Factorial ANOVA & Non-Parametric Tests Flashcards Preview

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Flashcards in Factorial ANOVA & Non-Parametric Tests Deck (26)
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1
Q

What are the advantages of using factorial ANOVA?

A

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?)

2
Q

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

A

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

3
Q

What are marginal means?;

What are cell means?

A

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

4
Q

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

A

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

5
Q

On the graph, what do parallel lines indicate?;

What provides evidence for main effects?

A

No interaction;

Differences in the average height of the factor levels

6
Q

How do we examine the simple effects?

A

Calculate the cell means

7
Q

What is the difference between ordinal & disordinal interactions?

A

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

8
Q

How many factors does a factorial design have?

A

At least 2 factors, each with at least 2 levels

9
Q

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

A

6

10
Q

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

Describe the first one

A

Additive or Interactive effect;

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

11
Q

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

A

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)?

12
Q

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

A

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

13
Q

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

A

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

14
Q

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

A

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

15
Q

What are some disadvantages of non-parametric tests?

A

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

16
Q

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

A

Independent groups t test;

Repeated measures t test

17
Q

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

A

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

18
Q

How does ranking work?

A

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

19
Q

What principle is Wilcoxon’s rank sum based upon?

A

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

20
Q

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

A

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)

21
Q

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

A

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

22
Q

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?

A

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)

23
Q

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

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

A

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

z-test (normal approximation method)

24
Q

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

A

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

25
Q

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

A

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

26
Q

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

A

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)