language and thought lecture 2 whorf categorical perception statistics

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Language and Thought Language and Thought Lecture 2 Lecture 2 Whorf Whorf Categorical Perception Categorical Perception Statistics Statistics

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Page 1: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Language and Language and ThoughtThought

Lecture 2Lecture 2

WhorfWhorf

Categorical PerceptionCategorical Perception

StatisticsStatistics

Page 2: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

1897 1907 1917 1927 1937 1947

Benjamin WhorfBenjamin Whorf

1956

1941 Died at 44.

Born Winthrop, MA

MITChem. E.

FirePreventionEngineer

Interest inLinguistics

First PaperNahuatlNahuatl Aztec

YaleE. Sapir

FieldworkArizona –Arizona –Modern Modern NahuatlNahuatl

Yale: Research FellowshipsLecturer

Introduction to Linguistic Relativity

Page 3: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Whorfian HypothesisWhorfian Hypothesis(Sapir-Whorf Hypothesis)(Sapir-Whorf Hypothesis)

Whorf (1956, p. 213): The categories and types

that we isolate from the world of phenomena we do not find there because they stare every observer in the face; on the contrary, the world is presented as a kaleidoscopic flux of impressions which has to be organized by our minds – and this means largely by the linguistic systems in our minds.

Page 4: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

TerminologiesTerminologies

Linguistic Determinism (strong)Linguistic Determinism (strong) Linguistic Relativity (weak)Linguistic Relativity (weak)

Page 5: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Whorf as a fire Whorf as a fire prevention engineerprevention engineer

Observation: Many fires are started because of Observation: Many fires are started because of terrible language.terrible language.– E.g. carelessness around “Empty” gasoline E.g. carelessness around “Empty” gasoline

drums. drums.

“Empty” ok to flick cigarette butt

Empty-looking “Empty” ok to flick cigarette butt

Thought Language/Behavior.

Language Thought/Behavior.

Page 6: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Whorf’s argumentWhorf’s argument ArgumentArgument

– Languages vary in their conceptual Languages vary in their conceptual repertoire. repertoire.

– Thought is dependent on language.Thought is dependent on language.– Thus, speakers of different Thus, speakers of different

languages think differently.languages think differently. Evidence?Evidence?

– Languages vary!Languages vary!

FIX: Need separate measure of thought!

Page 7: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Another problem?Another problem? Suppose it is true that Suppose it is true that

1.1. Eskimos make fine discriminations of snow, and Eskimos make fine discriminations of snow, and Americans do not.Americans do not.

2.2. Eskimos have more words for snow than Eskimos have more words for snow than AmericansAmericans

– Now what’s the cause & effect?Now what’s the cause & effect?

Eskimos make fine snow discriminations BECAUSE Eskimos make fine snow discriminations BECAUSE they have lots of snow words. they have lots of snow words.

OROR

Eskimos learn to make fine snow discriminations Eskimos learn to make fine snow discriminations AND SO they have lots of snow words.AND SO they have lots of snow words.

Now how do you tease things apart???

Page 8: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Dissociating language Dissociating language and circumstanceand circumstance Move Americans to Vail or AspenMove Americans to Vail or Aspen

‘‘sugar’sugar’ ‘granule’‘granule’ ‘powder’‘powder’

Move Eskimos to BermudaMove Eskimos to Bermuda

Page 9: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Experiments in various Experiments in various domainsdomains

Some examples:Some examples: ColorColor ObjectObject Space Space TimeTime Number Number Theory of MindTheory of Mind

Page 10: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

People who grew up without learning language.

Infants who have not learned language.

Animals who do not speak a language.

Subject PopulationSubject PopulationSpeakers of another language.

Aphasics: patients who suffered brain damage leading to language problems.

Page 11: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

ColorColor

Page 12: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Ring ON Pole

Cup ON Saucer

Telephone ON Wall

Lady ON TV

Moustache ON Face

Spatial PrepositionsSpatial Prepositions

IM? UM?

AUF?

AN?

IM?

Page 13: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

• “Where is the girl?”

– The girl is south of the umbrella.

– The girl is at the tilted side of the umbrella.

– The girl is to the left of the umbrella.

FigureReference Object

Spatial Frames of Spatial Frames of ReferenceReference

Page 14: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

ReorientationReorientation

“Left of the blue wall”

Page 15: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

NumberNumberPiraha:“one-two-many” counting system.

