Chapter 9 - ANOVA

Question 1

State the hypothesis for ANOVA comparisons for the differences between sample means

Answer 1

H0: u1=u2=u3=u4…

H1: The means are not all the same

Question 2

Formula for the sum of squares between

Answer 2

Question 3

Formular for sum of squares within

Answer 3

Question 4

Formula for sum of squares total

Answer 4

Question 5

Formula for sum of squares total

Answer 5

Question 6

Give the formulas for the degrees of freedom in ANOVA (for sample mean comparisons)

Answer 6

df-between: k-1

df-within: n-k

df-total: n-1

Question 7

What is the F-Value in the ANOVA table (in sample mean comparisons)?

Answer 7

MSB/MSW

Question 8

State the ANOVA assumptions for sample mean comparison

Answer 8

1. Errors/Populations are normally distributed (check historgram of residuals)
2. Error/population has constant variances (check residuals against fitted values, should be no pattern)
3. Errors/populations are independent (We don’t deal with checking this)

Question 9

What is a residual & fitted value in the context of an ANOVA table (for sample mean comparison)

Answer 9

The difference between each observation and the mean of its sample. The fitted value is just that sample mean.

Question 10

What is the Turkey-Kramer formula?

What is the turkey formula?

Answer 10

Question 11

How is the value from the turkey (& kramer) formula used?

Answer 11

All the sample means are sorted by increasing value. Their differences are calculated. Any means with a difference larget then the value calculated from the T(K) formula are considered statistically diffenent

Question 12

Under ANOVA for sample mean differences, show how to calculate confidence intervals for an indervidual sample mean?

Answer 12

Question 13

Under ANOVA for sample mean differences, show how to calculate a confidence interval for an individual sample mean

Answer 13