Wk 9 - ANOVA 4

Question 1

What are the advantages of using factorial ANOVA? (x2)

Which allows us to… (X1)

Answer 1

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?

Question 2

What are main effects based on? (x1)
Define them (x1)
How can they be misleading?

Answer 2

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

Question 3

What are marginal means? (x1)

Answer 3

The overall mean of each factor/IV

Question 4

What is the difference between ordinal and disordinal interactions? (x2)

Answer 4

Ordinal - non-parallel lines do not cross

Disordinal - they do

Question 5

Why are non-parametric tests also referred to as ‘distribution free’ tests? (x1)

Answer 5

Because no a priori assumptions are made about the shape of distribution of the population from which data were randomly sampled

Question 6

What type of data do we prefer to use non-parametric tests for? (x2)

Answer 6

Nominal - categorical, discrete, qualitative; and

Ordinal - names + meaningful numbers; continuous, measurement, quantitative

Question 7

What principle is the Wilcoxon’s rank-sum test based on? (the null and experimental hypotheses)

Answer 7

H0: samples drawn at random from identical pops
H1: samples drawn from different pops

Question 8

What are simple effects based on? (x1)
Define them (x1)

Answer 8

Cell means

The effect of one factor/IV at one level of another - the combining of variables

Question 9

What are interactions in factorial analysis? (x2)

Answer 9

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

Question 10

How does the rank test work? (x2)

Answer 10

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

Question 11

What types of research designs can be used for factorial ANOVA tests? (x3)

Answer 11

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)

Question 12

When plotting main effects and interactions, the x- and y- axes are for… (x2)
And the second factor is… (x1)

Answer 12

The factor with most levels, or most theoretically important
The DV
One with fewer levels - rep with separate lines on graph

Question 13

What are the advantages of non-parametric tests? (x4)

Answer 13

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

Question 14

What are the disadvantages of non-parametric tests? (x3)

Answer 14

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

Question 15

What does ranking do?

Answer 15

Provides a standard distribution of scores with standard characteristics

Question 16

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)

Answer 16

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

Question 17

What is the non-para equivalent of the independent groups t-test?

Answer 17

Wilcoxon’s rank sum test

Question 18

What are the equivalents of the RM t-test? (x2)

Answer 18

Wilcoxon’s matched-pairs signed ranks test, or

Sign test

Question 19

What is the non-para equivalent of an independent groups ANOVA?

Answer 19

Kruskal-Wallis one-way ANOVA

Question 20

What is the non-para equivalent of RM ANOVA?

Answer 20

Friedman’s rank test for k correlated samples

Question 21

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)

Answer 21

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

Question 22

If the smaller group in Wilcoxon’s rank-sum test has the larger rank sum, calculate W’s by…

Answer 22

Subtracting Ws from 2Wbar
Where Ws is the rank sum of the smaller group, and
2Wbar is looked up in table

Question 23

Name two alternatives toi the Wilcoxon’s rank sum test

Answer 23

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

Question 24

What is an additive effect in factorial ANOVA?

Answer 24

When the ratio of change stays the same over time

ie lines are parallel

Question 25

When do we use non-para tests? (x2)

Answer 25

When assumptions are violated, ie skewed/non-normal

If nature of data doesn’t allow para tests

Question 26

What is the non-para equivalent of Pearson’s r?

Answer 26

Spearman’s rho correlation

Question 27

What are the parametric equivalents of chi-square goodness of fit and independence/contingency tests? (x1)

Answer 27

There aren’t any