1. Sum of squares (SS) is a method for quantifying the variation in some data of interest, e.g., the price of homes in a certain city, test scores, wins in a professionals sports season, etc. Conceptually it measures how much the data values differ from their mean.

ANOVA breaks the overall SS variation in your data into that portion related to one of more factors, and all other unknown factors.

What is the SS of this set of data: 5, 10, 15, 20, 25? See the note about SS at the end of your notes. And....the sum of squares function in Excel does something different, so don't use that!

2.

The hints talked about the fact that ANOVA tests a presumed hypothesis about several population means being equal (or not), all at the same time and thus avoiding a large number of combinations of pair-wise t tests about two population means being equal or not. Besides the convenience of the combined test, it also avoids the problem with multiple comparisons increasing the liklihood of making more type I errors.

Think of this example. If I am testing the presumed fairness of a coin (that the population proportion of heads in all coin tosses is p=.5) and I am using a level of significance alpha of .05, then I will reject the presumed fairness of the coin if the observed sample proportion of heads is in the extreme 5% of possibilities. If I am just testing a single coin, then I will make the type I error with 5% probability, simply because the rare outcomes from fair coins will happen sometimes.

But if I am testing many coins at once, then choose the correct answer below:

Group of answer choices:

a.The probability of making a type I error on at least one of the coins is much greater than 5 percent.

b.The probability of making at least one Type I error is still just 5%