Lecture 31: ANOVA

Question 1

What is ANOVA?

Answer 1

A statistical method that tests the equality of three or
more population means by analyzing sample variances or variation
in the data.

Question 2

What is the simplest ANOVA problem?

Answer 2

Single-factor,
single-classification or one-way ANOVA

Question 3

What are the 3 assumptions for ANOVA?

Answer 3

• For each population, the response variable is normally distributed.

*The variance of the response variable is same for all the
populations

*Data are independent

Question 4

How are variations measured in ANOVA?

Answer 4

By sums of squares (SS)

Question 5

What are the two sources of total variation in the data?

Answer 5

• Variation between groups/treatments (SSTr - treatment sum of squares)

*Variation withing groups/treatments
(SSE - Error sum of squares)

Question 6

What is the relationship between sample size and SSE?

Answer 6

If we increase sample size, SSE will be increased.

Question 7

What is the mean squares error a measure of?

Answer 7

MSE is a measure of within-samples variability

Question 8

What is the relationship between groups and SSTr (treatment sum of squares)?

Answer 8

If we consider more groups, SST r will be increased

Question 9

Why is the mean squares used to calculate the test statistics?

Answer 9

Because we want a test statistic that works in general to test hypotheses,
no matter the size of your sample or the number of groups we
have.