Factorial Designs2

Factorial Designs

Identifying and Interpreting

Main Effects and Interactions

Factorial Designs

A simple experiment allows us to compare two conditions

Reading times (ms) for a lexical decision task

How would you compare the reading times for regular and irregular words?

Regularity

Regular Irregular

500 500

Factorial Designs But maybe the difference between regular and irregular words

DEPENDS on whether the words are common (hi frequency) or uncommon (lo frequency)

This is a factorial design and it allows us to ask more interesting questions

Regularity

Frequency Regular Irregular

Hi 500 500

Lo 500 700

Factorial Designs

Factorial designs allow us to do two experiments at one time One that compares regular to irregular words One that compares hi frequency to lo frequency

words These are called main effects

Factorial Designs

Factorial designs also allow us to see if… The effect of frequency depends on whether the

words are regular or irregular

OR The effect of regularity depends on whether the

words are hi or low frequency

These are called interactions

Factorial Designs

When looking at factorial designs, it helps to make a graph

It is easier to see the effects if you use line graphs Even if your really should be using bar graphs in

the actual graphs that go in your paper

Factorial Designs

Graphing the Means If there is an interaction between variables the

lines are not parallel – they have different slopes

The DV always goes on the y-axis

One IV always goes on the x-axis

The other IV is plotted

Regularity

700500Lo

500500Hi

IrregularRegularFrequency

400

500

600

700

800

Lo Hi

Irregular

Regular

Factorial Designs

There is a main effect of frequency such that the responses were faster to hi frequency than lo frequency words

400

500

600

700

800

Lo Hi

Irregular

Regular

Factorial Designs

There is a main effect of regularity such that the responses were faster to regular words than irregular words

400

500

600

700

800

Lo Hi

Irregular

Regular

Factorial Designs

There is an interaction between frequency and regularity such that

for regular words there was no effect of frequency, however for irregular words responses were slower for lo frequency than hi frequency words

OR for high frequency words there was no effect of regularity,

however for low frequency words responses were faster for regular than irregular words

Factorial Designs

There are always two ways to describe a two-way interaction

Both are correct

However, one often makes more sense than the other, or answers the research question better

Main Effects & Interactions

Two kinds of information can be gleaned from factorial designs…

Main Effects: An effect of a single IV There is a main effect for each IV

Interactions: The effect of each IV across the levels of the other IV The effect of one IV depends on the level of the other IV


Main Effect The main effect of each IV tells us about the

relationship between that IV and the DV Do different levels of an IV bring about different

changes in the DV?

Need to look at row and column means


Word Type

5

5

5

10

Rote

Imagery

AbstractConcreteRehearsal

Type


Word Type

Column Means

5

5

5

10

Rote

Imagery

Row Means


Type


Word Type

57.5Column Means

5

7.5

5

5

5

10

Rote

Imagery

Row Means


Type


So what does this mean?

A main effect of Word Type tells us that more words are recalled when they are concrete

A main effect of Rehearsal Type tells us that more words are recalled when imagery is used

Regularity

Frequency Regular Irregular Mean

Hi 500 500

Lo 500 700

Mean

For Example...

Frequency If you are talking about a main effect of frequency you are comparing hi

frequency to lo frequency words PEROID. The word “regularity” should not appear in the sentence

Regularity If you are talking about a main effect of regularity you are comparing

regular to irregular words PEROID. The word “frequency” should not appear in the sentence


Is there an Interaction?

If so, then the main effects will have to be qualified, because an interaction indicates that the effect of one IV is different at different levels of the other IV


Interactions in your everyday life “It depends” – indicates that what we do in one situation

depends on some other variable

For example: Whether or not you go to a party DEPENDS on whether you have to work and who is going to be there If you have to work you will not go If you do not have to work, you might go if a certain person

is there


To calculate interactions we are interested in differences

If the differences are different then you have a two-way interaction

Regularity

Frequency Regular Irregular Difference

Hi 500 500 0

Lo 500 700 200

Difference 0 200


Word Type

Difference

5

5

5

10

Rote

Imagery

DifferenceAbstractConcreteRehearsal

Type


Word Type

05Difference

0

5

5

5

5

10

Rote

Imagery

DifferenceAbstractConcreteRehearsal

Type

Describing Main Effects and Interactions

In a 2x2 design there are THREE possible effects A main effect of IV(A) A main effect of IV(B) A IV(A) x IV(B) interaction

