Hi everyone. In the previous lecture, we talked about longitudinal studies, and how these studies induce correlation by looking at repeated measures over time. In this lecture, we will talk about another way studied designed can induce correlation through a single level of clustering. We will define what a level is, and what a single level study entails. We will also discuss how this study design induces correlation. The term clustering will also be defined. Finally, we'll learn how to recognize a study level when we see one, and we're going to recognize that there are many other terms used in many different fields that are synonymous with the term level we'll be using in this course. It is important you realize this as when you see this terms in other fields, you will be able to recognize them, and understand what they mean with this terminology. When we refer to a level of data, we're just referring to a position within a hierarchy. Studies can have any number of levels, and this course will look at both single level and multi-level designs. To make this easier to understand, we will look at an example of levels. A school has a hierarchical structure. Another way to put this is that schools have levels. For example, within each school is a number of classrooms, then in each of these classrooms is the number of students. This tells us that there are two levels within the school. The whole reason we care about this for power and sample size analysis is because levels within a study induce correlation. For example, measurements from students within a classroom will be correlated because they have the same teacher, do similar activities et cetera. Measurements from classrooms within the same school will be correlated because they take part in the same admitted a shrine of leadership team, wanted this same halls ways, interact et cetera. As stated earlier, we're looking at a single level studies today. The single layer induces only one layer of correlation. Going back to the school example a single level could be that of classrooms within schools are correlated. Do you remember the term independent sampling unit from the previous lecture? The schools are the independent sampling unit. This is because we can assume that one school is independent of another school. Inside the school however, we have classrooms which are correlated. Now, the whole name of this game, we're going to be focusing throughout the course, we'll be talking about what is correlated and what is independent. So this is what you have to be aware of when you are designing studies, and when you're doing statistical analyses of these studies, and when you're conducting power and sample size analysis. We can make more complex designs by adding more levels. Suppose we have schools, we have classrooms within schools, and we have students within classrooms. This is a two level or a multi-level study. There can also be no levels in a study. There can be a single level studies or there can be multiple levels. In the school example, we saw that a single level study contains one layer of correlation. Units of observation which could be something like classroom average test scores in our example within independent sampling unit, the school in our example will be correlated. Remember that, some authors use different terms to portray the same idea of correlated levels. Make sure you are able to recognize the terms like group or cluster-randomized trial, observational study, as synonymous with the use of level terminology. To gain a better understanding of single level designs, let's look at another example. A study looked at efficacy of workplace training program to reduce the amount of alcohol that has been consumed. Workplaces were randomized into two groups. One group had a training program, the intervention group and the other group had no training, the non-intervention group. Each worker was measured for post-treatment drinking rate. Here's the study design. The first step was randomizing workplaces. We randomize them either to no training, which is the control group or to their workplace training program. After the training program or doing nothing for the control group, we measure the post-treatment frequency of drinking, and we stop. Our null hypothesis here is that there's no difference in post drinking frequency between workers who received no training and those who receive workplace programs. The scientists were hoping for workplace training programs to reduce drinking frequency. The single level at play here is the workers within each workplace. The outcome measurements of workers within a single workplace are correlated because these workers have the same supervisors to hang out during work, and they may drink together after work et cetera. Here the independent sampling unit is the workplace as observations from one workplace will be independent of those from another. The unit of observation is the post drinking rate for each worker. The between independent sampling unit was the intervention. The intervention had two levels. It was either a control or the workplace drinking program. Though within independent sampling unit factor is cluster membership, which just means workers belong to the same workplace. Looking at the factor levels just depends on the setting and the research question. Remember, the goal was to reject a null hypothesis meaning the training program would reduce the drinking rate of workers. The single level workers within the workplace creates correlation among measurements of drinking rates of workers within the workplace. In defining feature of a cluster members is a changeability. This just means that there's a pattern of equal correlation in which the correlation between any two members of a cluster or the same as any other pair. In other words, identifications can be exchanged without affecting correlation patterns. The inter-class correlation coefficient tells us the common correlation for a cluster, which is induced by changeability. The random assignment of clusters allowed the researchers to make two important assumptions. The first, the average correlation between any two workers in an intervention group is equal to the average correlation between any two workers in the control group. This is just accepted because we assume that human nature is about the same. The second assumption is that pre-existing employees factors do not biased study outcomes in any way. By using randomization, we were able to examine the effect of the treatment independent of pre-existing factors. Once more, this is just a reminder that terms like group randomized trial, cluster randomized trial, or observational study are used to describe level terminology. When we refer to groups, we're just referring to smaller non-random collections that are created nationally by looking at some kind of connection among the members. These connections can be made by where people live, what they do socially, where they go to school, and more. In this example we talked about earlier, the group was 400 based on where they work. So while these groups we just talked about are not randomly created, the assignment of these groups to treatment and control is completely random. This is just called group randomized trial, and creates exchange stability and leads to meeting the assumptions we discussed earlier about cluster designs. While the terms clusters and groups are used by different authors, the important thing at hand is the validity of the assumption of changeability of members at a level. If this is valid, the terms are essentially synonymous. Let's do a quick review summary. Single level studies have one level of correlation. Like all students being in a classroom, that is one hierarchical levels. So it's single level study. Just as a reminder, there are different terms used to describe levels in a study. You may hear things like group or cluster randomized trials or even terms like an observational cluster or just hierarchical study. It is important to note these terms so you can recognize these types of studies in different fields. That's all for this lecture, thank you for your time.
