ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005...
Transcript of ANOVA (GLM- Repeated measures) · ANOVA (GLM- Repeated measures) Jantien Donkers. March 14, 2005...
March 14, 2005 Methodology & Statistics
ANOVA (GLM- Repeated measures)
Jantien Donkers
March 14, 2005 Methodology & Statistics
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
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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)
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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
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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)
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This experiment
o 6 conditions testing 2 independent variables
o Dependent variable: reading time
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o a self-paced reading study in Dutch
o “who” and “which” questions
o specificity and structure
This experiment (2)
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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
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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
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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
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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
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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
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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
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Terwijl de dronken bediende een hapje at, zocht de nuchtere bediendede keizer in de kelder.
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+
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Wie
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heeft
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de keizer
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gezocht
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in de kelder?
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de nuchtere bediende
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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
March 14, 2005 Methodology & Statistics
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)
March 14, 2005 Methodology & Statistics
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
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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
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Repeated measures/ SPSS
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Data
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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
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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)
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Data pre-processing (3)
o Write syntax script
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Data pre-processing (4)
o Write syntax script
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Data pre-processing (5)
o Write syntax script
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GLM – Repeated measures
o SPSS data file with subject meanso SPSS data file with item means
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GLM – Repeated measures
March 14, 2005 Methodology & Statistics
GLM – Repeated measures
March 14, 2005 Methodology & Statistics
GLM – Repeated measures
March 14, 2005 Methodology & Statistics
GLM – Repeated measures
March 14, 2005 Methodology & Statistics
GLM – Repeated measures
March 14, 2005 Methodology & Statistics
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)
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Effect or interaction?
o Plot you data!o Mistake in labellingo Effect can be counter-intuitiveo Post-hoc analyses
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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
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o The data suggest that answers following OS structures are more difficult to judge that those following SO questions.
Accuracy
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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
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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)
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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**
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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 *
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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)
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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?
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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)
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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)
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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)
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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
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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
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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
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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.
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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)