You need to describe each in English

No Main Effect of Word Type No Main Effect of Rehearsal Type No Interaction

0

2

4

6

8

10

Abstract Concrete

# o

f W

ord

s R

eca

lled

Rote Imagery

Main Effect of Word Type (line is on a diagonal)

No Main Effect of Rehearsal Type No Interaction

0

2

4

6

8

10

Abstract Concrete

# o

f W

ord

s R

ecal

led

Rote Imagery

No Main Effect of Word Type Main Effect of Rehearsal Type (space between lines)

No Interaction

0

2

4

6

8

10

Abstract Concrete

# o

f W

ord

s R

ecal

led

Rote Imagery

Main Effect of Word Type Main Effect of Rehearsal Type No Interaction

0

2

4

6

8

10

Abstract Concrete

# o

f W

ord

s R

ecal

led

Rote Imagery

Main Effect of Word Type Main Effect of Rehearsal Type Interaction (lines are not parallel)

0

2

4

6

8

10

Abstract Concrete

# o

f W

ord

s R

ecal

led

Rote Imagery

Main Effect of Word Type No Main Effect of Rehearsal Type Interaction

0

2

4

6

8

10

Abstract Concrete

# o

f W

ord

s R

ecal

led

Rote Imagery

No Main Effect of Word Type Main Effect of Rehearsal Type Interaction

0

2

4

6

8

10

Abstract Concrete

# o

f W

ord

s R

ecal

led

Rote Imagery

No Main Effect of Word Type No Main Effect of Rehearsal Type Interaction

0

2

4

6

8

10

Abstract Concrete

# o

f W

ord

s R

ecal

led

Rote Imagery

Practice Makes Perfect!

For each of the following data sets:

1. Identify the IVs and their levels

2. Sketch a graph (by hand)

3. Calculate the main effects and interactions

4. Describe the main effects and interactions

Factorial Designs

Reaction Time (ms) to identify target

Spatial Cue

Gender Valid Invalid

Men

Women

500

500

600

600

400

450

500

550

600

650

700

Valid Invalid

Men Women

Factorial Designs

Reading Times (ms) to identify target

Luminance

Frequency Lo Hi

Lo

Hi

600

500

500

400

350

400

450

500

550

600

650

700

Lo Lum Hi Lum

Lo Freq Hi Freq

Factorial Designs

Reaction Time (ms) on Stroop Task

Age

Stimuli 6 yrs 18 yrs

Consistent

Inconsistent

1000

1100

600

900

500

650

800

950

1100

1250

1400

1550

6yrs 18 yrs

Consistent Inconsistent

Factorial Designs

Recognition Accuracy (%)

Visual Field

Stimuli Left Right

Words

Faces

80

75

90

65

40

60

80

100

LVF RVF

Words Faces

See you Thursday!

Practice Makes Perfect!

For each of the following data sets:

1. Identify the IVs and their levels

2. Sketch a graph (by hand)

3. Calculate the main effects and interactions

4. Describe the main effects and interactions

Number of Words Recalled

Level of Processing

Sex Shallow Deep

Men

Women

50

50

70

70


Level of Processing

Sex Shallow Deep Mean Diff

Men

Women

50

50

70

70

60

60

20

20

Mean

Diff

50

0

70

0


40

60

80

100

Shallow Deep

Men Women

There is a main effect of levels of processing such that participants recalled more words with deep processing than with shallow processing

Reaction Time (ms)

Word Frequency

Word Type Lo Hi

Abstract

Concrete

800

900

400

500

Reaction Time (ms)

Word Frequency

Word Type

Lo Hi Mean Diff

Abstract

Concrete

800

900

400

500

600

700

400

400

Mean

Diff

450

100

850

100

Reaction Time (ms)

0

200

400

600

800

1000

Lo Hi

Abstract Concrete

There is a main effect of word frequency such that participants were faster at processing hi frequency words than lo frequency words

The is a main effect of word type such that participants were faster at processing abstract words than concrete words


Visual Field

Stimuli Left Right

Words

Faces

40

60

20

20


Visual Field

Stimuli Left Right Mean

30

40

Diff

20

40

Words

Faces

40

60

20

20

Mean

Diff

50

20

20

0


0

20

40

60

80

100

LVF RVF

Words Faces

There is a main effect of stimulus type, such that participants were more accurate recognizing face stimuli than word stimuli

The is a main effect of visual field, such that participants were more accurate recognizing stimuli in the LVF than in the RVF

