Okay, In this video, we're going to discuss some basic aspects of experimental design for experiments that can be analyzed with us. Sorry, for experiments that have a single factor and two or more treatments. So if there's only two treatments than this discussion would apply to experiments that can be analyzed, say, with a t-test. And if there's more than two treatments. This discussion will apply to experiments that can be analyzed by a one-way ANOVA or one factor generally a model. Equivalently, we're going to frame our discussion around the assumptions that need to be met in order to analyze the data with a one-way analysis of variance or one factor general linear model. And the two assumptions we're going to focus on our random sampling, which actually refers to the random allocation of subjects to treatments and independence. So let's start with random allocation to treatments. So this is the most important assumption for this type of experiment. And what it refers to is the need to randomly assign the subjects or biological material to the various treatments that are involved in your experiment. So for example, if we hadn't experiments that was using a number of mice, then what we could do is we could number each of our mice and then randomly assign each of our mice to each of our treatments in our experiment. And ideally we would do this with something like random number generator. Or even just by putting numbers on a piece paper, dropping them in a hat, and then pulling those numbers out of the hat after having given it a good shake. Okay, Now, why is random assignment important? We talk about this in detail in some other videos where we discuss experimental design more generally. But if you haven't watched those videos yet, just stop and think about this for a moment. So random assignment is reticle to this type of experiment because it ensures that the only systematic difference between the subjects or between the measurements that we get from our three different treatments will be due to the treatments themselves. Okay, just say that again. Random assignment is important to ensure that the only systematic differences between this set of data, this set of data and this set of data is due to the treatment effects themselves. And when that's true, we, if we find evidence for there being differences among our treatments, we can ascribe those differences to the experimental manipulations and not due to some other factor or do some other effect. I mean. So there's another approach that we could take to randomly assign our subjects to our treatments. And that might be that we might first group our subjects or our biological material according to some characteristics. So for example, let's imagine our mice and varied in size than we might group them according to size. And if we have, if we had three treatments in our experiment, we might make each group just comprised of three individuals. And so here's a group of individuals that fall into our smallest size class. And what we could do is we could randomly assign each of the individuals within this smallest group to our three treatments. So here's an example of a really nice study that takes us approach. It does. The study involves manipulations of this species of plant here. And the authors of this study examined these plants in their natural habitat. So in a field where they were growing or forced a calendar which and what they did is they mapped the individual locations of all the individuals in their study because they wanted to account for spatial effects in their experiment. And. What they did as a part of their experimental design is they grouped the subjects that we're living in this field into triose. So into groups of three like we have here. And then they randomly assigned the subjects within each trio. Two, there are three different treatments which are listed here, either intact or male emasculation or bisexual an escalation. Exactly what that means doesn't matter for the point of this video. If you want to find out, you can go read the paper. Okay. I'm just highlighting this as an example of a study where the subjects were grouped by some particular characteristic. In this case, they're grouped by their spatial location. And then within those groups, subjects were allocated randomly to the three treatments, making sure that each trio had one member of each of the three treatments. Okay. So we've just been highlighting that it's important to randomly assign your subjects to the individual treatments in your experiment. Want to take a slight tangent here and talk about how we actually obtain our subjects in the first place. In many cases, we ideally want to choose our subjects for experiment by randomly sampling them from a population of interest. And we want to do that ideally, because a random sample from a population will, sorry, if we randomly sample our subjects from a population, that process will ensure that our subjects that we're working with are unbiased representation of the population that we wish to understand. And as a result, any conclusions that we reach from our experiment will be applicable to that population that we wish to make inferences about. In other words, by randomly sampling subjects from a population of interest. This helps to ensure the generality of the conclusions that we make. In other words, we put ourselves in a position to be certain that the conclusions that we draw from our experiment, it will apply to our population that we're trying to understand. Okay? Now, having said that, randomly sampling individuals from a population of interest is not actually strictly speaking on an assumption that's needs to be met for the experimental designs we're talking about in this video. Okay? So there are many disciplines in which experiments make use of individ, make use of subjects that we're not a random sample from a larger population. Strictly speaking, that's okay in terms of how our experiments are conducted and how we interpret them. The one limitation though, is that when we interpret results from experiments like that, we need to be cognizant of the limitations that our experiment will have in terms of what's type of population, our samples, or what type of population our experiment would be able to extrapolate too. Okay, so now we've talked about randomization and specifically random assignment of subjects to treatments. I now want to speak very briefly about the assumption of independence. We're going to deal with the subject very briefly because we already have a whole series of videos that deal with the notion of independence. That deal with what independence actually means. And that deal with the general concept of pseudo