ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005...

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March 14, 2005 Methodology & Statistics ANOVA (GLM- Repeated measures) Jantien Donkers

Transcript of ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005...

Page 1: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

March 14, 2005 Methodology & Statistics

ANOVA (GLM- Repeated measures)

Jantien Donkers

Page 2: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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When to use..

o T-test: 2 conditions testing 1 independent variable (e.g. text complexity –simple/complex in relation to number of recalled words)

o ANOVA: 3 or more conditions testing 1 (one way ANOVA) or more (two way ANOVA) variables

Page 3: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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ANOVA’s

o F-ratioo Size of the variance due to the experimental

conditions in relation to the error (unexpected) variance

o Degrees of freedom (df)

Page 4: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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ANOVA’s (2)

o H0: all means are equalo Alternative: all of means are different, or

just one of them

o Variation among groups is compared to variation within groups: a relatively large difference is evidence against H0

Page 5: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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Parametric assumptions

o Experimental scores are measured on an interval scale

o Scores are normally distributedo Variabiliy of scores for each conditions

should be roughly the same (homogeneity of variance)

Page 6: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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This experiment

o 6 conditions testing 2 independent variables

o Dependent variable: reading time

Page 7: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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o a self-paced reading study in Dutch

o “who” and “which” questions

o specificity and structure

This experiment (2)

Page 8: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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Why?

o In various research it is observed that “which” questions are more difficicult than “who” questions, but:

o It has never been addressed why this is the case

Page 9: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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“Who” Wie heeft de keizer gezocht in de kelder?

“Which” generic Welke persoon heeft de keizer gezocht in de kelder?

“Which” specific Welke bediende heeft de keizer gezocht in de kelder?

Variable 1: specificity

Page 10: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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o Sentence structure is manipulated by context:

SOTerwijl de dronken bediende een dutje deed, zocht de nuchtere bediende de keizer in de kelder.

OSTerwijl de dronken bediende een dutje deed zocht de keizer de nuchtere bediende in de kelder.

Variable 2: structure

Page 11: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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o 3x2 design: 6 conditions

Who SO OSWhichGen SO OSWhichSpec SO OS

o 8 scenario/question combinations per conditions(total of 48)

Overview conditions

Page 12: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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o 48 (14 male, 34 female)o Mean age 22.1 (sd 2.34)o Normal or corrected to normal visiono Paid for participation

Participants

Page 13: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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o Phrase-by-phrase self-paced reading(using E-prime software package)o“Moving window”

o Accuracy: participants had to judge aprovided answer (correct/incorrect) by pressingthe corresponding button

o Reading times and accuracy analyzed

Procedure & analysis

Page 14: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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Terwijl de dronken bediende een hapje at, zocht de nuchtere bediendede keizer in de kelder.

Page 15: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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+

Page 16: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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Wie

Page 17: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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heeft

Page 18: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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de keizer

Page 19: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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gezocht

Page 20: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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in de kelder?

Page 21: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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Page 22: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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de nuchtere bediende

Page 23: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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Hypotheses

o Set-restriction (“specificity”) is a (the?) complicating factor during wh-question processingo Also when the questions are presented within

an appropriate contexto BUTo Processing difficulties in set-restricted wh-

questions interact with difficulties in sentence structure

Page 24: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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Hypothesis 1

o Set-restriction is a complicating factor during wh-question processing

�WhichSpec > WhichGen = WhoAlternatives:�WhichSpec = WhichGen > Who�WhichSpec = WhichGen = Who(in reading times (RTs)

Page 25: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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Hypothesis 2

o Processing difficulties in set-restricted wh-questions interact with difficulties in sentence structure

� WhichSpec OS > WhichGen OS = Who OS�WhichSpec SO = WhichGen SO = Who SO

Possible alternative:�All wh-types OS > SO

Page 26: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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Segment of interest

o “Point of integration”:

Welke bediende heeft de keizer gezocht in de kelder?

o At this position (i.e. participle) it becomes clear which role each individual NP (Wh-phrase and “de keizer”) plays

Page 27: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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Repeated measures/ SPSS

Page 28: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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Data

Page 29: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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Data pre-processing (1)

o Define conditions (in terms of factors)o Cond 1 or 2: Qtype 1 (Who)o Cond 1 or 4 or 5: Order 1 (SO)

o Define item groupso Define lists

Page 30: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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Data pre-processing (2)

o Define cut-offs (outliers)o Calculate segment means and sds

o Per subjecto Per item

o Define limits (mean+ 2sd)o Replace outliers and >limits by mean+2sdo Data-transformation (suitable for SPSS)

