Differences Across Three Groups (ANOVA)

Question 1

What is a Type 1 error?

Answer 1

When you conclude that there is a genuine differnce between the populations when in fact there is not

Question 2

What is the alpha level?

Answer 2

Probability of having a type 1 error, typically 0.05 using conventional criteria

Question 3

What is a Type 2 error?

Answer 3

When you conclude that there is no difference between the population when in reality, there is

Question 4

What is the beta level?

Answer 4

Probability of having a Type 2 error

Question 5

If the H0 is true and we reject the H0, what type of error is this?

Answer 5

Type 1 error

Question 6

If the H0 is false and we fail to reject H0, what type of error is this?

Answer 6

Type 2 error

Question 7

What is the Bonferroni correction?

Answer 7

Way to maintain an overall Type 1 error rate of 5%, by dividing alpha by the number of comparions, k

Question 8

Name a disadvantage of the Bonferroni correction?

Answer 8

Time consuming

Question 9

What is ANOVA used for?

Answer 9

Testing the differences in means in three or more groups

Question 10

What is the null hypothesis for ANOVA?

Answer 10

Group means are identical

Question 11

What is the F test statistic?

Answer 11

ratio of variability BETWEEN groups/variability WITHIN groups

Question 12

What is the degrees of freedom for between groups?

Answer 12

k - 1

Question 13

What is the degrees of freedom for residuals?

Answer 13

Ntot - k

Question 14

How is the Sum Square column calculated for between groups?

Answer 14

Sum of Squares between, total of the differences between the sample mean for the ith group and sample mean across all groups combined

Question 15

How is the Sum Square column calculated for residuals?

Answer 15

Sum of Squares within, represents variability within groups

Question 16

How is the Mean Square column calculated?

Answer 16

Sum of squares divided by the degrees of freedom

Question 17

What should the F statistic be if H0 is true?

Answer 17

Small

Question 18

What are the two degrees of freedom for the reference distribution for ANOVA?

Answer 18

df1 = k - 1
df2 = ntot - k

Question 19

What does a 5% family error rate mean?

Answer 19

We are 95% confident that the full set of intervals contain the true mean difference

Question 20

What is assumed for our data when doing ANOVA?

Answer 20

1) Independence of data within and between the groups
2) Equal standard deviations
3) Normally distributed data

Question 21

How can we check independence of data within and between the groups?

Answer 21

Looking at sampling design

Question 22

What does the Kruskal Wallis test assume?

Answer 22

• Different groups have the same standard deviation

- Groups with different standard deviations have different distributions

Question 23

What is heteroscedastic data?

Answer 23

Data with no similar standard deviations for each group

Question 24

What test should you use if your data is heteroscedastic?

Answer 24

Welch’s ANOVA

Question 25

What are the two hypotheses for Welch’s ANOVA?

Answer 25

H0: That the median of the groups are the same
H1: At least one median is different from another one

Question 26

Describe what happens in Welch’s ANOVA

Answer 26

Data are assigned ranks
Smallest score is given rank 1 and the largest is given rank N, which N is the total number of independent observations
Average rank is calculated for each group and assessed using the KW test statistic
Small test statistic suggests differences are expected among random samples