainty and it it is it is practically useful in in several domains and if you look up any experimental research work reported you will see level of significance reports of statistical I mean of any experimental data that you will see such terms being used. You know we can certify something up to some level of significance which means they are putting a bound on the type 1 error. So, in in statistical quality control certification sampling survey marketing you know anything where you are relying on for example, sampling from a small set of data or where you are doing experiments which are subject to uncertainty you have to make some statements and this is one of the standard ways of making it. So, it is it is worth knowing about this from a purely practical point of view it will help you understand what is the way people talk about uncertainty in a in a formal way. So, just two small things to to wind up one is that at least in the quality control type of literature where you are you are supposed to inspect and this thing the the term OC is used operating characteristic that is a curve I mean that just a plot of so in this case for example, P is the probability of success of that treatment I plot that on the x axis and I plot the probability of accepting the hypothesis. So, that is called operating characteristic and 1 minus that is the power of the test. So, that the term OC is used. So, that will be some. So, in this case as P increases my probability of accepting the null hypothesis decreases. So, it will you can you can easily see that this this function B is some decrease.


Do do then do followed by do do make the last word original do Duh genius. Oh, how can you so creative? Oh Calvin and duo want a new song wait. Yeah, I'm with the prince from Snow White. Give me a second.  She's a hit. What should we call it? Baby shark Yeah, sorry, it's my nephew. He's telling me what he wants for Christmas. Okay It's gonna work so well. Oh, Sean wants a new song. These are my diabetes test results negative It isn't in my blood I'm gonna call Sean and tell him that we got a new song.  Let's go travel. No, no. Come on. Let's go to Havana. We got a hit. Yes I'd like to make myself believe that Planet Earth turns Hey, can you buy a drug later? We have some to write now I heard that you and Billy are a thing now, huh? Uh, no, no, no, no Billy Jean is not my mother Okay, she's just a girl. Okay claims that I'm the one. Uh-huh. Okay, Bruce So before we write you a song, we need to know a little bit more about you. So Where are you born? Well, you're gonna make a song about that, are you? Oh, um, you know who cares about clever lyrics BTS wants a new song. No They're gonna pay a few millions the fans are crazy about them a few millions you say okay for the love of music Wait, we can't speak Korean. They want to mix both English and Korean and most fans don't really get the Korean part Anyways, so we have the toughest job. So trying to make it very very generic Love baby, I love us True lovers Okay now to make it original give me a random word DNA done the dog wants a song It's a worldwide But it's been units for so many years But it's those okay guys. I got thank you next. Thank you next. Thank you Why are you writing next? No, not now. Can we have the pillow talk later? Well, you think you could live without me, huh? Oh, yeah, how's the brain? I don't like carrots That's some 24 carat man.  I'm hurt. Oh, is it too late now to say sorry Look what you made me do Oh nice. Why are you gonna be so rude? Wait, no, there's a blank space here and our action


Hello friends, welcome back to another episode here on the channel. I hope you're all doing great. And for anyone new to the channel, my name is Lee, also known as Osiris. In today's episode, we are wrapping up the week with our series 11 sample teams. And today we'll be featuring a team from a Veltel. So if you've missed any of the episodes from earlier in this week, do go back and check them out from Monday through to Friday this week. We've had a different team and normally what I would do at the start of the week is just have a bunch of them ready for you to kind of pick off and use. But I thought this time around what we do is break them up and have a few battles with each team as we go through the week. And it gives you the chance to see the teams being piloted, kind of understand them a little bit more and give you a bit more insight into getting into using them in series 11. So hopefully you've enjoyed this layout more than what we would normally do and getting a bit more benefit from it. These rental codes will stay up for four weeks from this episode. So after that, they will come down if you do message after that point. Unfortunately, they will be replaced because we do like to put more teams out onto the rental system as we go through and feature more teams on the channel. Unfortunately, it's just Pokemon. You're only allowed five spaces at a time, which is just ridiculous. So hopefully that improves in the next generation, but that's an argument for another time. Getting on to today's episode. We have got an Veltel team and supporting cast of Reggie Steel, a lander as Tapu Fini, Incinero and Amungus. So we've got things in here where we can help some of the options in the team set up. The Veltel are very good against a lot of the format, you know, with the Assault Vest as well. Does have its threats that it needs to watch out for, but the Assault Vest kind of helps mitigate against a lot of those. You've got the Amungus in there with the redirection, which is going to be pretty big for this team. And then you're going to have to cover things like Zashian for sure because you're going to have Incinero in there to help with that. Intimidate. You've got double Intimidate with the lander is there to help shut down Zashian threats. You've got the Life Orb on lander. It's just to give us a little bit more extra power. And I feel like you can get away with it in this team with the redirection support from the Amungus. You've got a lot of set up you can see in the team and that's kind of supported by Fakeout and by the redirection from the Amungus. The other thing that you would think that would cause us a few issues would be maybe something like Shadow Rider Calyx, which Veltel deals with pretty handily. So you're primarily going to be looking at Tapu Finis to set up with the combines in the right situation. All that Reggie Steel that can pretty much win a game by itself with a combination of Amnesia