But is that difference purely random? Random chance? Or can I be pretty confident that it's due to actual differences in the population means, of all of the people who would ever take food 3 vs food 2 vs food 1? So, my question here is, are the means and the true population means the same? This is a sample mean based on 3 samples. And I want to figure out if the type of food people take going into the test really affect their scores? If you look at these means, it looks like they perform best in group 3, than in group 2 or 1. So this is food 1, food 2, and then this over here is food 3. Let's say that I gave 3 different types of pills or 3 different types of food to people taking a test. We've been dealing with them abstractly right now, but you can imagine these are the results of some type of experiment. What I want to do is to put some context around these groups. What I want to do in this video, is actually use this type of information, essentially these statistics we've calculated, to do some inferential statistics, to come to some time of conclusion, or maybe not to come to some type of conclusion. And then the balance of this, 30, the balance of this variation, came from variation between the groups, and we calculated it, We got 24. Then we asked ourselves, how much of that variation is due to variation WITHIN each of these groups, versus variation BETWEEN the groups themselves? So, for the variation within the groups we have our Sum of Squares within. In the last couple of videos we first figured out the TOTAL variation in these 9 data points right here and we got 30, that's our Total Sum of Squares.
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