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Factorial Designs Flashcards

1
Q

Much experimental psychology asks the question:

A

What effect does a single independent variable have on a single dependent variable?

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2
Q

It is quite reasonable to ask the following question as well:

A

What effects do multiple independent variables have on a single dependent variable?

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3
Q

Factorial designs are:

A

Designs which include multiple independent variables

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4
Q

An example of a factorial design

If we were looking at GENDER and TIME OF EXAM

A

these would be two independent factors
•GENDER would only have two levels: male or female
•TIME OF EXAM might have multiple levels, e.g. morning, noon or night
•This is a factorial design

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5
Q

The name of an experimental design depends on three pieces of information:

A
  • The number of independent variables
  • The number of levels of each independent variable
  • The kind of independent variable
  • Between Groups
  • Within Subjects (or Repeated Measures)
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6
Q

If there is only one independent variable then:

A

The design is a one-way design (e.g. does coffee drinking influence exam scores)

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7
Q

If there are two independent variables:

A

The design is a two-way design (e.g. does time of day or coffee drinking influence exam scores).

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8
Q

If there are three independent variables:

A

The design is a three-way design (e.g. does time of day, coffee drinking or age influence exam scores).

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9
Q

Analytical comparisons in general

A
  • If there are more than two levels of a Factor
  • And, if there is a significant effect (either main effect or simple main effect)
  • Analytical comparisons are required.
  • Post hoc comparisons include tukey tests, Scheffé test or t-tests (bonferroni corrected).
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10
Q

Using ExperStat it possible to conduct a

A

simple main effects analysis relatively easily

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11
Q

Simple main effects analysis

A
  • We can think of a two-way between groups analysis of variance as a combination of smaller one-way anovas.
  • The analysis of simple main effects partitions the overall experiment in this way
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12
Q

Experimental design names

A
  • If there are 2 levels of the first IV and 3 levels of the second IV
  • It is a 2x3 design
  • E.G.: coffee drinking x time of day
  • Factor coffee has two levels: cup of coffee or cup of water
  • Factor time of day has three levels: morning, noon and night
  • If there are 3 levels of the first IV, 2 levels of the second IV and 4 levels of the third IV
  • It is a 3x2x4 design
  • E.G.: coffee drinking x time of day x exam duration
  • Factor coffee has three levels: 1 cup, 2 cup 3 cups
  • Factor time of day has two levels: morning or night
  • Factor exam duration has 4 levels: 30min, 60min, 90min, 120min
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13
Q

If all the IVs are between groups then

A

It is a Between Groups design

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14
Q

If all the IVs are repeated measures

A

It is a Repeated Measures design

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15
Q

If at least one IV is between groups and at least one IV is repeated measures

A

is a Mixed or Split-Plot design

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16
Q

Experimental design names

Three IVS

A
  • IV 1 is between groups and has two levels (e.g. a.m., p.m.)
  • IV 2 is between groups and has two levels (e.g. coffee, water).
  • IV 3 is repeated measures and has 3 levels (e.g. 1st year, 2nd year and 3rd year).
  • The design is:
  • A three-way (2x2x3) mixed design.
17
Q

What is a main effect?

A

The effect of a single variable

18
Q

What is an interaction?

A

The effect of two variables considered together

19
Q

For the two-way between groups design, an F-ratio is calculated for each of the following:

A
  • The main effect of the first variable
  • The main effect of the second variable
  • The interaction between the first and second variables
20
Q

To analyse the two-way between groups design we have to follow the same steps as the one-way between groups design:

A
  • State the Null Hypotheses
  • Partition the Variability
  • Calculate the Mean Squares
  • Calculate the F-Ratios
21
Q

A significant interaction effect

A
  • “There was a significant interaction between the lecture and worksheet factors (F1,16=16.178, MSe=11.500, p=0.001)”
  • However, we cannot at this point say anything specific about the differences between the means unless we look at the null hypothesis

•Many researches prefer to continue to make more specific observations.

22
Q

A significant main effect of Factor A

A

There was a significant main effect of lectures (F1,16=37.604, MSe=11.500, p<0.001). The students who attended lectures on average scored higher (mean=22.100) than those who did not (mean=12.800).

23
Q

No significant effect of Factor B

A

•“The main effect of worksheets was not significant (F1,16=0.039, MSe=11.500, p=0.846)”

24
Q

An example 2x2 between groups ANOVA

A
  • Factor A - Lectures (2 levels: yes, no)
  • Factor B - Worksheets (2 levels: yes, no)
  • Dependent Variable - Exam performance (0…30)
25
Q

There are 3 null hypotheses for the two-way (between groups design:

A

The means of the different levels of the first IV will be the same,

The means of the different levels of the second IV will be the same,

The differences between the means of the different levels of the interaction are the same,

26
Q

An example null hypothesis for an interaction

A

The differences betweens the levels of factor A are not the same.

27
Q

Partitioning the variability

If we consider the different levels of a one-way ANOVA then we can look at the deviations due to the between groups variability and the within groups variability.

A

If we substitute AB into the above equation we get

This provides the deviations associated with between and within groups variability for the two-way between groups design.

28
Q

Partitioning the variability

The between groups deviation can be thought of as a deviation that is comprised of three effects:

A

In other words the between groups variability is due to the effect of the first independent variable A, the effect of the second variable B, and the interaction between the two variables AxB.

29
Q

Partitioning the variability

The effect of A is given by

A

A-T

30
Q

Partitioning the variability

The effect of B is given by

A

B-T

31
Q

Partitioning the variability

The effect of the interaction AxB equals

A

(AB-T)-(Ā-T)-(B-T)

32
Q

The effect of the interaction AXB is known as the

A

Residual

33
Q

The F ratio for the first main effect is

A

MSA / MSSAB

34
Q

The F ratio for the second main effect is

A

MSB/ MSSAB

35
Q

The F ratio for the interaction is

A

MSAB/MSSAB

36
Q

In order to calculate F-Ratios we must calculate an Mean Square associated with
…

A

The Main Effect of the first IV
The Main Effect of the second IV
The Interaction.
The Error Term

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