or Iron Defense and then the leftover combination with that body press. So friends, here's the rental code. We'll have a couple of games of the team now. Hopefully have some successful games. So that'd be great. And then we'll wrap up with the rental at the end of the episode and that will wrap up our series 11 sample week. So hopefully you've been enjoying the episode so far this week and hopefully you enjoyed today's one. So without further ado, let's jump into game one of today's video. Okay. So first up today, we have a Raichu polytode, Galarian Maltres, Kingdra, Ushifu and Lugia team. So, you know, like on face value of it, we've got a pretty good matchup to kick us off with today. We've obviously got a lot of threats in there, like the rain cold that will cause us a few issues. But with the assault vest, alleviates a Veltals kind of pressure a little bit on that and respect of things. I think the one thing we could say is the Maltres probably gives us a few issues. I think we can get around the Raichu to a certain extent with our Amungus redirection. We do have Cobra very in there as well, but having the Veltal out in the field, it does give the Dark Aura boost to Maltres, which can be a little bit obnoxious to deal with. I think we're going to have to rely quite heavily on Tappofini in this one. It does pretty well against most things on my opponent's team. I've got a bit of a toss up here between like Incineroar, Landerous and Registiel. Like Landerous doesn't really offer us too much against the rain cold. It can hit Maltres for good damage, but if that's water, I think the Registiel, if that's water fighting Ushifu, then it gives us a hard time. Same with, can be said with Incineroar. Whereas I think if we've got Registiel, at least we've got a little bit of stability with something like Amnesia. We've got Iron Defense. We can kind of stack up on top of each other, which will help a little bit more. So we'll see. I can definitely see the Raichu coming here. I think it's going to be the big thing that my opponent probably utilizes to deal with the Veltal threat because it is going to be difficult for my opponent to kind of manage at least. We do see the Raichu and the Luga come out. And the one thing he would say is like, okay, do they have Fling? Do they have a way to proc potentially a weakness policy on the Luga? If they do, we can kind of mitigate that with the redirection. And I think here, rather than go for a dark type attack, initially we probably want to go for an airstream to try and at least get some speed control here. Although they're probably likely to go for airstream anyway into Amungus. We do have the Koba Berry to kind of compensate for that little bit of this turn. And then at least with the multiscale broken, what we can do the next turn is potentially go after with a dark type attack. But we're not going to see that. We're just going to see Polytod come in. Okay, which is not as bad really. I don't really know what to expect from the Raichu here other than a fake out, which it may go for. All right, there's a rage powder from Amungus. So we'll draw in a nuzzle potentially, which is, yeah, that's fine. And we get the speed jump on the Raichu the next turn. We still have access to Spore as well with Amungus, you know. That's the one thing that you could say about this team that you could maybe look at improving. I think the trick room matchup's not great. So that's kind of why I tended to go with a slow Amungus in this team. But you could say, because you do have that airstream with the Veltor, you could go max speed Amungus to take advantage of that. But I think probably better off going for max darkness into Raichu here just to try and get rid of it and rage powder at the same time. Because there's always going to be the risk at some point where Amungus might be paralyzed and then we've got that nuzzle threat. So if we can remove that, because it's bound to be sad. Oh, it's not even sashed. It is a fling variant. So we do remove it pretty quickly on the field. Special defense drop on the Polytod's going to be useful. It's just got, of course, hypnosis, but not going to be affecting our good old Amungus because we are paralyzed. So that complicates things and then the Lugia to come back in. Yeah, it's going to be a little bit difficult for my opponent to kind of get much momentum here. Because I think we'll rage powder again. But what we want to do here is kind of look at the power. So this is physical. We've got special 130, 120, 110. So we want to go for that. Ah, that's physical though, isn't it? It's physical, physical. And 110. Is it going to be enough to get the Polytod? I don't know after the special defense. We'll probably better off just going for the physical Max Darkness. It is going to be aura boosted. So we should get it from this range anyway. Just Polytod's more generally bulky on the special defensive side and the Lugia are going to Max here. So we'll probably see an airstream into Amungus, I would imagine. But as soon as that multi-skills broke, then Yveltos got, okay, up in hand, up in hand. Amungus is paralyzed. So what are we going to see? The thing is with the Lugia as well, is it is predominantly going to be special attacking. So if it attacks into Yveltos here, it's not really going to be able to do that much damage behind the assault vest anyway. As the airstream is into the Amungus. So we should take this, even help behind boosted. As I've said many times before, the issue with Lugia is it's pretty, it's pretty wiffy on its power output unless you've got a weakness policy and even then it's still going to struggle to damage, to get the damage out that you'd want it to. But with airstream coming out, yeah, we've got the redirection and we've got Snarl to break the multi-scale. Although saying that, we don't want to break the multi-scale with prior to the Lugia is going to attack first and the airstream is going to attack second. We might be better off switching. Like pulling a double switch here might not be a bad play. It's just then we kind of leave the... Yeah, I should feel kind of... Yeah, because they're going to airstream into Amungus and they're going to a surgeon strike. I just prefer to keep Evaltor at this point. I know it seems a bit like we could just attack here and rage powder, but we rage powder, they have the rain up for one. They're going to airstream into Amungus and then they're going to get the surgeon strikes into Arivaltor, which is not really... We don't want to