 We are doing inferential statistics and I told you in previous lecture that there are two basic components of inferential statistics. Number one, estimating population parameter and then number two, testing hypothesis. Basically, all the concepts are interrelated and they are connected and estimating population parameter is very much linked with the testing hypothesis. So, aajam particulari statistical testing karenge hypothesis testing kanda, let us do some definitions and try to understand what do we mean when we talk about testing hypothesis. So what is logical hypothesis testing? Basically we hypothesis testing is a statistical procedure that allows researcher to use sample data to draw inference about the population of interest. For example, like we talked about the average IQ of the university students that is 100. We drew sample say 50, 30, as much as we drew sample and we thought sample that is greater than 100. And our sample mean, average that is 15, now we basically have to go with an assumption, we will start with a neutral assumption and we will make some assumption about the population. Overall, university students average IQ that is 100, like mu is equal to 100. But you collected sample and your mean is 150 in that sample, your EI. So now, how we will test the population parameter, what will happen? We talked in last lectures that it is not possible to study the entire population and we talked about how we estimate the mean or standard deviation of the population. That was point estimation or by making confidence interval and estimating the mean of the population between the two values. So now if we say that the average IQ is 100 but your sample is 115, then we will make some assumptions. So that is what hypothesis testing does, it allows researcher to use sample data. So you already have a sample data, which has the average mean of 115. So you will use this data to make some assumptions about the population or draw inference about the population. Now how will you draw inference, you will either say that the mean of population is not 100 or you will say that the mean of population is 100. So this is we are going to test the assumption through testing hypothesis. So hypothesis testing is a statistical method that uses sample data to evaluate a hypothesis about a population. So your sample data, your statistical data you have, you will use that data to draw an inference about the population parameter, whether the population's parameter will be the same or not. So we will use different statistical tests in the future. Starting with the logic of hypothesis testing, what is the definition of hypothesis? Hypothesis basically is an assumption or is a tentative statement, right? Hypothesis is a good hypothesis that is testable, any statement that you can test based on the sample data and you definitely make assumptions about the population. So let me say hypothesis is an assumption made about a population, remember hypothesis is tentative statement which we test, after testing we evaluate the statistical value and then on the basis of its statistical value we decide what inference we have drawn about the population which we will do step by step in a moment. Before we select the sample we use the hypothesis to predict the characteristic that the sample should have. Before we select the sample we use hypothesis, that means before collecting the sample you make a hypothesis and then you test that assumption. Now you will say that if the sample is not collected then how will I make an assumption, right? So basically I would like to talk about deductive and inductive approach, mostly when we are doing deductive research then we already have theories, our theoretical framework like you will do the thesis, you will do the research then you have to give a clear theoretical framework. So our theories, our research is already guiding us towards one side, right? So then we make a hypothesis on its basis and then we collect the data to test the hypothesis and then we test it and then we draw the inference about the population. Next we obtain a random sample from the population and finally we compare the obtained sample with the prediction that was made from the hypothesis. That means we will first see what it is, we will make a hypothesis on it, we will collect the data, we will test the data on the sample and then we will draw the inference. Let me give you an example of the logic of testing hypothesis, first let's say there is a stock market and there is a XYZ company in the stock market whose shares are there. If I draw it here then over the last 10 years the fluctuation of the shares is like this. So from 2000 to 2020 the rates of the XYZ company shares in the stock market are like this. Now you can see that there is a zigzag in it and there are ups and downs in it but if you look at it overall then you can see that the trend is increasing and in 20 years the price of the shares has gone up significantly. Now we have to make a hypothesis on it that whether the company's shares are profitable or whether the XYZ company which we have seen the data is like there is a trend which will continue or there is a trend of increase in the price of the shares or it is just a random noise that it is zigzagging and so we then make a hypothesis for it. So the logic of hypothesis testing is that whatever assumptions you have in the real world you keep it in a hypothetical scenario and then you test it to make it real to make it concrete. So the basic idea is like having reason about the real world by setting up a hypothetical world. I mean I have a real world data like the price of the stock is up and down but overall a trend is there. So I want to take this example from the real world and I want to make it a hypothetical world where the XYZ company which is the stock's price of shares is in an increasing trend for the last 20 years but against that we will talk about the null hypothesis or alternative in which we can say that there is no such trend, this is a random noise or this is just a random walk. The observed patterns of the data are then compared to what would be generated in the hypothetical world. So just as I have told you that our previous 20 years of data, if I base it on that then I will say that there is a trend of increase, so I will build my hypothesis which is research hypothesis then I will collect some more data about the XYZ company and then I will test that it is just a random noise or there is a trend in the price increase. So hypothesis testing helps us to test the real world problems in an objective way, put a statistical test on it and then we install inference that what are the things happening in the real world that we can test and what conclusions about the bigger population we can give. When you being a scientist always remember that we are interested in the bigger population, we want to draw inference about the bigger population rather than just the small sample. So in the next video we will see what are the steps for hypothesis testing,