replication. Okay? So I'm not going to go into all those issues in detail in this video. Instead, I'm going to say that if those concepts are not already the tip of your mind, that say you should go watch those other videos on pseudo replication. What I'm gonna do just now is I'm just going to pull out a couple slides from those series of videos just to highlight some key points. Okay? And the key point for this video is that if we wish to analyze an experiment with one factor and two or more treatments, we want to analyze it using a one-factor general linear model or a one-way ANOVA. Then we need to ensure that our measurements within our treatments, so the measurements within each of our treatments are independent. Okay. And so I'll just highlight, or I'll just orient you to the slide. Each of these letters here represents a measurement that comes from a particular subject. And I've highlighted down here at the bottom that non independent measurements share a letter. Okay, so what I want you to see here is that here we have an experiment that involves three treatments, treatment 1, 2, and 3. And I want you to notice that within each of these treatments, all of our measurements have separate letters. So they have different letters. So what that means is that all the data within this treatment and within this treatment and within this treatment, these are all independent measurements within by treatments. And so this experimental design would meet the assumption of independence. Okay? This experimental design which we have on the right, also meets the assumption of independence. Which you can see here, is that there are some measurements that share a letter. So this measurement and this measurement and this measurement, they'll have letter a and so they are not independent of one another. But in terms of meeting the assumptions for this type of experiment, This doesn't matter. What really matters is effects that all of the data within each of our treatments are independent. Okay? So this experimental design and this experimental design both meets the assumptions of or meet the assumption of independence for this type of experimental design. Okay? Here's an example of a case that does not meet the assumption of independence. So you can see in this case, we now have more than one measurement within each of our treatments or and where those measurements are not independent. So these two measurements are not independent. These are not, these are not, et cetera. Okay? So this situation violates the assumption of independence. And we would need to do something additional in order to analyze the data from an experiment like this, to avoid worrying about pseudo replication. And exactly what we do. That's something we talk about in this other separate set of videos or we discuss pseudo replication. So I refer you there. Next we're going to talk about sample size, okay? In order to run an experiment that has a single factor, add at least two treatments are at least two levels within that factor. The minimum requirement for our sample size that we have to have at least two independent measurements within each of our treatments. Okay, and that's, I'll try to illustrate here. This represents two independent measurements within treatment 1, treatment 2, and 2 within treatment three. Okay? So we have to have at least two independent measurements within each of our treatments. Now, usually we're going to want to have more than two independent measurements per treatment. And this leads us to the more general question of how many samples are, how many independent measurements do we need within each of our treatments? That question can be answered with a formal, formal power analysis. And if you want to know more about power analysis, then again, I'm going to refer you to a separate set of videos that discusses power analysis. The last topic that we're going to discuss is how many treatments should an experiments like this have? Well, really the number of treatments that you want to include will depend on the nature of your experiment and exactly what you want to learn from your experiment, okay? So exactly how many treatments you should include will depend on what it is you want to test. Having said that, there is one general principle that I want to draw to your attention, okay? And we're going to lead up to that principle by having you answer this question. So we've got two different experiments here. One that has three treatments, where within each treatment we have four independent measurements. And I want you to compare this experiments to the one beneath where we have four treatments. And in this case we have three independent measurements within each treatment. Okay? So notice that the total number of independent measurements is the same within each of these experiments. So they both have 12 independent measurements. But which of these experiments do you think has greater power, greater statistical power to detect effects among the treatments generally. Okay. I want you to think about this for a moment. Okay? Well, the answer is the top one. Okay. We're not going to go into exactly why that is. But I'm just instead just can leave you with this general, this general principle, okay? For a given amount of resources. In other words, for a given an overall sample size, the power of an experiment like this will decrease with the number of treatments that are included. In other words, as if you have a certain number of subjects, for example, you might want to use in an experiment. So in this case, you might say we have 12 subjects. The power of the experiments that you would use will decrease as you divide those subjects into a larger number of treatments. What that means is that when you're designing your experiment, you wants to design your experiment such a way that you minimize the number of treatments, that you only include. The smallest number of treatments that allows you to answer the question that you're interested in. Okay. So in this video, I've tried to highlight for general or do had tried to highlight some principles that address for different aspects of experimental design for an experiment that could be analyzed with a one factor general linear model. We've talked about the importance of random sampling, or specifically the random allocation of subjects to treatments. We've talked about the importance of independence. We've talked about the minimum requirements for sample size. And we've also talked about some general, a general principle to consider when you're thinking about the number of treatments that you did want to include in an experiment like this. I hope this video has been helpful. I'll end it there and I'll say, thank you very much.