kind of leave it out in the rain against that. I should be protecting here, okay. There's the airstream. Whereas now we're in a much better position where we can just go for a moon blast into the Urshaphuse, switch Regi, steal into Amungus because it's likely we'll see the surgeon strikes it into that slot or at least across combat, which Amungus are going to be able to soak up. And by doing that as well, kind of getting the regenerator activated as well. So it makes a bit more sense and puts us at a bit less risk as well. So we've got that moon blast this turn we can go into. We know the Urshaphuse protected that last turn. So tap-a-fini not in any sort of danger of getting knocked out here. I don't think even by a crit, I think we'll take it from Lugia. I'd be confident enough to say that they will be able to take that. So, ooh, Max Quake coming out. That's the choice. That would have been the switch into, ooh. I guess that's a nice player because you get the special defense boost, although not going to save Urshaphuse. But if they close combat into that Regi steal, yeah, that special defense spitter boost that they've got kind of lost. So the moon blast still going to be able to take it down to the sash and then Lugia. In a position where we can just go for muddy water the next turn, rage powder, and then get him Veltol and kind of clean up from that point. Because I think the one thing that we want to stop doing or not do is hit that Lugia with a dark type attack before we break the sash because if it has got the weakness policy like you would expect it to have just because the right you didn't have a focus sash kind of indicates it probably got weakness policy. As you prove protecting. Yeah, that's fine. I mean, that's still fine because like we just at this point want to break the multi-scale on the Lugia. We are slowing things down as the era blast comes in. Finally takes down Amungus. Hopefully the muddy water doesn't miss. That's all we want. Muddy water misses. Makes the game a bit longer, but it does hit. Thank you, Tapu Finney. And there is the multi-scale bust. So paving the way for Veltol to come back in. We still got Reggie Steel in the back. We can go for a snarl here if you want. Probably not a valid idea because then we'd only put the Lugia onto. We'll get rid of the Urshifu. And yeah, we'll just go for a moon blast as well because the snarl just gets rid of the Urshifu. Ooh, we are seeing calm mind. Okay, so the snarl is pretty useful in this situation at least. But we do have foul play as well that we can kind of fall back on. We're not seeing an Aquajet cover. Ooh. I guess with the speed boost, I didn't really account for that. But that's all right. The weakness policy here that I would be worried about. Yeah. But I think Veltol draws enough attention to itself where we've got Sucker Punch where we can Sucker Punch Moon Blast. Sucker Punch Moon Blast, Sucker Punch Moon Blast. We get the drop as well because that's pretty big if we do. No, no drop. No drop. Yeah, Sucker Punch should be enough. And then we can Moon Blast again. I mean, the other thing is we could Sucker Punch and calm mind here. But I think they expect Sucker Punch. But they're in a pretty awkward spot. The other thing to do as well, we do get it. So that should be enough. Ooh, not enough. Not enough. Arrow Blast. I don't think it's still even being enough. But oh, it's not. It's not. Okay, the imaginary sash there. Veltol hanging on and Tapu Fini able to kind of pick up the pieces. So Lugia, the one thing you can say about it is it is an absolute tank. It can take hits like nothing else in this game. So really good game to my opponent. Nice one for us to kick off with. Pretty close even though we had the definite advantage with matchup there. But what we'll do, friends, is we'll finish this one up and move straight into game two. Okay. Next up, we have number eight on the ladder and they are playing a team of Kyogre, Whimsicott, Zaptos, Metagross, Urshifu and Rillaboom. So looking at the speed control options, first off, you've got the Whimsicott with the tailwind there. You're going to have to worry about things like switcheroo as well, but not really too concerned with that in regards to Veltol. Because see with the dark type in there, it does give us a little bit of momentum around that. I think Veltol is actually really good in this matchup, especially if we've got like a Moongus support. The only thing you would have to worry about a little bit would be, obviously the Kyogre water spout gets around the redirection, makes things a little bit more tricky for us, of course, and Zaptos as well, because it does have the max airstream, but we do have the opportunity where we could potentially put it to sleep. Do you like the lead of Veltol and Moongus? Think in the back, think like Finney and maybe Reggie Steel could actually not be a bad option. It just leaves us a little bit short against Rillaboom, but I mean with the Moongus and Veltol, if we kind of protect them well enough, we should be in a good enough spot to kind of deal with those threats and then have everything kind of left, else left over. So let's lock in with these and see what my opponent locks in with. Veltol feels very hard in this format though, you know, it really does. It feels very difficult. It feels a lot more difficult than I would even say, I don't know, like Xerneas feels difficult in this format in particular, but Veltol feels very difficult at the minute. So we're going to see Whim's Cut and Zaptos come out. We've also got threats of like taunt that can shut down our Moongus, but we can go for an airstream into Whimmy Turn 1. Obviously we can't rage powder if the Whimmy decides to go for a Moonblast here, but that's kind of not the worst if they do. I think we've got to try and keep pace with the Zaptos. They could just tailwind here and go max airstream themselves. But with the Assault Vest on Veltol, we've got a little bit of stability against this kind of team. So it's just kind of carving out and trying to get rid of the support options. Obviously trying to mitigate as much damage as possible here against the big threats because Zaptos, definitely a big threat against Veltol. You know, it's the thing that Veltol doesn't really want to face down against, but we'll stay in. Landerous is very hard to bring to this game, especially when you're not playing Assault Vest Lando. I think it becomes a bit more difficult. Assault Vest Lando against this sort of team you could probably