Page 31: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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Data pre-processing (3)

o Write syntax script

Page 32: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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Data pre-processing (4)

o Write syntax script

Page 33: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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Data pre-processing (5)

o Write syntax script

Page 34: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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GLM – Repeated measures

o SPSS data file with subject meanso SPSS data file with item means

Page 35: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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GLM – Repeated measures

Page 36: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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GLM – Repeated measures

Page 37: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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GLM – Repeated measures

Page 38: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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GLM – Repeated measures

Page 39: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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GLM – Repeated measures

Page 40: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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Effects (subject analysis)

o Main effect of question type (who, whichGen, whichSpec)

o Main effect of order (SO, OS)o Interaction question type by ordero (Interaction …by list)

Page 41: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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Effect or interaction?

o Plot you data!o Mistake in labellingo Effect can be counter-intuitiveo Post-hoc analyses

Page 42: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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Accuracy

0,84

0,86

0,88

0,90

0,92

0,94

0,96

0,98

SO OS SO OS SO OS

Who WhichGen WhichSpec

Accuracy

Page 43: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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o The data suggest that answers following OS structures are more difficult to judge that those following SO questions.

Accuracy

Page 44: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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Mean reading times per segment

300,00

400,00

500,00

600,00

700,00

800,00

900,00

Wh aux NP2 participle PP

Segment

Rea

ding

tim

e

Who SO

Who OS

WhichGen SO

WhichGen OS

WhichSpec SO

WhichSpec OS

Reading times

Page 45: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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Phrase 1

300,00

350,00

400,00

450,00

500,00

550,00

600,00

SO OS SO OS SO OS

Who WhichGen WhichSpec

o Phrase 1: wh-element

Reading times (2)

Page 46: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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o Phrase 2: auxiliary

Phrase 2

350,00360,00370,00380,00390,00400,00410,00420,00430,00

SO OS SO OS SO OS

Who WhichGen WhichSpec

Reading times (3)

ns ns**

Page 47: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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o Phrase 3: NP2Phrase 3

380,00400,00420,00440,00

460,00480,00500,00520,00

SO OS SO OS SO OS

Who WhichGen WhichSpec

Reading times (4)

*ns *

Page 48: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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o Phrase 4: ParticiplePhrase 4

500,00550,00600,00650,00700,00750,00800,00850,00900,00

SO OS SO OS SO OS

Who WhichGen WhichSpec

Reading times (5)

Page 49: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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What do I want to know?

o So the separate question types behave differently?

o Is this connected to word order complexity?

Page 50: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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o Phrase 4: ParticiplePhrase 4

500,00550,00600,00650,00700,00750,00800,00850,00900,00

SO OS SO OS SO OS

Who WhichGen WhichSpec

Reading times (5)

Page 51: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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o Phrase 4: ParticiplePhrase 4

500,00550,00600,00650,00700,00750,00800,00850,00900,00

SO OS SO OS SO OS

Who WhichGen WhichSpec

Reading times (5)

Page 52: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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o Phrase 4: ParticiplePhrase 4

500,00550,00600,00650,00700,00750,00800,00850,00900,00

SO OS SO OS SO OS

Who WhichGen WhichSpec

Reading times (5)

Page 53: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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What do I want to know?

o So the separate question types behave differently?

�Who and WhichGen seem to pattern alike, compared to WhichSpec

Page 54: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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Reading times SO

Mean reading times per segment

300,00

400,00

500,00

600,00

700,00

800,00

900,00

Wh aux NP2 participle PP

Segment

Rea

ding

tim

e

Who SO

WhichGen SO

WhichSpec SO

Page 55: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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Reading times OS

Mean reading times per segment

300,00

400,00

500,00

600,00

700,00

800,00

900,00

Wh aux NP2 participle PP

Segment

Rea

ding

tim

e

Who OS

WhichGen OS

WhichSpec OS

Page 56: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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What do I want to know?

o Is a different pattern for the WhichSpec condition only connected to word order complexity?

�The increased reading times for WhichSpec are confined to the OS structure-conditions. In SO conditions the average reading times were comparable.

Page 57: ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005 Methodology & Statistics When to use.. o T-test: 2 conditions testing 1 independent

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o Phrase 5: PPPhrase 5

0,00100,00200,00300,00400,00500,00600,00700,00800,00

SO OS SO OS SO OS

Who WhichGen WhichSpec

Reading times (6)