ANOVA Derivations - L3

Question 1

Learning Objectives

Answer 1

Derive degrees of freedom for each type of deviation.

Compute mean squared error – or variance – from sums of squares and degrees of freedom.

Compute an F-ratio from mean squared error, describe an F-value and explain how it can be used to perform hypothesis testing.

Interpret an ANOVA summary table containing the above values.

Question 2

What do the degrees of freedom associated with SS represent?

Answer 2

The DF associated with an SS represent the number of scores with independent information which enter into the calculation of the SS

Question 3

What are the degrees of freedom?

Answer 3

The df is the number of distinct “quantities” that are used to describe your data
(sample size) subtracted by all the “constraints” that the data must satisfy.

Question 4

How do we know that a + b + c = 10, we has two degrees of freedom.

Answer 4

• If we know a = 2 and we know b = 4, then we don’t need to know c, we can simply solve for it:

c= 10 - a - b = 10 - 2 - 4 = 4