get away with, but it's not what we got. So we have to deal with what we have at hand. But I think the big thing my opponent's going to want to do is try and get rid of the Veltol soon as possible. We've got to worry about potentially like safety goggles on that Zaptos as well. That could be something that really throws a spider in the works. And if you take a max line in here, turn one, that could be pretty bad because they could both pretty much ignore what Amungus throws out here, you know, trying to redirect and both attacks just go into Veltol. So we do see the switcheroo is going to be with the Amungus. I'm going to take a Kobo Berry and they're going to take it. So that's a really nice play from my opponent because now they're going to be able to just get rid of the Amungus pretty easily. So you can see the utility there. And you know, we do obviously take the eject button, but now this Whimsicob is going to be in a spot where it is going to be able to actually take our max air stream, which is pretty impressive.  But I mean, it makes more sense to have the Kobo Berry, especially staying in against something like Zaptos. You're going to have that item. So not ideal, not an ideal start for us. Do we bring in Finny or do we bring in Reggie Steel and start getting some amnesias up? It's just a taunt. Do they have taunt? Have switcheroo, but that item is gone. And I think they have the max light in this next turn. So I think we'll air stream again and we'll go for an amnesia here. And we'll see what this Whimmy does. They may double into Veltol here, but if they're doubling into Veltol, they have to kind of get away from using air stream and go for max lightning. So it may be a case where the Whimsycut goes for a tailwind and its last kind of turns. Okay, it's going for the taunt. Want it to up to shut down the Reggie Steel. Okay, and they're going to persist with these air streams. We take that pretty well and we'll be able to get rid of the Whimsycut in the process, which is good. So this is not, like all hope is not lost just yet. Just yet. Um, obviously going to have a max lightning to have to contend with the next turn, but we do finally get rid of the Whimsycut, which is always good. But Reggie Steel being taunted is not ideal because we can't actually use the amnesia, which we're going to really rely on quite heavily in this match. All right, imagine Kyogre to come in here because you can air stream. Yeah, but it forces the Zapdos to air stream here and not go for lightning. Because if they don't air stream, then the Velta will outspeed the Kyogre and get some big damage off. Um, so we'll go for the air stream again. We'll switch out Steel into Tapu Finney. It'll be interesting to see where the Zapdos goes with this play, whether they go lightning to just try and knock out the Velta, which they're not going to be able to do with our Assault Vest or if they go air stream to kind of just get that initial chip and then get the big water spout damage onto the Velta going into the next turn. The thing is we still have Sucker Punch. So as long as the Velta can kind of stay like hold out this turn, we might be in with a chance. We may be. We'll see. Can the Velta do the work? They still got three Pokemon. We got three Pokemon, but that might change after this turn, of course. So there's the air stream again going for the air stream water spout. We should take the water spout from this range. And Tapu Finney undoubtedly will. But it's going to be about getting enough damage onto the Kyogre, really. Oh, we have to speed the Kyogre. So if they do water spout, at least we are weakening it. That's that's pretty huge for us. So let's see what this Kyogre does. Water spout would be. Oh, it's Origin Pulse. So they knew they knew. So we've got a sucker punch that we can utilize. Just where we go with the sucker punch, really. I mean, we could sucker punch.  Probably want to sucker punch the Kyogre, to be honest. We'll probably get a bit more mileage. Sucker punching Kyogre. Do we protect here or do we attack? There's a Zapdos. I think the Zapdos goes after the Velta here, which could leave us free. That's why it might be better to, in all honesty, like going for the sucker punch into Zapdos and then going muddy water into it as well and hope that the Zapdos attacks into the Velta. Yeah. Okay. It's really, really, really boom. It's not ideal. But if we can get rid of the Zapdos here, that's huge for us. Huge. I don't think we're going to be able to get rid of it. Thunder into the Velta. Yep. It's just about whether this muddy water can pick up the knockout onto Zapdos or not. Should be able to if it hits. Connects in the rain. Yeah. Obviously, we've got to contend with the Rillaboom now, which makes our lives way, way, way, way, way harder. But if there's ever a mon that can beat these, it's going to be Reggie Steel. With one amnesia, we might be all right because the rain will be stopping soon. Well, stopping soon, I say a couple of turns. Still got two turns left, I think. So let's see how many turns we've got left. All right, we've got three. Three is too many. Are they going to, are they going to fake out here? Maybe not. Okay. Let's just double protect around this fake out because it just gets around the rain that little bit longer. What we need to do this next turn after this is amnesia, take a origin pulse and then protect again. And then the rain's gone. There's the fake out. Yeah. And on origin pulse, we could have gone attack off with Finney, but we didn't. So let's see, let's see, let's see, let's see. Right. We need the amnesia. I'm not too worried about the, the, the really boom. I don't think that damage is like that crazy. We could try and get a cheeky moon blast into the, the Kyogre. Cause if you get the special attack drop, that's, that's pretty big. But I think though the really boom probably goes grassy gliding to Finney now and take this origin pulse down to a single target attack, which is what I probably wants to do. But if it misses, oh, the water spouting, huh? Oh, jeez, juice, the juice. Right. We don't need to worry about Kyogre anymore. It's more the really boom I think that we're worried about. Um, so we need to get an eye and a fence up really. I mean, we protect this turn and then the rain stops, but the grassy terrain actually helping us out. Probably a little bit more than it is my opponent, to be honest. And that's the next thing we need to, to try and see, like, hopefully stall out the grassy terrain. Cause the really boom is still going to hit us hard, you know, especially if it's got like wood hammer. And I don't know if we'll be able to take the double up. So water spout, water spout, the rains, nowhere near as, as, yeah, the knockoff. That's not good. Yeah. The knockoff is not good. Yeah. Cause then we lose our way to, um, I'm going to be very, very close. Yeah. We lose our way to stall, especially cause the, um, the grassy terrain is going to be gone soon. So right. Let's go for an eye and a fence. Let's see. Let's see. It's going to be close regardless here. There's a water spout. Right. You know, we take that pretty well, pretty well. I don't know if we're going to be able to take. Yeah. The knockoff. Okay. That's not too bad. It's not going to do as much the next turn.  