Wk 9 - ANOVA 4 Flashcards
What are the advantages of using factorial ANOVA? (x2)
Which allows us to… (X1)
You can examine multiple IV’s/factors simultaneously
ie treatment and time can be crossed
ie allows more questions - is there main/simple effects, interactions?
What are main effects based on? (x1)
Define them (x1)
How can they be misleading?
Revealed by marginal means
Is the effect of each factor/IV overall
Effect on DV can be seen as coming from all levels of the other IV, when may be just one
What are marginal means? (x1)
The overall mean of each factor/IV
What is the difference between ordinal and disordinal interactions? (x2)
Ordinal - non-parallel lines do not cross
Disordinal - they do
Why are non-parametric tests also referred to as ‘distribution free’ tests? (x1)
Because no a priori assumptions are made about the shape of distribution of the population from which data were randomly sampled
What type of data do we prefer to use non-parametric tests for? (x2)
Nominal - categorical, discrete, qualitative; and
Ordinal - names + meaningful numbers; continuous, measurement, quantitative
What principle is the Wilcoxon’s rank-sum test based on? (the null and experimental hypotheses)
H0: samples drawn at random from identical pops
H1: samples drawn from different pops
What are simple effects based on? (x1) Define them (x1)
Cell means
The effect of one factor/IV at one level of another - the combining of variables
What are interactions in factorial analysis? (x2)
When the change in DV as a function of one IV depends on the level of another
When one IV moderates/qualifies the impact of a second
How does the rank test work? (x2)
Compares the sum of ranks (R) between groups:
If scores in one group generally lower, we would expect low ranks to fall into first group, and higher into second
What types of research designs can be used for factorial ANOVA tests? (x3)
Between-subjects (different people in each condition)
Within-subjects (same people in each condition)
Mixed model (a mix of between-subjects and within-subjects factors)
When plotting main effects and interactions, the x- and y- axes are for… (x2)
And the second factor is… (x1)
The factor with most levels, or most theoretically important
The DV
One with fewer levels - rep with separate lines on graph
What are the advantages of non-parametric tests? (x4)
Do not require normality and homogeneity of variances – skewed data can be analysed
Ideal for small samples – often skewed
Easier to calculate
Use of ranks reduces outlier effects
What are the disadvantages of non-parametric tests? (x3)
If pops are normally distributed, gives less power – increase in Type 2 errors (retaining false H0), so needs larger N for same power as analogous parametric test
Scales of measurement used are less sensitive than those in para tests
Less flexible – some para tests don’t have a non-para equivalent
What does ranking do?
Provides a standard distribution of scores with standard characteristics
The goal of non-parametric tests differs from para because… (x1)
Making the null hypothesis… (x1)
And so rejecting the null just means that… (x1)
Establish overall diffs between 2 or more distributions, not diff between any particular parameter
More general: samples come from identical pops, not just ones with the same mean
Pops differ (perhaps not just on central tendency
What is the non-para equivalent of the independent groups t-test?
Wilcoxon’s rank sum test
What are the equivalents of the RM t-test? (x2)
Wilcoxon’s matched-pairs signed ranks test, or
Sign test
What is the non-para equivalent of an independent groups ANOVA?
Kruskal-Wallis one-way ANOVA
What is the non-para equivalent of RM ANOVA?
Friedman’s rank test for k correlated samples
Wilcoxon’s rank-sum test is the non-para equivalent of…?
What are the calculation steps, for when smaller group has the smaller rank sum? (x6)
Independent groups t-test
Rank all scores from low to high, irrespective of which condition the score falls in
Check work - overall rank sum should = N(N + 1)/2
Need to account for different sized groups, so Wilcoxon’s uses sum of ranks of the smaller group, Ws – this is our obtained value
If groups are of equal size, use the smaller rank sum as Ws
Look Ws table – need to divide alpha/2 to use, ie .025; N1 = smaller group, N2 is larger
Significant if obtained Ws from the smaller group is less than the critical value from table
If the smaller group in Wilcoxon’s rank-sum test has the larger rank sum, calculate W’s by…
Subtracting Ws from 2Wbar
Where Ws is the rank sum of the smaller group, and
2Wbar is looked up in table
Name two alternatives toi the Wilcoxon’s rank sum test
Mann-Whitney U-test is calculated by computers - linearly related to Wilcoxon’s W, therefor redundant
For sample size > 50, there’s a normal approximation method (z-test) with critical at 1.96
What is an additive effect in factorial ANOVA?
When the ratio of change stays the same over time
ie lines are parallel
When do we use non-para tests? (x2)
When assumptions are violated, ie skewed/non-normal
If nature of data doesn’t allow para tests
What is the non-para equivalent of Pearson’s r?
Spearman’s rho correlation
What are the parametric equivalents of chi-square goodness of fit and independence/contingency tests? (x1)
There aren’t any