There is a significant interaction between stimulus type and visual field, such that in the LVF participants were more accurate recognizing face stimuli than visual stimuli, whereas in the RVF there was no difference in the recognition accuracy for face and word stimuli

Analyzing Factorial Designs

Getting to know and love SPSS


In a 2x2 design, both factors can be … Both between-participants Both within-participants One between-participants and one within-

participants

SPSS is different depending on the design


We use SPSS to tell us if our main effects and interactions are significant

SPSS is a good tool to support your analysis of what is going on in your data – it should NOT drive your analysis


Calculate means (the ANOVA will do this for you – but just look at the means for now

BY HAND… Make a 2x2 table of the means Calculate the main effects and interactions Draw graphs of the means

Describe the main effects and interaction in English

Use SPSS ANOVA output to see if the main effects and interactions are significant


A 2 x2 between-participants design Randomized or Factorial

A 2 x2 between-participants and within-participants design Mixed

A 2 x2 within-participants design Repeated Measures

A 2 x2 between-participants design

LOP: Deep Shallow

Stimulus Type: Visual Auditory

DV: Number of words

recalled

Descriptive Stats SPSS

LOP

Stimulus Shallow Deep

Auditory

Visual


LOP

Stimuli Shallow Deep

Auditory

Visual

2.5

3.4

5.8

7.0 0

2

4

6

8

10

Shallow Deep

Auditory Visual


LOP

Stimuli Shallow DeepMean Diff

Auditory

Visual

2.5

3.4

5.8

7.0

Mean

Diff


LOP

Stimuli Shallow Deep Mean

4.15

5.2

Diff

3.3

3.6

Auditory

Visual

2.5

3.4

5.8

7.0

Mean

Diff

2.95

.9

6.4

1.2


Tests of Between-Subjects Effects

Source Sum of Squares df Mean Square FSig.

ENCODE 119.025 1 119.025 231.616 .000STIM 11.025 1 11.025 21.454

.000ENC * STIM .225 1 .225 .438

.512Error 18.500 36 .514


Two-way ANOVA Indicates that there are two IVs Two main effects and one interaction

df main effects number of levels of the factor- 1 df interaction (A-1)(B-1) df error AB(n -1)

F(1,28) = 13.95, p<.05


The number of items remembered was analyzed in a 2 (encoding: shallow, deep) x 2 (stimulus: visual, auditory) factorial analysis of variance (ANOVA). There was a main effect of encoding, F (1,36) = 231.616, p < .001, such that recall was better with deep encoding (M = 6.400 , SD = .160) than with shallow encoding (M = 2.590, SD = .160). There was a main effect of stimulus, F (1, 36) = 21.454, p < .001, such that recall was better for visual (M = 5.200 , SD = .160) than for auditory stimuli (M = 4.150 , SD = .0160). There was no significant interaction between encoding and stimulus, F (1, 36) = .436, p > .05.

A 2 x2 mixed design

Sex: Men Women

Attention: Focused Divided

DV: Number of words

recalled


Sex

Attention Men Women

Focused

Divided

A 2 x2 mixed design

Sex

Attention Men Women

Focused

Divided

7.06

4.00

7.44

3.56 0

2

4

6

8

10

Focused Divided

Men Women

A 2 x2 mixed design

Sex

Attention Men Women Mean Diff

Focused

Divided

7.06

4.00

7.44

3.56

Mean

Diff

A 2 x2 mixed design

Sex

Attention Men Women Mean

7.25

3.78

Diff

.38

.44

Focused

Divided

7.06

4.00

7.44

3.56

Mean

Diff

5.53

3.06

5.50

3.88

A 2 x2 mixed design

Tests of Within-Subjects Effects

Source Sum of Squares df Mean Square F Sig.ATTEN

Sphericity Assumed 192.516 1 192.516 124.622 .000 Greenhouse-Geisser 192.516 1.000 192.516 124.622 .000 Huynh-Feldt 192.516 1.000 192.516 124.622 .000 Lower-bound 192.516 1.000 192.516 124.622 .000ATTEN * SEX

Sphericity Assumed 2.641 1 2.641 1.709 .201 Greenhouse-Geisser 2.641 1.000 2.641 1.709 .201 Huynh-Feldt 2.641 1.000 2.641 1.709 .201 Lower-bound 2.641 1.000 2.641 1.709 .201Error(ATTEN)

Sphericity Assumed 46.344 30 1.545 Greenhouse-Geisser 46.344 30.000 1.545 Huynh-Feldt 46.344 30.000 1.545 Lower-bound 46.344 30.000 1.545

A 2 x2 mixed design

Tests of Between-Subjects Effects

Measure: MEASURE_1

Transformed Variable: Average

1947.016 1 1947.016 1443.347 .000

.016 1 .016 .012 .915

40.469 30 1.349

SourceIntercept

SEX

Error

Type III Sumof Squares df Mean Square F Sig.

