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.