We'll get a grassy terrain boot. We're not going to be able to do it. We're not going to be able to do it without our leftovers. We can't do it with leftovers. Yes. Without leftovers. No, no chance. I don't think I think we'd have to have them go for a, I could see them protecting with Kyogre here. We'd need them to go Origin Pulse and miss and then I think we could maybe do it, but I think water spout going to be too strong. Yeah. Okay. We'll go get into my opponent. They're pretty high up on the ladder able to kind of cut us out of being able to kind of function there. But we've seen two good games with the Avaltel team today. So I hope you have enjoyed them and I hope if you do try the team out for yourself, you do have a lot of fun with it. It is another Pokemon to consider to look at and try and see if you can get it working in this format because I do think it has a lot of positives and it does act pretty well. So we'll wrap up now with the rental code for today's team. Okay, friends here is today's rental code. If you do try it out, I hope we have a lot of fun with it. Thank you so much for tuning in. Do leave your comments down below if you do try the team out and let me know your thoughts on Avaltel in general. I feel like it is a difficult Pokemon to play in the format at the minute. It does have some really nice matchups, but it also has some very difficult ones in the current format, especially in the early stages. But it is another restricted to try out that will be on the radar of a lot of players going forward in series 11. So thank you so much for tuning in. Friends have a great rest of your day and I will catch up with you all again on another episode on the channel. So until then, take care and bye bye.


Hi there today. We have a fountain pen a boxing for you. This is the stipula Castoni chic fountain pen and you have the red and gold Packaging from stipula and the sleeve just pull off and inside is another red box The pin is nested right on this white slash ivory velvety liner and so a false bottom You can access the brochure full of all the warranty information and a brand information about stipula and their pins And then underneath that is their certificate of authenticity for your stipula cast on the chic fountain pen Okay, let's get a better look at this lapis lazuli and here's the beautiful High-grade resin and this is a handcrafted Italian resin And it is trimmed in a chrome plated trim You do see the name stipula engraved on the barrel as well as made in Italy, but it is a really subtle engraving And sometimes it's really really obvious, but this one is actually very subtle So the chrome trim you'll see in this the center ring at the bottom of the cap and then another in the pin clip as well as the Ring around the top of the cap and then one more ring at the bottom of the barrel. I do love the Fluting on the cap and that gives it that unique shape right the pin clip It comes to its thinnest point at the cap right at the pin clap attachment point. Here's a look at the nib Your stipula cast on the chic fountain pen is going to be fitted with the number five stainless steel nib And I do like the engraving that they have here. It's it's very subtle again, but it's nice Here's a look at the feed for you And you do see that the section matches the Barrel so it's just resin same resin as the cap and barrel And it does post it's a friction post and I didn't note specifically all though You can very obviously see it that they do have an embellishment on the end of the pin clip And it's a spring metal clip and that embellishment is going to coordinate with the color that you choose So this is the lapis lazuli. So it has a lapis lazuli vivid blue colored Stone or not stone embellishment. I'm not sure that it's actually a stone Okay to access the cartridge converter filling system you just remove the barrel from the section and Either put in your converter that's included in it with the pin for fountain pen safe bottled ink Or you can replace that with an ink cartridge and it's a standard international size If you want more information visit pinchlay.com


Before I get into this video, I want to remind you that we're on our road to 133,000 subscribers and I would appreciate if you just subscribe to the channel and help me chase my dreams of being a full-time YouTuber. Now on top of that, we have a giveaway going on as well for a replica Hylian Shield along with two Zelda OLED Switch editions and two Tears of the Kingdom Collector's editions as well. This is a kickoff giveaway for Prime Gaming Fest which begins on June 8th next week. We'll give more details on Prime Gaming Fest by the end of the week with an announcement video and more, but that being said, we gotta get into this video. Now we made a video, I don't know, a week, two weeks ago talking about the impossible, how devs are so impressed by what's happening with Tears of the Kingdom that they can't help but be having their jaws to the floor.  