A 2 x2 mixed design

Accuracies were analyzed in a 2 (sex: men, women) x 2 (attention: focused, divided) mixed analysis of variance (ANOVA). There was a main effect of attention, F (1, 30) = 124.622, p < .001, such that accuracy was better under focused attention conditions (M = 7.250 , SD = .211) than under divided attention conditions (M = 3.781, SD = .214). There was no main effect of sex, F (1, 30) = .012, p > .05, nor was there a sex by attention interaction, F (1, 30) = 1.709, p > .05.

A 2 x2 mixed design

Frequency: Lo Hi

Regularity: Regular Irregular

DV: Reaction Time

(ms)


Frequency

Regularity Lo Hi

Regular

Irregular

A 2 x2 mixed design

Frequency

Regularity Lo Hi

Regular

Irregular

572

699

540

544 300

500

700

Lo Hi

Regular Irregular

A 2 x2 mixed design

Frequency

Regularity Lo Hi Mean Diff

Regular

Irregular

572

699

540

544

Mean

Diff

A 2 x2 mixed design

Frequency

Regularity Lo HiMean

556

622

Diff

32

155

Regular

Irregular

572

699

540

544

Mean

Diff

636

127

542

4

Tests of Within-Subjects Effects

Measure: MEASURE_1

68578.516 1 68578.516 53.809 .000

68578.516 1.000 68578.516 53.809 .000

68578.516 1.000 68578.516 53.809 .000

68578.516 1.000 68578.516 53.809 .000

19117.234 15 1274.482

19117.234 15.000 1274.482

19117.234 15.000 1274.482

19117.234 15.000 1274.482

139782.516 1 139782.516 190.608 .000

139782.516 1.000 139782.516 190.608 .000

139782.516 1.000 139782.516 190.608 .000

139782.516 1.000 139782.516 190.608 .000

11000.234 15 733.349

11000.234 15.000 733.349

11000.234 15.000 733.349

11000.234 15.000 733.349

60823.891 1 60823.891 63.673 .000

60823.891 1.000 60823.891 63.673 .000

60823.891 1.000 60823.891 63.673 .000

60823.891 1.000 60823.891 63.673 .000

14328.859 15 955.257

14328.859 15.000 955.257

14328.859 15.000 955.257

14328.859 15.000 955.257

Sphericity Assumed

Greenhouse-Geisser

Huynh-Feldt

Lower-bound

Sphericity Assumed

Greenhouse-Geisser

Huynh-Feldt

Lower-bound

Sphericity Assumed

Greenhouse-Geisser

Huynh-Feldt

Lower-bound

Sphericity Assumed

Greenhouse-Geisser

Huynh-Feldt

Lower-bound

Sphericity Assumed

Greenhouse-Geisser

Huynh-Feldt

Lower-bound

Sphericity Assumed

Greenhouse-Geisser

Huynh-Feldt

Lower-bound

SourceFREQ

Error(FREQ)

REG

Error(REG)

FREQ * REG

Error(FREQ*REG)

Type III Sumof Squares df Mean Square F Sig.

A 2 x2 within-participants design

Response times were analyzed in a 2 (frequency: hi, lo) x 2 (regularity: regular, irregular) repeated-measure analysis of variance (ANOVA). There was a main effect of regularity, F (1, 15) = 190.608, p<.001, such that responses were faster to regular words (M = 542.594 , SD = 24.610) than irregular words (M = 636.063 , SD = 23.638). There was a main effect of frequency, F (1, 15) = 53.809, p<.001, such that responses were faster to hi frequency words (M = 556.594 , SD = 23.787) than to low frequency words (M = 622.063 , SD = 24.810). There was a significant frequency by regularity interaction, F (1, 15) = 63.673, p<.001, such that there was an effect of frequency for irregular words, but not regular words.