Page 16: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Theory of MindTheory of Mind

Page 17: Language and Thought Lecture 2 Whorf Categorical Perception Statistics
Page 18: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

What is categorical What is categorical Perception?Perception?

Page 19: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Fre

quen

cy (

Hz)

Time (msec)

ba da ga

What is Categorical What is Categorical Perception?Perception?

Example of Categorical Perception

Page 20: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

SpeakingSpeaking

Vocal Tract: Vocal Fold Lips(Modeled as a tube)

Vocal Fold Lips

Average Man - Length = 17.4cm

Page 21: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Vocal Tract ModelVocal Tract Model

F1

F2

F3

Vocal Tract = 17.4 cmSpeed of sound = 34800 cm/sec

Speed = Distance/Time = Wavelength x Frequency

Freq = Speed/Wavelength

L = 17.4cm

500Hz

1500Hz

2500Hz

λ = 4L

λ = 4L/3

λ = 4L/5

Page 22: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

SpeakingSpeaking

c d

a

b

c da bon top of his deck

Voca

l fo

lds

Lip

s

Page 23: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Vocal TractVocal Tract

http://www.exploratorium.edu/exhibits/vocal_vowels/vocal_vowels.html

ee

oo

oh

ah

eh

Page 24: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

SpectrogramSpectrogram

Time --------------

frequ

ency

Page 25: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

http://www.haskins.yale.edu/featured/patplay.html

Pattern Playback Pattern Playback MachineMachine

Page 26: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

SpectrogramSpectrogram

Steady StateSteady State Transitional StateTransitional State

Page 27: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Methods for Testing Methods for Testing Categorical PerceptionCategorical Perception

IdentificationIdentification– Randomly play the audio clips and Randomly play the audio clips and

asked to identify the phonemeasked to identify the phoneme DiscriminationDiscrimination

– Randomly play pairs and asked to make Randomly play pairs and asked to make Same-different JudgmentSame-different Judgment Same pairsSame pairs Different pairsDifferent pairs

Page 28: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

IdentificationIdentification

IdentificationIdentification– Randomly play the audio clips and asked to Randomly play the audio clips and asked to

identify the phonemeidentify the phoneme If there is CP, what should the graph If there is CP, what should the graph

look like? look like? – X-axis stimuli arranged in a continuum X-axis stimuli arranged in a continuum with with

very small incremental differencevery small incremental difference between between the stimulithe stimuli

– Y-axis % Identification as the tested Y-axis % Identification as the tested categorycategory

Page 29: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

IdentificationIdentification(idealized results)(idealized results)

% Iden

tifica

tion a

s C

ate

gory

X

0

20

40

60

80

100

2 3 4 5 6

Stimulus #

1 7

Page 30: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Fre

quen

cy (

Hz)

Time (msec)

ba da ga

What is Categorical What is Categorical Perception?Perception?

Page 31: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

0

10

20

30

40

50

60

70

80

90

100

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

Stimulus ID

% I

den

tifi

cati

on

ba

da

ga

Categorical PerceptionCategorical Perception(Idealized Data)(Idealized Data)

Page 32: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Methods for Testing Methods for Testing Categorical PerceptionCategorical Perception

IdentificationIdentification– Randomly play the audio clips and Randomly play the audio clips and

asked to identify the phonemeasked to identify the phoneme DiscriminationDiscrimination

– Randomly play pairs and asked to make Randomly play pairs and asked to make Same-different JudgmentSame-different Judgment Same pairsSame pairs Different pairsDifferent pairs

Page 33: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Discrimination StudyDiscrimination Study

Last example of ba/da/ga varied Last example of ba/da/ga varied transitional state (up, down of F2).transitional state (up, down of F2).

In this example, Varying Voice Onset In this example, Varying Voice Onset Time.Time.

