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We have two factor factorial design with factors A and B having and levels respectively: If the design is replicated 3 times_ what is the degrees of freedom for AB?...

Question

We have two factor factorial design with factors A and B having and levels respectively: If the design is replicated 3 times_ what is the degrees of freedom for AB?

We have two factor factorial design with factors A and B having and levels respectively: If the design is replicated 3 times_ what is the degrees of freedom for AB?



Answers


If factor A has 2 levels and factor $\mathrm{B}$ has 3 levels in a two-way ANOVA, we have a $_{-} \times_{-}$ factorial design.

Okay, so we see that there are three repeated factors of to and to repeated factors of three.

Hello. This is problem 13.67. And this is the Sky Square independence chest. Um And if we're talking about the chi square statistics, we need to um all Katou things let's say you have one variable And that there are six choices. Uh huh. Or six values for that variable. And then there's another variable and that that variable has four choices or four values in order to find the degrees of freedom of the chi score. So just like when you look at dysfunction, the degrees of freedom is equal to AR -1 time. It's multiplied by C -1. Which is Ego too. This are it's pretty much just how many choices over. Very well you have solidity That it's going to be this six. So we plug it in 6, 1 is one and then see is going to be the choices of the other variable. Right? So this is C. So it's going to be for values four minus one And in total is going to be 15.

The given problem is ember d my city.

In this problem, we're being asked to find the degree of the given polynomial for part B. So as you can see, I wrote down the polynomial X to the fourth minus two, X plus one. Well, in order to find a degree of the whole polynomial, we have to find a degree of each term first. So if we're looking at the first term X to the fourth, the degree of this term is its exponents, which in this case would be for now, we'll look at the second term negative two. X. Keep in mind when you don't see an exponent, it's an imaginary one, which means that the degree of the second term is equal to one. Now, for the last term you might be thinking well there is no variable. Well, the reason why it's not there is because we would rewrite this as X raised one X to the zero power because remember X to the zero is equal to one. So any time you have a constant term is degrees zero. So the degree for the entire polynomial is the largest of these numbers, which in this case is for, So this polynomial is said to have a degree of four.


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