week 6 Factorial Anova

Question 1

simple effect

Answer 1

the effect of one factor at one level of the other factor.eg. gender on low anxiety only.(ie split data)

In general, we only look at simple effects, when a significant interaction has been found.A simple effect is the comparison of any 2 groups in the analysis.

Simple effects manifest the same as main effects but are NOT confounded byinteractions. Investigating simple effects, is the follow-up to having found a significant interaction.

Calculation is as per a main effect in a one-way anova BUT we use MS_error from the overall degsign.

The simple effect SS_{A at B1 only} AND SS_{Aat B2 only} =SS_A + SS_AB

The df for simple effects are the same as per main effects as the same number of means are being compared.

When we have split the data, the critical F value remains as per prior to split.

Carrying out multiple simple-effects tests raises the problem of inflated Type 1 errorr rates. Therefore:

a) set up a priori limited set of relevant simple effects test to be conducted in the event of a significant interaction

or

b) if no a priori guideline established, when find a significant interaction, plot data and chooseto test those only which most clearly explain the nature of the interaction.

Question 2

main effect

Answer 2

the overall effect of one factor on the dv, without considering any other iv’s.

Main effects can mask important interactional relationships.

A main effect occurs when we can detect differences between levels on a single factor within a factorial anova (eg main effect of alcohol on driving performance). Note that calculating means by hand is a different process than anova calculating main effects via SS etc.

Question 3

interactions

Answer 3

an Interaction occurs when the effect of one factor on the dependent variable, is not the same at all levels of the other factor.

Even if the lines do not cross, if they are not parallel, there is an interaction somewhere.

Above, lines are parallel, no interaction.

Main effects can be found with simple one-way anova’s, but to find interactions, need factorial anovas.

When there is an interaction, MUST BE VERY CAUTIOUS interpreting the main effects as main effects do not consider interactions.

Question 4

simple interactions

Answer 4

4

Question 5

levels

Answer 5

subsets of the independent variables. eg if have independent variables of eating disorder, and food restriction. The levels would be anorexia/bulaemia/normal for eating disorder, and restraint/non restraint for food restriction.

Question 6

factors

Answer 6

independent variables

Question 7

factorial anova

Answer 7

is used when we have more than 1 independent variable. A two-way anova=2 factors. A 3x2 anova=3 levels in 1st factor, and 2 in second.

A 2-way factorial anova will answer the following questions; a)main effect for factor A? b)main effect of factor B? & c) AxB interaction?

Steps;

a) always plot data and considerwhat they mean before attempting to interpret.
b) Find interactions and main effects. If find an interaction, discard the main effects, and look for simple effects.
b2) no inetraction found, just go with main effects
c) interaction found. Split date for investigation into simple effects. plot and consider.Calculate.

Question 8

calculations

Answer 8

Calculate Sum of Squares, Mean Squares, then F statistic. Need an F value for each statistical question (eg, A, B and AxB).

SS in the DV= SS_A + SS_B + SS_AB + SS_{residual(unexplained variance model)}

df_AB =df_A x df_B

df_A=number of levels-1

df_B=number of levels -1

IF the df=1. then SS wil equal MS

For F_{(numerator effect, denominator residual)}

F>critical F is significant, as considered unlikely to occur if the null hypothesis is true.

Question 9

Higher Order Factorial designs

Answer 9

In a 3-way design, we have 3 iv’s.Thus there are:

3 main effects (A,B,C)

three 2-way interactions (AB,AC,BC)

one three-way interaction (ABC).

Question 10

1st order interaction

Answer 10

= a two-way interaction

Question 11

2nd order interaction

Answer 11

= a three-way interaction. A three-way interaction (ABC) can also be thought of asAB interaction interacting with C.

Question 12

graphing 3-factor design

Answer 12

Usually have 2 graphs(if have 2 levels in third factor). ie dv on y, iv1 on x, and 2 lines (onefor each level of factor 2), 1st graph with factor 3 level 1, and 2nd graph with factor 3 level 2.

which way it is graphed does not matter, but different ways do give a different perspective.

Question 13

higher order main effects

Answer 13

Calculate means for individual levelsof each factor (across the other 2 factors), to see if there may be a main effect. Calculate F ratios.

Question 14

higher order 2-way interactions

Answer 14

there are 3 2-way interactions to be calculated with F ratios. MUST not confuse these with the 2-way interaction graphs used to explore the 3-way interaction.

Question 15

higher order worked example

Answer 15

The above shows mean credibility ratings (rated 1-5, 5 being credible). DV=credibility. iv’s are age, gender, criminal/not

1.Calculate means for individual levels for each factor (across the other 2 factors). From this can gauge if may have a significant main effect.

ie Mean for criminal=(1+4+1+1+2)/6=1.67

Mean for not criminal= (4+4+4+4+4+4)/6=4

therefore looks likely to have a main effect

Mean for minor age=2.5, yound adult=3.5 and old adult=2.5

therefore not looking like yound adults have fractionally higher credibility

Female mean=3 and male mean 2.6

therefore a gender main effect is possible (but looks mild??)

Calculate F ratios.

2. Two-way interactions;(2 variables averaging over the 3rd variable)

age by gender, age by record, record by gender

eg record(criminal or not) by gender

ie average the scores for all ages across record

Then age x record interaction;

Then gender x age

Two-way interactions DO NOT give the whole picture, as we are averaging over A THIRD variable. Any case where there is a different interaction for different levels of a third vairiable, is A THREE-WAY INTERACTION.

process;

A)if the 3-way interaction is significant;graph it and test simple interaction effects

A2) if any of the simple interactions are significant, graph them and test the simple effects. Remember in order to avoid inflating type 1 errors, limit which simple interactions are analysed.

B)If the 3-way interaction is not significant, look at 2-way interactions. (A2)

C)If none of the 2-way interactions are significant , look at main effects.

Question 16

3-way anova guide

Answer 16

https://sway.office.com/rQH7m2MRZkeYopzS?authoringPlay=true&publish3-way anova guide

A two-way interaction is said to occur when the effect of one factor is not the same across all