So let's have a look at a contingency table, we're gonna make these rows and columns of values. Now we looked at an example in the introduction, but let's construct a more proper one. Still this study never existed, I just wanna show you the numbers. So let's do randomization by stratification. So we're taking random samples by some mutually exclusive trait in our population. We're going to do a cross-sectional study. In other words, something like a survey, so we're going to hand out a questionnaire. A questionnaire answers is going to be likert style and of an odd scale. In other words, five choices or seven or nine choices to choose from when they do answer a question and let's just look at the results of a certain question. Now let's imagine that the stratification was by hospital department. So that's in the mutually exclusive trait, anyone who works in either one department or the other department. The choices that they could make, this likert scale is scaled anywhere from strongly disagree to strongly agree and it's asking the question, does the university need a medical education department? Now in many third world universities, there is not an individual department that just looks at medical education left up to the individual clinical departments themselves. So let's look at that. Our stratification was by department and here, we have a surgery department and a medicine department and what we're interested in is not the individual choices. We now want to make lists of those values and get the mean and the variance and compare those means to each other. We just wanted to know in the surgery department and in the medicine department, how many times that the choice strongly disagree occurs? So twice for the surgery, three times for medicine. If we look down the surgery column, we can add all of those values up and that will show us that there were 23 individuals who took part in the surgery department and 21 in the medicine department. So those are for the columns, but we can also tackle the rows. So we can now see that there were five individuals who chose strongly disagree and ten individuals who chose strongly agree. We've got to ask ourselves now, what do we do with this table? What does this table mean? Well, it is a table just about observations. We just totaled our observations in tabular form. Let's just construct another one before we go any further. Let's just look at the development of COPD in smokers. So we take a random sample of patients with chronic obstructive airway disease, there were 248 of them in the history. We note that 23 of them had a substantial history of smoking, then we took 1,001 patients without any pulmonary disease and we note 49 of them had a substantial history of smoking. So with that information, do we construct a contingency table of observations? Well, this is how we go about it. Remember in the pneumonia disease group, there was a total of 248. There were 23 that smoked. You just have to subtract those two from each other to get the no smoke, which is 225 the non-smokers, so that will be our contingency table of our observationsa as long as those totals add up completely and correctly and we can now also see the row totals there. There were 72 with a history of smoking and 1,177 who didn't. Those are contingency tables of observation. You're going to ask yourself a question, so we have this data, how do we set our hypothesis? How do we go about,? What design or null or alternative hypothesis? Well, the null hypothesis really is that there is no association. So for our last example, there would be no association between disease and smoking. For our first example, there will be no association between which department an individual came from and the choices. The alternative hypothesis states that there is an association. There is an association between smoking and smoking and the development of COPD. There is an association between which department someone came and the choices that they made. So those would be where we have a p-value if our significance level was 0.05, a value less than 0.05 and we said, it was unlikely to find this type of observation. This is the table of observed values and we say that it was unlikely. Therefore, there has to be some association. A null hypothesis, there is no association between the various groups. In the next section, we're going to move away from this observed values to what we would have expected, because we're going to compare this observed values to some expected values to work out a p-value.