Okay, in this video we're going to address this question. How does the interpretation of random effects differ from interpretation of fixed effects? To address this question, I want you to imagine this study. I want you to imagine a study where we use litres of pigs coming from three pigs in order to study the effect of a diets treatment on growth. And we're going to imagine analyzing the study either only using fixed effects or using random effects. And we're going to talk about how our interpretation of those results would differ between those two different approaches. So first, let's just talk about the experimental design. So here we have our three litres of pigs. You'll notice that each mother has eight piglets. And what we're going to imagine is that we randomly assign these eight piglets into the two different treatments. So we would randomly assign for piglets to a standard feed treatment. And that would mean that the other four piglets that are randomly chosen by being randomly left over will be allocated to a treatment where the feed has some supplement. And that's true for all three of these litres. We can describe this experiment in this diagram here, where you can see each x represents a particular piglet. And horizontally we've organized the data that all came from the same pig or the same litter. So we have, all of these are the data that came from piglet or from pig a. These data from pig B, and these the data from pig C. Okay? And these piglets again have been randomly allocated to the either supplement present or supplement absent treatments. Now at first glance, we might imagine analyzing or analyzing these data with something like a t-test. Because we're really mostly interested in understanding the difference between a supplement present and the settlement absent. And so we're really most interested in comparing two different groups with one another. But e2 appreciate, or you might appreciate when looking at this, that the data points within each of our treatments are not independent. And that's because we have multiple data points within our supplement present as well. Within our supplement absent treatments that all come from the same pig. So we have multiple piglets within the supplements. Within the supplement added treatment that come from pig a, safer peg B seem for pig C. And as a result, these data are not independent. Because of that lack of independence, we cannot analyze these data with something like a two-sample t-test, even though we're really only interested biologically. And determining the difference between supplement presence and supplement absent. Instead, we need to do something extra to account for that non-independence. What we can do to account for that non-independence as we can actually model the variation among our different letters. And so we can do that by imagining that supplement present or absent represents one factor in an experiment. And this, the mother or litre represents a second factor, where the second factor has three different levels. Pig a, pig B, and pig C. And buy. Analyzing these data in this way, which looks a lot like a two factor general linear model. This allows us to control for the variation among our data points due to the effects of the mother. And this will account for the pseudo replication that was getting in our way of performing something like a two-sample t-test. Just a bit of terminology here. This kind of design would be called a randomized block design, where we say that pig is our blocking factor. And I just mentioned that in case you've already come across this term in some of our other videos. If you've not come across this term in our videos yet, then don't worry. This term is it's not central to what we're talking about. Okay? So let's imagine now that we did try to analyze this experiment with, say, a two factor general linear model in order to account for this non-independence. In that case, our model might look like this. We'd use something like the lm function with modal growth. And then we'd have to fixed effects. We'd have one effective feed and one effect of litter. This approach is perfectly fine if for specifically interested in the offspring of these three pigs. Okay, but usually when we conduct an experiment to biology, we're not so interested in learning about such a small group of a larger population. Usually we want to make conclusions that apply much more generally to a larger group of pigs. For example, if this experiment was being performed in order to develop a new type of feed, then presumably the people who are developing the feed and who want to sell it. Presumably, they want to know how this feed will affect pigs in general, not just offspring from three particular pigs. So even though this approach can account for the pseudo replication, it has severe limitations. And these limitations go back to how we think about fixed effects. So she remember, fixed effects are involve factors where the levels are picked for a particular reason and what we're specifically interested in those particular levels. Specifically, that means that the levels of a fixed effect were not chosen at random from a larger population. And because they were not chosen at random from a larger population. The conclusions that we make about a fixed effect will not apply to a larger population. Instead, when we are interpreting the results for a fixed effect, than our conclusions will only relate to the specific levels of that fixed effect or that fixed factor. Now, let's consider a different situation. Now instead of modelling litter or mother pig as a fixed effect, let's imagine. Or let's consider how we would interpret this study if we modeled litter or the mother as a random effect. And we could do that as follows. We can use a different functions, not Lm, but LM, E, r. This is a very commonly used function to perform mixed effects models. And the, the format of this model is very similar to the LM function. We still say growth is a function of feed and litter, but we specify litter slightly differently. And we use this notation here in order to specify to R or to specify to this function that we wants the effective litter to be analyzed as a random effect. At this point. Remember that when we model something as a random effect, we are saying that we can view our data as Or we can view the levels of this random effect. So we can view our three different pigs, which are the three different levels of the random factor litter. We Can, we say that those three pigs came from a larger population of pigs that were interested in. That's how we're modeling this random effect. As a result of that. That means that the results from this analysis will not only apply to the three particular pigs that we used in our study, but we can apply the conclusions from this study to the larger population that those pigs were sampled from. In other words, when we model lit her as a random effects, this allows us to make conclusions that are much more general and we're making conclusions about the larger population that those pigs came from. So just to recap here, we had this experimental design and we've considered two different ways of modeling the factor, pig or litre. If we treat pig as a fixed factor than our conclusions from this study will only apply to these particular pigs and o. In other words, we'd only be able to tell, we'd only be able to make conclusions about how the supplement influences these three pigs. If instead, we're model pig as a random factor, in which case we're recognizing at these pigs should have been selected at random from a larger population. And the function will model them accordingly. In that case, our conclusions will apply to the population of pigs from which these samples came. And as a result, we can make conclusions about how supplement influences growth for the entire population at these pigs came from. Which is probably, what's the people producing this supplement would want us to do if we're analyzing these data for them. Okay. So we'll just end with this slide with a very brief summary of why considering random versus fixed effects matter. First, I haven't shown you what the results would look like, but we'd be very likely to come to different answers from an analysis where we considered litter as either a fixed effect or random effect. I haven't showed you that, but that's very likely to be true. The second, the second, which is the emphasis of this video, is that the approach that we take has really strong conclusion, has really strong consequences for the conclusions that we can make from our experiment. What will our conclusions apply to a very narrow number of pigs that we actually worked with? Or will they apply more generally? That's our discussion of interpreting fixed versus random effects. I hope this has been helpful and I'll say, thank you very much.