Let's get into this article by Polygon which describes this in more detail from even more developers including people who have worked on games like The Last of Us Part 2, God of War Raiden Rock, you know, not just some highly praised games that haven't out there for quite some time, so it says why Tears of the Kingdom Bridge physics have gained developers wowed. Again, this is by Nicholas Carpenter, an article that he wrote over on Polygon. So there's a bridge across the lava pit in The Legend of Zelda, Tears of the Kingdom, the Mara Kuguk Shrine, I still don't know how to pronounce any of the shrines in Tears of the Kingdom, but it's broken. More than half the bridge is piled up on top of itself on one side of the pit with one clipped off segment on the other. The bridge is the obvious choice for crossing the lava, but how to fix it? A clip showing the potential solution went viral on Twitter shortly after Tears of the Kingdom's release. The player uses Link's Ultra Hand ability to unfurl the stacked bridge by attaching it to a wheeled platform in the lava. When the wheel platform now attaches to the edge of the bridge, activates and moves forward, it pulls the bridge taut, splashing lava as it goes until the suspension bridge is actually suspended and can be crossed. But it wasn't the solution itself that resonated with players. Instead, the clip had game developers' jaws on the ground, and all of how Nintendo's team wrangled the game's physics system to do that. To players, it's simply a bridge, but to game developers, it's a miracle. And then here's that clip in question. You guys might remember this shrine, I know I remember doing this shrine vividly, and this is the thing, or one of the many things in this game that has developers just in awe of this physics engine. You can look at all of the individual interacting bridge pieces, plus this, a different physics item going across the lava, which is a different physics item, and then obviously you can actually walk across that bridge. Alright, so the most complicated part of this game is when different systems and features start touching each other, says Sanya Moon, a technical producer who's worked on games like 2018's God of War Reboot and its sequel, God of War Ragnarok, to Polygon. It's really impressive. The amount of dynamic objects is why there are so many different kinds of solutions to this puzzle in particular. There are so many ways that this could break. Moon pointed towards the individual segments of the bridge that operate independently. Then there's the lava, the cart, and the fact you can use Link's ultra hand ability to tie any of these things together, even the bridge back onto itself. Nintendo reportedly used a full year of Tears of the Kingdom's development for polish and it shows. The amount of different options available is a testament to the amount of work that every single person at every level of the team did, especially the QA testers Moon said. Open world games with a ton of real time physics objects like this are notoriously difficult to QA test. Another big game that inspired this sort of physics based shock and awe from game developers on social media was in 2020 when the last of this part 2 included a rope necessary for solving a puzzle. Tears of the Kingdom's bridge, the rope, and its natural seeming movement were just something players expected to work, but game developers could see how much work went into the development of it. The bridge has a ton of different points that are pulling on each other within the physics system. So Luna Nielsen, a software engineer who goes by Luna the Fox girl online and live streams about the complexities of game engines. It gets into some pretty mathy stuff. It can get really funky when something pulls a bit too much and suddenly the bridge is inside of itself. So it has to push it out. And then one thing has to move too far back. It starts getting really bad because the pieces of the bridge are basically distinct from each other's movements. Software engineer Cole Wardell put it another way. Imagine the lava bridge above. When you grab the end of it, you will pull part of it to one side, he said. Well now that drags the other attached piece a little bit with it. And the piece moving along makes the next piece move. And so on and so forth. And if any one element of the track collides with something, it has to be nudged or slid back into somewhere that doesn't collide, which moves the pieces next to it, which moves the pieces next to it, etc, etc, etc. Last time I saw something this impressive, physics and gameplay wise with the rope in Last of Us Part 2. And the rope only appeared in a few very controlled scenarios. Said Rocksteady Games senior gameplay and programmer Adit Doshi on Twitter. To be able to confidently present the player with a stack of blocks that are linked with chains that move in accurate ways without clipping, without objects shaking like crazy as it tries to figure out what it needs to do is awe inspiring. Here's The Kingdom also has its own rope like physics flex. Another viral clip shows a door opening using four wheels and a chain. That's a complex interaction and takes no shortcuts. Wardell told Polygon, as a rule, physics engines take a lot of shortcuts and make a lot of assumptions. Both for the optimization purposes and to keep developers from pulling their own hair out, Wardell said. Almost all of these shortcuts, whether it's collision-free ropes or rotating objects, only apply forces in specific ways, which would make this kind of mechanism flat out and not work. Or the chains start vibrating until it disappears from view in a single frame or some other infamous physics glitch. And this is the video you're talking about here. You see the wheels here while we're riding this here. And you hit it and you can see that it rewinds this rope all the way up the wheel and it does it on wheels on four sides to open and lower the door. So it's wrapping rope around the wheels. Pretty interesting. He said that rope bugs vibrating out of control are so common because of these problems. If you don't do everything just right, one movement will cause the other parts of the rope to move and their movement will cause more collisions. God forbid you want the rope to collide with itself. Those collisions will cause more nudges, which is more movement, which ends up with your rope vibrating out of the map. Doshi explained that complex physics are common in games, but said tears of the kingdom pushes the limits of its engine to create exceptional gameplay and puzzles. Realistic physics simulations take hours to do calculations to make sure it is highly precise and accurate. Game physics need to produce similar results every 16 to 32 milliseconds or 60 to 30 frames per second. Some games are able to avoid these complexities by designing around them. Doshi said that means restricting players actions, which is the antithesis of tears of the kingdom's design. There are constraints, but somehow in this game it still feels like nothing is off limits. In game development, it's not if physics will break down, but when gravity will senior engineer and former Call of Duty developer Josh Hortelli told Polygon. That's why there's a whole Reddit page about physics goose, other