Page 34: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Voice Onset Time Voice Onset Time (VOT)(VOT)

VOT: VOT: time between consonant release and vocal cord vibration

[p][b]

So what is the difference in VOT between So what is the difference in VOT between VOICELESS [b] and VOICED [p]?VOICELESS [b] and VOICED [p]?– SHORT VOT SHORT VOT voiced voiced– LONG VOT LONG VOT voiced voiced

Page 35: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Voice Onset Time Voice Onset Time (VOT)(VOT)

Short VOT = ?Short VOT = ? Long VOT = ?Long VOT = ? Which one is /di/ Which one is /di/

and which one and which one is /ti/?is /ti/?

di ti

Page 36: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Discrimination StudyDiscrimination Study

Same/Different?0ms 60ms

Same/Different?0ms 10ms

Same/Different?40ms 40ms

Why is this pair difficult?

(i) Acoustically similar?

(ii) Same Category?

Page 37: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

DiscriminationDiscrimination

Same/Different0ms 60ms

Same/Different0ms 10ms

Same/Different40ms 40ms

A More Systematic Test

0ms

20ms

40ms

20ms

40ms

60ms

D T

D

T T

D

Within-Category Discrimination is Hard

Page 38: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Categorical PerceptionCategorical Perception(Idealized Discrimination Data)(Idealized Discrimination Data)

% C

orr

ect

Dis

crim

inati

on

0

20

40

60

80

100

1-2 2-3 3-4 4-5 5-6

Pairs by VOT

Page 39: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Question 1Question 1

Is speech perception innate?Is speech perception innate?– Do newborns have categorical Do newborns have categorical

perception?perception? If CP requires exposure to language If CP requires exposure to language

(e.g., knowledge of minimal pairs in (e.g., knowledge of minimal pairs in one’s language), then NO.one’s language), then NO.

If CP is innate, then YES.If CP is innate, then YES.

– How do we test newborns?How do we test newborns?

Page 40: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

High Amplitude High Amplitude Sucking ProcedureSucking Procedure

Infant given a pacifier that Infant given a pacifier that measures sucking ratemeasures sucking rate

HabituationHabituation – Infant sucks – Infant sucks to hear sound (e.g. ba) until to hear sound (e.g. ba) until bored.bored.

TestTest – Play sound (e.g., ba – Play sound (e.g., ba or pa). Is there or pa). Is there dishabituationdishabituation??– Infants will suck to hear sound Infants will suck to hear sound

if the sound is no longer if the sound is no longer boring.boring.http://psych.rice.edu/mmtbn/language/sPerception/video/sucking_h.movhttp://psych.rice.edu/mmtbn/language/sPerception/video/sucking_h.mov

http://www.learner.org/vod/vod_window.html?pid=1620 (2:50 min. into videoclip) http://www.learner.org/vod/vod_window.html?pid=1620 (2:50 min. into videoclip)

Page 41: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Stimuli for Eimas et. Stimuli for Eimas et. al’s Studyal’s Study BA vs. PABA vs. PA Vary Voice Onset Time (VOT): time btw Vary Voice Onset Time (VOT): time btw

consonant release and vocal cord consonant release and vocal cord vibrationvibration

VOT in milliseconds

0 20 40 60 80

PABA

Page 42: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

PredictionsPredictions

Between Between CategoryCategory

BABA11-PA-PA

Within Within CategoryCategory

BABA11-BA-BA22

Within Within CategoryCategory

ControlControl

BABA11-BA-BA11

Innate Innate Categorical Categorical PerceptionPerception

dishabituatdishabituatee

remain remain habituatedhabituated

remain remain habituatedhabituated

Untuned Untuned SensitivitySensitivity

dishabituatdishabituatee

dishabituatdishabituatee

remain remain habituatedhabituated

InsensitiveInsensitive remain remain habituatedhabituated

remain remain habituatedhabituated

remain remain habituatedhabituated

BA1 = VOT 20ms; BA2 = VOT 0ms; PA = VOT 40ms

Page 43: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Results for Eimas et. al’s Results for Eimas et. al’s StudyStudy

ME

AN

NU

MB

ER

OF

SU

CK

ING

RE

SP

ON

SE

dishab

no

no

Page 44: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Question 1 AnswerQuestion 1 Answer

Q1: Is Speech Perception Innate?Q1: Is Speech Perception Innate? Many other studies since tested:Many other studies since tested:

– Infants (Neonates) on other contrasts.Infants (Neonates) on other contrasts. Consensus: Yes to Innate Q. Consensus: Yes to Innate Q.

– Infants do not discriminate all physically Infants do not discriminate all physically equal acoustic difference; they show equal acoustic difference; they show heightened sensitivity to those that are heightened sensitivity to those that are important for language.important for language.

