Lecture 7: Research Questions for Group Differences II (Between-subjects for 3+ groups)

Question 1

What are factor variables?

Answer 1

Categorical variables

Question 2

What function can we use to transform factor variables to numerical values?

Answer 2

as.numeric()

Question 3

Why is it beneficial to declare the grouping variables as a factor type?

Answer 3

Because levels (e.g “1”, “2”) created automatically using the dummy code has no meaning.

Question 4

What is dummy coding?

Answer 4

It transforms a categorical variable with g categories into a meaningful set of g-1 dummy variables that each have values of either 0 or 1.

Question 5

What is a one-way design?

Answer 5

A design where there is only one group classified.

Question 6

What is a between-subject design?

Answer 6

A study of independent groups.

Question 7

How do we investigate the differences between 3 or more groups?

Answer 7

Using ANOVA (analysis of variance).

Question 8

What are omnibus investigations?

Answer 8

An investigation involving 3 or more groups.

Question 9

Why are omnibus investigations weak?

Answer 9

They do not tell us where the differences are found.

Question 10

What are focused investigations?

Answer 10

A stronger approach to investigating differences between 3 or more groups. It provides identifiable differences (where they can be found), and can explain everything found in omnibus investigations (under certain conditions).

Question 11

What is a linear contrast?

Answer 11

A set of weights that sum to zero (0 is used to exclude a group). The total number of contrasts is one less than the numbers of groups (levels of the factor).

Question 12

What is orthogonality?

Answer 12

Being uncorrelated. The design is balanced and the mean differences in each contrast do not overlap and do not contain redundancy.

Question 13

How do we identify if two contrasts are orthogonal?

Answer 13

By multiplying them together and summing the products up. If it equals to zero, they are orthogonal.

Question 14

What are the statistical assumptions for the group analysis of 3 or more groups?

Answer 14

The same as those for a two independent group analysis.

1. Independence of observations
2. Normality of observed scores
3. Homogeneity of group variances (most important)

Question 15

How do we test those assumptions?

Answer 15

1. Levene’s test

2. Fligner-Killeen test

Question 16

What arguments do we need to calculate the CIs for user-defined contrasts?

Answer 16

1. m: vector of group sample means
2. sd: vector of group sample standard deviations
3. n: vector of group sample sizes
4. c: vector of a set of contrast coefficients
5. level: level of confidence (default is .95)