players ragdolling into oblivion or enemies bouncing off the walls. It's not that games of physics bugs or glitches are poorly made. It's really easy for things to go wrong. Cartelli stressed, however, that tears of the kingdom's physics are not magic. It's clear that Nintendo greatly understands the physics interactions in the game. What's extremely technically impressive is how stable it is and how it all fits together in a way where there's no pre-programmed solution and players can solve puzzles with complete freedom, Cartelli added. Moon noted that it's not exactly that other studios can't reach this level of technical innovation, but they don't prioritize the resources needed to do it. Often that comes down to supporting the humans who make the games we play. Tears of the Kingdom was seemingly built on top of Breath of the Wild, reportedly with a large portion of the same team working on it. There's a problem within the games industry where we don't value institutional knowledge, Moon said. Companies will prioritize bringing someone from outside rather than keeping their junior or mid-level developers and training them up. We are shooting ourselves in the foot by not valuing that institutional knowledge. You can really see it in Tears of the Kingdom. It's an advancement of what made Breath of the Wild special. According to Moon, it's increasingly common for game developers to feel like they're holding some feature or another together with duct tape. Figuratively speaking, after the person who originally spearheaded its design got laid off. There's a lot of time when wasted reconfiguring and assessing how something was well done. It's not that Nintendo doesn't have its own problems because it certainly does. And Nintendo of America QA testers spoke about the frat house experience within Nintendo of America's Washington headquarters last year, but the company does appear to value the expertise of its development staff. In addition to the overall hard work of the team, the institutional knowledge is clearly a factor in why this ended up being so smoothly done, Moon said. The more stable and happy people are, the more they are able to make games of this quality.  And that last statement really hits home on what makes Tears of the Kingdom so special. Look, I've seen the comments out there. I've seen you guys, some of you people out there that responded to my last video, video sense saying, you know that this really isn't that impressive, the frame rates drop here and then, look guys, there's some technical limitations with the hardware, right? We've already noted from people like Modern Vintage Gamer that with some slight memory over clocks, you can actually make the frame rate in this game in almost every situation, be it a locked 30 FPS, right? It's literally a hardware limitation and it's already been proven and if Nintendo decided that they could mess with the clocks a little bit, just with those slight memory tweaks, they might be able to fix that but Nintendo isn't going to do that because who knows if it messes with other people's games. But the point is, the point in all of this is that the frame rate stuff might just be a technical limitation that is totally fixed by new hardware. That's not what people are talking about when they talk about how impressive this game is. This entire article by Polygon, which credit the Polygon for putting together an absolutely fantastic article, reaching out to big name developers to get their insight on this, how the industry works versus what Nintendo's doing, how they somehow made this seemingly impossible game and noting at the end that the reason that this seems impossible is because of how the rest of the industry works. Letting go of people who came up with an original concept in the first place, then having other people have to duct tape that back together and make it work, that's hard. Versus Nintendo where you have Owada cutting his own salary to keep game developers. This is something that we need to remember happened back in the Wii U and 3DS days. In the heyday, when those systems first came out, Nintendo wasn't doing very well. They had their first year ever of actual net loss and they actually had that happen two years in a row. It's the first time in video game history for Nintendo that happened. Nintendo was not in a good place and Nintendo, like many other companies, could have just done what is logical. Hey, the company isn't doing very well. We're losing millions and millions, hundreds of millions of dollars a year. You know what? Maybe it's time for us to cut our losses and start firing our developers. Instead, the entire executive team, including Owada himself, took massive pay cuts, trying to encourage keeping the development staff together, noting how important that team was going to be to turning the company around. Fast forward to the launch of Breath of the Wild and Super Mario Odyssey, Super Mario 3 and Animal Crossing and all the rest, you know, Pokemon notwithstanding in here. It's very obvious to see that continuity and keeping the same development staff around and keeping them happy and making them not wanna leave and just letting them finish what they started is something that has led to this being a one-of-a-kind experience that truly feels like only Nintendo seems to pull off because they are the opposite of the culture that exists in most of the game development world where a lot of companies view every staff member as dispensable and easily replaceable. Nintendo actually values each member of the team and knows the work they do is important and matters and can only become more important and matter even more the longer they're there and the more, you know, they get credit for what they're doing, whether it's through compensation or promotion, almost all of Nintendo's promotions have come from within the company starting from the bottom. So, you know, Nintendo, as they said, isn't without issues. Their QA testing team, you know, we covered all that extensively with all the speaking out at Nintendo of America, but at Nintendo of Japan, we don't seem to have these sort of problems happening and this is where a bulk of Nintendo's magic happens, those Japanese development studios. So, we gotta just give tears of the kingdom the credit deserves, the developers the credit it deserves. Whether you get mad about the frame rate or not or whatever, the fact that all of this stuff just works is something that us as gamers sort of take for granted. We took it for granted