Statistics: Analysis of Variance methods

Question 1

When do these methods apply?

Answer 1

When a quantitative response variable has a categorical explanatory variable.

Question 2

What is meant by ANOVA?

Answer 2

Comparing the means of several groups

Question 3

What is the difference between one way and two way anova

Answer 3

1 factor, two factors (categorical variables.)

Question 4

What are the null and alternative hypothesis formats for ANOVA test comparing means

Answer 4

H0: m1=m2=….m(n)
Ha: at least two of the population means are unequal

Question 5

What are the assumptions of the ANOVA test?

Answer 5

-The population distributions of the response variable
for the g groups are normal, with the same standard
deviation in each group.
-Randomisation

Question 6

Why is the ANOVA method called analysis of variance?

Answer 6

The test statistic uses evidence about two types of variability; between the means and within the samples.

Question 7

The mean square of the group row is based on ______ while the mean square error is _______

Answer 7

Variability between groups estimate of the population variance squared; variability within groups estimate sample variance squared of the population variance squared.

Question 8

What does the error label refer to?

Answer 8

It summarises the error from not being able to predict subject’s responses exactly if we know the only group to which they belong.

Question 9

How is the mean square calculated

Answer 9

Sum of the squares (SS) divided by the DF

Question 10

As the sample size increases the normality assumption becomes ______ important

Answer 10

less

Question 11

Discuss violations of the equal population assumption

Answer 11

Moderate violations are not serious. When the sample sizes are identical the f test still works quite well. When the sample sizes are not equal the f test works quite well as long as the standard deviation is no more than about twice the smaller groups standard deviation.

Question 12

What is the relationship between the T and F test?

Answer 12

The P-value for the F test is the same as the two sided P-value for the t test.

Question 13

Why do an F test instead of multiple t tests?

Answer 13

A single test helps control the Type 1 error probability

Question 14

What is the disadvantage of an F test?

Answer 14

Doesn’t tell us which groups are different or how different they are

Question 15

What is meant by the fisher method?

Answer 15

The ANOVA F test confidence interval

Question 16

When can we infer the population means are different?

Answer 16

When the confidence interval contains 0

Question 17

When is it preferable to use the confidence interval equation from chapter 10?

Answer 17

When the ratio of the largest standard deviation to the smallest is about 2 as it uses separate standard deviations.

Question 18

What is a multiple comparison method?

Answer 18

Compare pairs of means with a confidence level that applies simultaneously to the entire set of comparisons rather than each comparison.

Question 19

What is the bonferroni multiple comparison method?

Answer 19

For each level it uses a t score. ie five groups at a 95% confidence level = 0.05/5= 0.01 for each one (99% confidence)

Question 20

What method would we use?

Answer 20

Tukey Method