Writing the Results

Writing the Results

In the results section you are presenting the findings of your experiment

A good pattern is to report the results in statistical language, followed by a statement in English about what that means

Some experiments require you to do more than one set of analyses – put each set in a separate paragraph

Writing the Results

All results sections should begin with a statement about how you reduced the data, and then refer to a table or figure where you present the data itself

For example, in a typical RT experiment there are many trials, but those are reduced to the means for each condition for each subject Did you eliminate any subjects at this stage for having error

rates that were too high or other reasons that make their data suspicious? Report them here. Present the actual data in a table OR figure

Results: Tables OR Figures Tables OR figures help clarify the results

Generally, tables are used to present large arrays of data (15+ means)

In the text, refer to a table or figure by # and describe

“As shown in Figure 2, the aerobics group…”

Tables or figures supplement the text, they do NOT replace it

Writing the Results

There are no standards on the reporting of statistics Is there a difference Stats to back up difference How were they different

I would like you to report exact p values, to 3 decimal places

If SPSS tells you that p = .000, report that p< .001

t-Test (independent or paired)

Start with a description of your data

Report the results of the t-test, followed by an English statement of which mean was the higher A significant t-test tells you that two means are different, it

doesn’t tell you which one was higher

E.g., Number of items recalled in each encoding condition was compared with an independent t-test. There was a significant difference between conditions, t(32) = 2.95, p = .03. More words were recalled in the semantic encoding condition (M = 16, SD = 1.4) than in the phonological encoding condition (M = 12, SD = 1.2).

ANOVA

There are many types of ANOVAs, but they all have the same basic format: There are 2 or more factors (independent variables), each

of which has 2 or more level The factors can be either within-subjects or between-

subjects

Start with a statement about how you prepared the data for analysis

Present the data, either in a table OR a figure E.g., Mean response times were calculated for each

condition, and are presented in Table 1.

ANOVA

Introduce your ANOVA and present your design Mention each factor, and the levels of each factor If all of your factors are b/t, you can call it a factorial

ANOVA If all of your factors are w/in, you can call it a repeated

measures ANOVA If you have some of each, you call it a mixed ANOVA, and

then specify which factors are w/in and which are b/t

E.g., Response times were analyzed in a 2 (encoding: shallow, deep) x 2 (modality: auditory, visual) mixed Analysis of Variance (ANOVA), with encoding as a within-subjects factor and modality as a between-subjects factor.

ANOVA Report the main effects, one at a time In a very complex design (e.g., in a 2 x 2 x 2 x

3 design there are 4 main effects, 6 2-way interactions, 4 3-way interactions, and a 4-way interaction) you might report only the significant main effects, and the theoretically-interesting non-significant effects However, since you will be doing only very simple

designs, report ALL of your main effects and all of your interactions, significant or not

ANOVA When you report the effect, first describe the

effect in statistics, then in English (or, if you can combine them)

E.g., There was a main effect of gender, F(1, 23) = 3.16, p = .022, such that women were funnier than men.

OR E.g., Women were funnier than men, F(1, 23) =

3.16, p = .022

ANOVA

If the interaction is significant, you need to check to see if the main effect is still valid (sometimes it is, but sometimes it isn’t)

If the main effect is misleading (i.e., the effect holds for one level but not the other), you need to qualify it, so that your reader knows not to be fooled

E.g., There was a main effect of regularity, F(1, 31) = 5.67, p = .01, that was qualified by the frequency x regularity interaction (then you would go on to describe the interaction)

ANOVA

Describe the interaction

If it is NOT significant – just say that it’s not significant, and report the F (you can report the exact p, or you can report ns, which stands for not significant)

If it IS significant, report it, and then describe it in English E.g., There was an interaction between word frequency and

regularity, F(1, 31) = 5.67, p = .008. For high frequency words, response times were the same for regular and irregular words however, for low frequency words, response times were greater for irregular than for regular words.

ANOVA

Sometimes an interaction occurs when both levels show the same pattern of results, but the effect is greater for one than the other

E.g., There was an interaction between word frequency and regularity, F(1, 31) = 5.67, p = .008, such that irregular words produced greater slowing for low frequency words, than for high frequency words.

Assignment 3

Assignment #3 You will be given the data files for four questions

For each question, read the experiment description that I provide, analyze the data in SPSS, and write a one-paragraph results section

Your submitted assignment should consist of: Title Page Results sections, each on a separate page Tables (you need to put the data in a Table if you aren’t going to put

the means in the text) Figure captions Figures, each on a separate page

NOTE: You don’t need Tables or Figures for experiments you can analyze with a t-test, but you will need it for other experiments.

Documents

Factorial Designs2