with Breath of the Wild, but in Breath of the Wild, you know, there were some limiting factors with the abilities and those factors have just been cranked up to a thousand here and I'm just, I am utterly impressed. Every time I play this game, I'm amazed at the things that I can do, the things I can build, the way it interacts, the way the physics engine just works and makes sense. Like, say I send a Korok flying off with a rocket and I mess up, nothing about it felt like it didn't make sense. It wasn't like he teleported or bounced at a weird angle. All of it made sense. Oh, the rocket went this way, it exploded. He went over this direction and then maybe he hit a tree branch or a falling thing from the sky and that bounced him and it all just makes sense. The number of calculations happening in this game at all times and it's just flawlessly working without breaking, without clipping, without crazy shenanigans happening is utterly insane and while some of you guys might be able to point out a bug here or there, this is an open world game. This isn't happening in the controlled scenario room. Like, oh, the rope bridge or those wheels doing the rope or oh, here's that metal bridge that we're using multiple physics engine impossibilities to make work. Yeah, those might seem like enclosed rooms.  It works this way in the entire world of Tears of the Kingdom. So impressive what they're doing and I don't know that Tears of the Kingdom is ever gonna not feel impressive for many of these developers. I am happy to see that some of them said it's not that what Nintendo did with Tears of the Kingdom is impossible. It's not. Other developers work hard. Other developers could pull this off. They're just not really given the ability to do so. Sort of throwing shade at all of these AAA development studios that don't value the employees. If you start valuing the employees more even if they crunch whatever, if you have to value the employees more and they stick around and you don't fire them and you're not doing temporary contracts, maybe you could get this level of polish and capabilities in a game. But until then, lots of development tricks and even something that looks super impressive will be extremely limited like Last of Us Part Two with the rope stuff. Apparently that was very, very limited in how they could do that because of just, you know, just needing to make it that way that couldn't just make that the way the whole game works. There was very specific segments of the game. Guys, I'm really impressed by Tears of the Kingdom every single day and so is the rest of the game development industry. Thank you so much for tuning in and we'll catch you in the next video.


I am Dr. Sindhu Paul Kavilakat, consultant radiation oncologist working at Manipal Hospital, Bangalore. So, IMRT or Intensity Modulated Radiation Therapy is one of the most advanced forms of 3D CRT. In IMRT, each radiation beam is subdivided into hundreds of small beams or which are known as beamlets. Entity of or strength of each of these beamlets can be modulated or modified by using various beam modifying devices known as multi-leaf collimeters or MLCs. So, IMRT is of particularly it is valuable or useful in treating some targets with either a concave or complex shape or with close proximity to radio sensitive nearby structures. This technique is mainly useful in situations either we have to give a very high dose of radiation to the tumor or target, example carcinoma prostate or prostate cancer or where we have to restrict dose to adjacent critical radio sensitive vital organs, example as in head and neck cancer where the spinal cord will be coming in close proximity to the tumor or target. IMRT can be delivered by two mechanisms either the MLCs can move and treat this is known as a dynamic mode also known as a sliding window mode or MLCs will remain static will acquire some specific shapes and treat which is known as a static or segmented MLC technique. IMRT can also be used for intensity modulated arc treatment as well.


Hey guys, welcome back to my YouTube channel. This is Daniel Rosalha here. I want to do a video regarding how to downscale the resolution of a video using the Cadenlai video editor. I'm using it here on Ubuntu Linux. So something I was doing this morning was I'm working on a video from a conference that I attended a few days ago in Italy. This is a video of one of the panels that I received from the conference organizers and pulling out some clips for YouTube and I'm also going to put the whole video up. Now you can see what resolution you're working with usually by looking at the top of Cadenlai. You can see here it says 4K UHD 2160p. So the frame rate and the resolution is going to be automatically picked up by Cadenlai when you import your video clips. Now sometimes it just doesn't make sense to have 4K, you know, if this video is being shown distributed for viewing at a on a huge conference screen, that might make sense for putting something on YouTube. 4K is going to involve a large storage overhead and for, you know, a basic talking head video like this where it's two people talking one another, I think 1080p is better. It's going to take up less space and more importantly it's going to streamline my workflow process a lot. It's going to be a lot quicker to get that up on the internet with my bandwidth. So how do you do that? So when when you get to the rendering stage in Cadenlai, so you choose firstly your rendering profile, your usual quality settings, full project, etc. And then there's a little tick box here and it says rescale and it's actually by default selected for full HD, which is of course 1920 pixels across and 1080 pixels up. But the nice thing here is that you can choose it, you can choose to lock the aspect ratio. So for example, if I wanted to render this out in 720, it would pick that out. I'm not sure that it's whether that was locked or unlocked. But in any case, if you're working with 4K, and you want to get it to 1080p, aka FHD, full HD, this is probably the most common use that people will be making. So by default, this is unticked just like it is now. So what you want to do is tick on rescale, get the resolution that you want, you can see they're locked together now. And then when you render that video, it'll be in 1080p rather than 4K. And therefore it'll be much less space to store and quicker also to get up to the internet. Hope that video is useful. If you want to get more videos from me, please subscribe to this YouTube channel.