Factorial ANOVA & Non-Parametric Tests Flashcards
What are the advantages of using factorial ANOVA?
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?)
What are “main effects”, “interactions” & “simple effects”?
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
What are marginal means?;
What are cell means?
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
Which variable lies on the X axis?;
Which one on the Y-axis?
How are other factors represented?
Factor with the most levels or is most theoretically important;
Dependent variable;
Separate lines on the graph
On the graph, what do parallel lines indicate?;
What provides evidence for main effects?
No interaction;
Differences in the average height of the factor levels
How do we examine the simple effects?
Calculate the cell means
What is the difference between ordinal & disordinal interactions?
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
How many factors does a factorial design have?
At least 2 factors, each with at least 2 levels
If I had a 2x3 factorial ANOVA, how many cell means would I have?
6
What are the two ways a DV can change for more than one IV?;
Describe the first one
Additive or Interactive effect;
Both groups show much the same effect (lines move in parallel, pattern is constant)
What questions are asked in a two-way factorial design?
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)?
What’s the difference between parametric & non-parametric tests?
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
What type of data do we prefer to use non-parametric tests for?
Qualitative; nominal/categorical; discrete; ordinal; skewed; data which violates assumption of parametric tests
Why are non-parametric tests also referred to as “distribution free” tests?;
Name some other advantages
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
What are some disadvantages of non-parametric tests?
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
What is the parametric equivalent of the Wilcoxon’s rank sum test?
Wilcoxon’s matched-pairs signed-ranks test?
Independent groups t test;
Repeated measures t test
What are the conceptual hypotheses for Wilcoxon’s rank sum test?
Null: samples drawn at random from identical populations (roughly equal sums of ranks in each group); Alternative: samples drawn from different populations
How does ranking work?
Orders a set of scores from smallest to largest; provides a standard distribution of scores with standard characteristics
What principle is Wilcoxon’s rank sum based upon?
Compares sum of ranks (R); uses sums of ranks of the smaller group
What is the rank sum of the smaller group referred to as?;
What alpha do we use?;
When is Ws significant?
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)
Describe the process of performing a Wilcoxon’s rank-sum test
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
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?
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)
What is a computer program based alternative to this test?;
What can be used for a sample size greater than 50?
Mann-Whitney U-test (linearly related to Wilcoxon’s);
z-test (normal approximation method)
What are the conceptual hypotheses of Wilcoxon’s matched-pairs signed-ranks test?
Null: distribution of difference scores is symmetric around 0 (half positive, half negative); Alternative: distribution of difference scores is not symmetric around 0
Describe the process of performing a Wilcoxon’s matched-pairs signed-rank test
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
Name 2 non-parametric tests used with more than 2 groups
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)
