V20 Estimation

Welcome to part three of our video series on estimation. In this video, we're going to talk about independent populations or groups versus non-independent, or dependent, populations or groups. I'm Renee Clark from the Swanson School of Engineering at the University of Pittsburgh.

Okay, so, let's first talk about two independent populations and how that's defined. Okay, so, for populations to be independ… dependant, okay, the items in population one, or the first population, okay, are not the same as nor directly related to the items in population 2, or in the second population. In addition, the items are not meaningfully paired in any way. Okay, so, a good example of this is the following. Let's say we call population one all Pitt full-time undergraduate students, okay, and let's say we call population 2 all full-time undergraduate West Virginia University students. Okay, these two populations are independent, right, because you can't be both a full-time Pitt undergrad and a full-time West Virginia undergrad.

Okay, let's contrast that with dependent populations, which are the opposite of independent populations that we just talked about. Okay, so, with two dependent populations, there are two cases for this. The first is where the same population is analyzed twice or, perhaps, under two different circumstances. The second case of this is where the two populations are directly related but… but not necessarily the same. Okay, in the case of dependent ob… observations, we say they are paired, okay? Alright, so, let's talk about the case of paired observations that come from the same population. Okay, so, that almost that first case of dependent populations, okay, the… probably the most well-known example of this is what's known as before and after studies. Okay, so, an example of a before and after study would be when the weight of a person is measured both before, which we'll call X1, as well as after, which we'll call X2. A new diet regime… new diet regimen, or an exercise regimen, or maybe a medication, something that you're studying to try to see if there's an effect of this… of this new method or approach. Okay, so, in such a study, each… each person in the study, okay, their measurement is taken both before the regimen, or whatever is being tested, as well as after application of the regimen.

Okay, let's say there is another person in the study. This person's name is Lori. This person's measurements, again, are taken both before and after application of the treatment, and let's say there's a third person as well as others- Linda, weight measured both before and after the treatment.

Okay, and, because each person's measurements are taken, or the same person's measurements are taken… taken both before and after, that's why we say these are paired observations from the same population, okay, because the person remains the same both before and after. Renee's measurements are taken both before and after, and so on.

Okay, another really good example of a before and after study that you'll see a lot in the educational literature is where we're measuring the ability, let's say the math ability, of the same student both… both before and after a new teaching method, or something that we're trying out in the classroom. Okay? Okay. So, with before and after studies, what we're actually statistically analyzing, as you will see, are the differences, which we call d, okay, for each subject. So, we analyze actually each X1 minus X2. Okay, we do this for all subjects. So, if I were to add another column to this table called difference, okay, for Renee, that difference would be 10, or 135 less 125. For Lori, that difference would be five and for Linda it would be four. So, this is actually what's going to be analyzed statistically as we will see. Okay, let's take a look at examples of the second example, or the second case, of dependent populations. Okay, and this is the case in which the observations are paired but they come from, not the same population, but from directly related populations. Okay, so, some examples of this would be brother and sister pairs or husband and wife pairs. So, while the two populations are not the same, they are directly rel… related. Father and Son pairs, puppies from the same litter, or twin pairs. Okay, and you'll see a lot of examples of these types of pairings in the literature as well when studies are done.

We wish to thank the National Science Foundation under Grant 2335802 for supporting our work. Thank you for watching.