Experimental error is the variation in the responses among the experimental units, under the same treatment and under the same conditions, so that's your experimental error. So what is experimental error caused by? Well, natural differences in the experimental units before receiving their allocation or the treatment. They could also be variations in the devices that record the measurements. In the click through way, we have a very clean measurement right we know the number of clicks. But if you're measuring say the yield of a crop by weight, the scales might be different and so you might have slight differences in measurement. Also, you'll have variations in the treatment conditions, that's another cause of experimental error. All of these extraneous factors other than the treatment factors all this randomness in the world. It could be something as simple as someone bumping the table and they clicked the button by accident or they click the button not willfully but for other reasons. So that might confound your results. Okay. So how do scientists control for experimental error? We want to minimize the amount of errors so we can do that through the use of strict experimental procedures and following the procedures exactly the same way, every time so that we minimize experimental error in that dimension. Our choice of experimental units and measurement units also makes a difference. If we are trying to perhaps measure how far away an object is if we measure in kilometers and round off to only whole numbers. We're going to get less accurate results than if we measured it by millimeters and we can get down to the millimeter level. How we record the data? What kind of devices we use? Are they accurate devices? Also the type of experimental design, right now I'm talking about a very strict and controlled experimental design that might be used by scientists in general. But there are other experimental designs that you should be aware of, for example quasi-experimental design. These are things that are used in the social sciences when we can't really do experiments in the truest sense of the word. Finally, control variables, what are some things that might affect our outcome variable but really are not of interest to our study. Okay. So let's talk a little bit about experimental procedures and they are the conditions under which an experiment is run. They should try to be as constant as possible during the experiment. So temperature might be something you want to think about. In the web page example, you might want to the degree possible control for whether some people might like to use the Internet when the weather it's not as nice outside. So if one city happens to have a lot of rain such as the Northwest, they might be endorsed more often looking at these web pages. If the experimental procedures are not strictly followed the variance of the response can be inflated and the precision of our inferences or confidence intervals can be compromised right. So we'll have big variances wide swings so we're not going to be as confident about our estimates. Lastly, the experimental procedure should be conducted or performed as in the same manner for the duration of the experiment to the degree possible. Otherwise you might get an inflated variance or some bias in your results. A bias is a consistent overestimate or underestimate of the statistic that you're looking at. In most cases, you're looking at something like the average, what is the average response and you might overshoot that average or undershoot that average consistently and that's what's known as a bias. Experimental error variance the error variance may increase if the units in the experiment are not similar with respect to those characteristics. So if you're not picking cities of the same size or maybe picking a big city and some rural town that might make a difference. So you want to make sure that the experimental units are selected to match. Note that if the experimental units are overly uniform, then the generalizations to the population may be restricted. So if you're only picking big cities, your results may only apply to big cities and they may not apply to rural towns for example. So in the case of the web page example if we are trying to see how our web page grabs the attention of a student population. If we pick students from the same grade level or the same school system the experimental units that we select may achieve a more homogeneous set of measurement units. But the inferences how can we generalize this to the broader population might be affected by the choice of school or the grade level. So it applies to a first-grader I don't know if a first grade will be clicking on a web page, but what applies to a high school student may not necessarily apply to the behavior of a graduate student for example. Randomization of treatments, so some of these statistical procedures are based on the condition that the data were drawn from a population that was distributed normal. A normal distribution is the bell-shaped curve. When you study a new statistical procedure there's always a list of assumptions, X is drawn from a normal distribution. There's a linear relationship between X and Y in the case of regression etc. There's always these assumptions and whatever those assumptions are your actual sampling of the data may not follow the actual population distribution. So that's also something to keep in mind. So how do we randomize the treatments? There's a little process here. Suppose we have N experimental units. So those are the total number of experimental units we're using. In the case of the web page example, it's the number of cities that were decided upon. T is the number of treatments remember that's a mix of the factors and their levels. We wanted to run randomly assign the treatment to some experimental unit. Note that r is the replication number of replications per experimental unit. So when we add up all the hours how many times we repeat the study it should equal N and that's completely randomized design. You do this by figuring out the number of experimental units from one to N generate a list of random numbers that is a permutation of the numbers from one to N. Then assign them number one to experiment one for the first replication, assign treatment two of the experimental units to the second replication, etc. Then you just keep repeating this process until all the treatments are assigned. So that gives you a little bit of an overview about the purest form of experimental design in terms of control variables, your outcome variables and things that might affect your variance and your bias. Then in the next couple of videos, we'll talk about the statistical tests involved, and hopefully by seeing this and then seeing the actual statistical tests it'll all come together at the end.