Factorial ANOVA & Non-Parametric Tests

Question 1

What are the advantages of using factorial ANOVA?

Answer 1

More economical in terms of participants because we average over the other factor (for main effects); allows us to examine the interaction of IVs; generalisability of results can be assessed (do main effects hold over the other factor?)

Question 2

What are “main effects”, “interactions” & “simple effects”?

Answer 2

Main effect: the change in DV scores for one IV averaged across the levels of the other IV (examines one factor at a time); interaction: the effect of one factor depends upon the levels of the other factor; simple effect: the effect of a variable at each level of the other variable

Question 3

What are marginal means?;

What are cell means?

Answer 3

The means for each level of a factor averaged across the levels of another factor (help identify main effects by collapsing other factors);
Means of each individual cell

Question 4

Which variable lies on the X axis?;
Which one on the Y-axis?
How are other factors represented?

Answer 4

Factor with the most levels or is most theoretically important;
Dependent variable;
Separate lines on the graph

Question 5

On the graph, what do parallel lines indicate?;

What provides evidence for main effects?

Answer 5

No interaction;

Differences in the average height of the factor levels

Question 6

How do we examine the simple effects?

Answer 6

Calculate the cell means

Question 7

What is the difference between ordinal & disordinal interactions?

Answer 7

Ordinal: the lines don’t cross; disordinal: the lines do cross; they both moderate or “qualify” the impact of a second IV on the DV

Question 8

How many factors does a factorial design have?

Answer 8

At least 2 factors, each with at least 2 levels

Question 9

If I had a 2x3 factorial ANOVA, how many cell means would I have?

Answer 9

6

Question 10

What are the two ways a DV can change for more than one IV?;

Describe the first one

Answer 10

Additive or Interactive effect;

Both groups show much the same effect (lines move in parallel, pattern is constant)

Question 11

What questions are asked in a two-way factorial design?

Answer 11

Are the means of the population corresponding to the levels of the first factor different (main effect on factor 1)?; Are the means of the population corresponding to the second factor different (main effect on factor 2)?; Do the factors act in combination to affect scores on the DV (interaction)?

Question 12

What’s the difference between parametric & non-parametric tests?

Answer 12

Parametric tests involve the estimation of at least one population parameter; non-parametric tests don’t; goal is to establish overall differences between 2 or more distributions, not to identify differences between any particular parametres

Question 13

What type of data do we prefer to use non-parametric tests for?

Answer 13

Qualitative; nominal/categorical; discrete; ordinal; skewed; data which violates assumption of parametric tests

Question 14

Why are non-parametric tests also referred to as “distribution free” tests?;
Name some other advantages

Answer 14

Because they don’t make a priori assumptions about the specific shape of the distribution;
No assumptions of normality or homogeneity; smaller sample sizes can be used; less computation; use of ranks reduces effects of outliers

Question 15

What are some disadvantages of non-parametric tests?

Answer 15

Less power when normally distributed (larger sample size required); increase in type 2 error; scales of measurement (i.e. nominal/ordinal) are less sensitive than parametric; less flexible

Question 16

What is the parametric equivalent of the Wilcoxon’s rank sum test?
Wilcoxon’s matched-pairs signed-ranks test?

Answer 16

Independent groups t test;

Repeated measures t test

Question 17

What are the conceptual hypotheses for Wilcoxon’s rank sum test?

Answer 17

Null: samples drawn at random from identical populations (roughly equal sums of ranks in each group); Alternative: samples drawn from different populations

Question 18

How does ranking work?

Answer 18

Orders a set of scores from smallest to largest; provides a standard distribution of scores with standard characteristics

Question 19

What principle is Wilcoxon’s rank sum based upon?

Answer 19

Compares sum of ranks (R); uses sums of ranks of the smaller group

Question 20

What is the rank sum of the smaller group referred to as?;
What alpha do we use?;
When is Ws significant?

Answer 20

Ws;
.025 (1-tailed test table so divide by 2);
If obtained value from smaller group is less than the critical value (n1 is smaller group)

Question 21

Describe the process of performing a Wilcoxon’s rank-sum test

Answer 21

Rank scores from lowest to highest (ignoring group); compare sum of ranks between groups (R); look up critical Ws from smaller group (if different n) or smaller rank sum (if the same n); compare Ws obtained; interpret result

Question 22

Since it’s a one-way test, the effects only work if smaller group has significantly smaller scores than bigger group, so what happens if the smaller group has significantly bigger scores?

Answer 22

Calculate W’s (W prime s), which is 2W(bar)s (found in table) minus Ws; then pick the smaller of Ws or W’s & compare critical value (obtained must be smaller to reject null)

Question 23

What is a computer program based alternative to this test?;

What can be used for a sample size greater than 50?

Answer 23

Mann-Whitney U-test (linearly related to Wilcoxon’s);

z-test (normal approximation method)

Question 24

What are the conceptual hypotheses of Wilcoxon’s matched-pairs signed-ranks test?

Answer 24

Null: distribution of difference scores is symmetric around 0 (half positive, half negative); Alternative: distribution of difference scores is not symmetric around 0

Question 25

Describe the process of performing a Wilcoxon’s matched-pairs signed-rank test

Answer 25

Calculate the difference scores (delete 0’s); rank difference scores (ignoring the sign); reattach signs to ranks; add positive & negative separately; evaluate smallest absolute value against critical Wilcoxon’s T (using N); interpret results

Question 26

Name 2 non-parametric tests used with more than 2 groups

Answer 26

Kruskal Wallis one-way ANOVA H test (alternative to independent groups ANOVA); Friedman’s rank test for k correlated samples (equivalent to repeated measures ANOVA)