– BUT… there is language-specific fine-tuning…BUT… there is language-specific fine-tuning…

Page 45: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Provisional ConclusionsProvisional Conclusions

Speech Perception makes use of Speech Perception makes use of some auditory mechanisms which some auditory mechanisms which evolved prior to languageevolved prior to language– These abilities are innateThese abilities are innate

Page 46: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Becoming a Native Becoming a Native ListenerListener Languages differ in their Languages differ in their

inventories of phonemes.inventories of phonemes.

What develops or changes in our What develops or changes in our speech perception abilities?speech perception abilities?

Language Specific Fine Tuning

Page 47: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Japanese vs. EnglishJapanese vs. English(Miyawaki et al. 1975)(Miyawaki et al. 1975)

RA

LA

AMERICANS

Page 48: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Dental Stop – tip of tongue touching back of front teeth

Retroflex Stop – tongue curled so tip is behind alveolar ridge

Hindi (spoken in India)

unvoiced unaspirated retroflex vs. dental stop

(English /t/ is typically somewhere between the two)

Page 49: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Can you hear the Can you hear the difference?difference?

Hindi

dental

retroflex

Page 50: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Uvular – tongue is raised against the velum

Velar – tongue is raised behind the velum

Salish (Native North American language):

glotalized voiceless stops

(they are actually ejectives - ejective is produced by obstructing the airflow by raising the back of the tongue against or behind the velum)

Page 51: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

When does changes in When does changes in sensitivity occur?sensitivity occur?

Infancy

Adulthood

… And testing method?

Page 52: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Conditioned Head-TurnConditioned Head-Turn ConditioningConditioning

– Child hears a Child hears a string of sounds.string of sounds.

– Conditioned to Conditioned to turn head when turn head when detects a change detects a change (e.g., bell (e.g., bell whistle) with whistle) with rewardreward

TestTest– Speech sounds Speech sounds

(e.g., da, da, da, (e.g., da, da, da, da, ta,…)da, ta,…)

– Does the child Does the child turn his or her turn his or her head with head with changed from da changed from da to ta?to ta?

Werker: http://www.learner.org/vod/vod_window.html?pid=1630Kuhl: http://www.learner.org/vod/vod_window.html?pid=1631

Page 53: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

When does Change When does Change Occur?Occur?

6-8m 8-10m 10-12m 11-12m

6-8m 8-10m 10-12m 11-12m

Page 54: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

What is changing? What is changing? Two contrasting views: 1 or 2?Two contrasting views: 1 or 2?

Maintenance or LossMaintenance or Loss– If you don’t use it, you lose it.If you don’t use it, you lose it.– Parallel aspects of early visual Parallel aspects of early visual

development.development. Functional ReorganizationFunctional Reorganization

– Existing architecture reorganized for Existing architecture reorganized for higher level of processing.higher level of processing.

Page 55: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

What is changing? What is changing? Two contrasting viewsTwo contrasting views

Page 56: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

What is changing? What is changing? 1. Maintenance or Loss View1. Maintenance or Loss View

Structure-changingNon-native boundariesdisappear.Resulting in native language phonetics

Phonetics

Acoustics

Phonology

Page 57: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

What is changing? What is changing? 2. Functional Reorganization2. Functional Reorganization

Structure-buildingNative languagephonemesbuilt fromuniversal phones

Phonetics

Acoustics

Phonology

Page 58: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Which view?Which view? Werker (1997) noted some problems for Werker (1997) noted some problems for

the the maintenance or loss viewmaintenance or loss view..1. Many of the uncategorized sounds do appear in the 1. Many of the uncategorized sounds do appear in the

native language but just are not meaningful (e.g., as native language but just are not meaningful (e.g., as allophones), and speakers can be made aware of the allophones), and speakers can be made aware of the difference.difference.

Example:Example:– /p/ is only /p/ is only aspiratedaspirated in “pin” and not “spin’ in “pin” and not “spin’– /p/ in “pin” and “spin” are /p/ in “pin” and “spin” are allophonesallophones in English in English– But could be But could be minimal pairsminimal pairs in some other in some other

languages.languages.

Page 59: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Which view?Which view? Werker (1997) noted some problems for the Werker (1997) noted some problems for the

maintenance or loss viewmaintenance or loss view..1. Many of the uncategorized sounds do appear in the native 1. Many of the uncategorized sounds do appear in the native

language but just are not meaningful (e.g., as allophones), and language but just are not meaningful (e.g., as allophones), and speakers can be made aware of the difference.speakers can be made aware of the difference.

2. Children who fail to show categorical perception for non-native 2. Children who fail to show categorical perception for non-native phonemes can acquire a new language without an accent.phonemes can acquire a new language without an accent.

3. Adults can be trained to make non-native distinctions.3. Adults can be trained to make non-native distinctions.

4. Perceptual distinction is readily available for non-linguistic 4. Perceptual distinction is readily available for non-linguistic tasks.tasks.

Language Specific Fine Tuning

Page 60: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Which model?Which model?

Werker (1997): The evidence that poses Werker (1997): The evidence that poses problems for maintenance or loss view problems for maintenance or loss view supports the supports the functional reorganization functional reorganization viewview..

I.e., the view that:I.e., the view that:– Those perceptual categories which are Those perceptual categories which are

meaningful in the native language become meaningful in the native language become speech categories.speech categories.

– The remainder are perceived but not The remainder are perceived but not recruited in speech perception.recruited in speech perception.

Language Specific Fine Tuning

Page 61: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

StatisticsStatistics

Page 62: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

OutlineOutline Stats Terms SimplifiedStats Terms Simplified

– t-testst-tests– ANOVAs, Main effects and ANOVAs, Main effects and

InteractionsInteractions– Regressions, CorrelationsRegressions, Correlations

Page 63: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

T-tests and ANOVAsT-tests and ANOVAs

T-tests: Compare 2 means.T-tests: Compare 2 means. ANOVA (Analysis of Variance): ANOVA (Analysis of Variance):

Compare multiple meansCompare multiple means– Yields significance of main or Yields significance of main or

interaction effectsinteraction effects

Page 64: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Hypothetical ExperimentHypothetical Experiment(Example of Main & Interactions (Example of Main & Interactions Effects)Effects) Dependent Measure: Number of Dependent Measure: Number of

GirlfriendsGirlfriends Independent Measure: Independent Measure:

– Wealth of bachelors according to Income Wealth of bachelors according to Income (Rich, Poor)(Rich, Poor)

– Looks of same bachelors according to Looks of same bachelors according to Oprah Oprah

(Handsome, Ugly)(Handsome, Ugly)

Page 65: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Design 2 x 2Design 2 x 2

RichRich PoorPoor

Hand-someHand-some

UglyUgly

# of GF

# of GF

# of GF

# of GF

Page 66: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Hypothetical Hypothetical ExperimentExperiment(Example of ANOVAs F1 vs. (Example of ANOVAs F1 vs. F2)F2) Is a female model more attractive Is a female model more attractive

in short or long skirt?in short or long skirt?– Model pictured in 10 different short Model pictured in 10 different short

skirts and 10 different long skirtsskirts and 10 different long skirts– 30 Males rated the model’s 30 Males rated the model’s

attractiveness in each skirt (1 = not attractiveness in each skirt (1 = not attractive to 7 = extremely attractive to 7 = extremely attractive)attractive)

Page 67: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Hypothetical Hypothetical ExperimentExperiment(Example of ANOVAs F1 vs. (Example of ANOVAs F1 vs. F2)F2) F1: Subject AnalysisF1: Subject Analysis

– Comparing subjectsComparing subjects– Averaging across items for each subjectAveraging across items for each subject

F2: Items AnalysisF2: Items Analysis– Comparing itemsComparing items– Averaging across subjects for each itemAveraging across subjects for each item

Page 68: Language and Thought Lecture 2 Whorf Categorical Perception Statistics

Hypothetical Hypothetical ExperimentExperiment(Example of ANOVAs F1 vs. (Example of ANOVAs F1 vs. F2)F2) F1: Subject AnalysisF1: Subject Analysis

F2: Items AnalysisF2: Items Analysis

Short LongFrederick H. 5.2 3.1Hef 7.0 7.0Rudy G. 5.2 4.9Bill C. 6.9 1.3

RatingShort Skirt 1 4.5Short Skirt 2 5.3…Long Skirt 1 6.7Long Skirt 2 3.5…