Statistiek 4
Francis Tuerlinckx
Inhoudsopgave
Chapter 3 contrasten: Wees specifieker! ................................................................................................................ 2
Gegevens voorbeeld MDD: Again treatment of depression .................................................................................... 2
Gegevensvoorbeeld MDD: beperkingen ...................................................................................................................... 3
Doel (van dit hoofdstuk) ......................................................................................................................................... 3
Terminologie .......................................................................................................................................................... 3
1 gepland contrast.................................................................................................................................................. 6
Afleiding van de SP-verdeling van ! ........................................................................................................................... 6
Statistische inferentie voor " ...................................................................................................................................... 8
Statistische inferentie voor ": CI ................................................................................................................................. 8
Statistische inferentie voor ": hypothese test ............................................................................................................. 9
Statistische inferentie voor ": Effectgrootte ............................................................................................................. 10
Statistische inferentie voor ": Street fighting statistics ............................................................................................ 11
Het veelvuldig testen van vele geplande contrasten ............................................................................................. 12
Multiple testing: many planned contrasts ................................................................................................................ 12
Paarsgewijze contrasten....................................................................................................................................... 15
Posthoc contrasten en fishing expeditions............................................................................................................ 18
Enkele bijkomende zoektochten naar contrasten ................................................................................................. 19
Class project ......................................................................................................................................................... 21
Chapter 4: sample size planning ........................................................................................................................... 23
Datavoorbeeld: Moral self-licensing ..................................................................................................................... 24
Doel ..................................................................................................................................................................... 25
Basisbegrippen van het statistical power/ onderscheidingsvermogen .................................................................. 25
De centrale en niet-centrale #-distributie ................................................................................................................. 26
De waarschijnlijkheid van $% verwerpen als dat waar is? ....................................................................................... 29
De waarschijnlijkheid van $% verwerpen als dat niet waar is? ................................................................................ 29
Power is afhankelijk van &, ( en effectgrootte ......................................................................................................... 30
Berekeningen van de steekproefomvang .................................................................................................................. 32
Discussie .............................................................................................................................................................. 34
1
,Chapter 5: Assumptions: There is no free lunch .................................................................................................... 35
Datavoorbeeld: Moral self-licensing ..................................................................................................................... 36
Doel ..................................................................................................................................................................... 36
Assumpties en uitschieters ................................................................................................................................... 37
Robuustheid tegen schendingen van assumpties...................................................................................................... 37
Homoscedasticiteit .................................................................................................................................................... 38
Normaliteit ................................................................................................................................................................ 39
Onafhankelijkheid ..................................................................................................................................................... 39
Uitschieters ............................................................................................................................................................... 39
Checken van de assumpties .................................................................................................................................. 39
Hoe om te gaan met geschonden assumpties en uitschieters?.............................................................................. 41
Transformaties .......................................................................................................................................................... 42
ANOVA op rangorde .................................................................................................................................................. 42
Simulatie gebaseerde methoden............................................................................................................................... 43
Gerandomizeerde tests ........................................................................................................................................ 43
Bootstrap .............................................................................................................................................................. 44
Hoe vermijdt u “the garden of forken paths”? ...................................................................................................... 45
Chapter 6: Multifactoriële ANOVA........................................................................................................................ 46
Datavoorbeeld: vruchtbaarheid, relaties en religiositeit ....................................................................................... 47
Doel ..................................................................................................................................................................... 48
Exploratieve analyse ............................................................................................................................................ 48
Introductie & notatie ........................................................................................................................................... 49
Gebalanceerd design ................................................................................................................................................. 50
Gebalanceerd design: illustratie ........................................................................................................................... 50
Gebalanceerd design: Vruchtbaarheidsgegevens ................................................................................................ 50
Gebalanceerd design: SP gemiddelden ................................................................................................................ 50
Interactie & hoofdeffect ....................................................................................................................................... 51
Geen interactie .......................................................................................................................................................... 51
Effect parameters ................................................................................................................................................. 54
Analyse van een gebalanceerd two-way factorieel design .................................................................................... 56
Interactie tussen A en B............................................................................................................................................. 56
Stap 1: Modellen en hypothesen ......................................................................................................................... 56
Stap 2: Keuze van de toetsstatistiek..................................................................................................................... 58
Stap 3: de steekproefverdeling van ) onder *0 .................................................................................................. 59
Stap 4: Bepaal de grootte van uw effect .............................................................................................................. 59
Hoofdeffect van A ..................................................................................................................................................... 60
Stap 1: Modellen en hypotheses .......................................................................................................................... 60
2
, Stap 2: Keuze van de toetsstatistiek..................................................................................................................... 61
Stap 3: de steekproefverdeling van ) onder *0 .................................................................................................. 61
Stap 4: Bepaal de grootte van uw effect .............................................................................................................. 61
Wat te doen als het design ongebalanceerd is? .................................................................................................... 62
The data multiverse ............................................................................................................................................. 64
Enkele verschillende topics .................................................................................................................................. 65
Chapter 7: Repeated measures ............................................................................................................................. 66
Datavoorbeeld: E-cigarettes en craving ................................................................................................................ 67
Doel ..................................................................................................................................................................... 68
Terminologie en dataformaten ............................................................................................................................. 69
De eenvoudigste repeated metingen design ......................................................................................................... 69
Meer complexe designs ........................................................................................................................................ 71
1 within-subject factor .............................................................................................................................................. 71
1 between-subject en 1 within-subject factor ........................................................................................................... 74
Statistische interferentie ...................................................................................................................................... 75
1 within-subject factor .............................................................................................................................................. 76
1 between-subject en 1 within-subject factor ........................................................................................................... 78
Diverse topics....................................................................................................................................................... 80
Effectgrootte ............................................................................................................................................................. 80
Assumpties ................................................................................................................................................................ 80
Steekproefgrootte berekenen ................................................................................................................................... 82
Chapter 8: Simple lineair regression ..................................................................................................................... 83
Chapter 8: Eenvoudige lineaire regressie: Simple but powerful ............................................................................ 83
Datavoorbeeld: Predicatie van 100 m in 2020....................................................................................................... 84
Doel ..................................................................................................................................................................... 85
Exploratieve (of verkennende) dataanalyse .......................................................................................................... 85
Notatie & interpretatie ........................................................................................................................................ 86
Populatie model ........................................................................................................................................................ 86
Interpretatie van ,- ................................................................................................................................................. 87
Interpretatie van ,% ................................................................................................................................................. 88
Statistische inferentie .......................................................................................................................................... 90
Schatting van de regressiecoëfficiënten .................................................................................................................... 90
Onzekerheid van ,% en ,- ....................................................................................................................................... 91
3
, Betrouwbaarheidsinterval......................................................................................................................................... 93
Hypothesetests .......................................................................................................................................................... 93
Effectgrootte ............................................................................................................................................................. 95
Effectgrootte: Associatie sterkte .......................................................................................................................... 95
Effectgrootte: ruw regressiegewicht en bijbehorend CI ...................................................................................... 95
Effectgrootte: gestandaardiseerd regressiegewicht ............................................................................................ 96
Predictie ............................................................................................................................................................... 96
Assumpties .......................................................................................................................................................... 97
Assumpties: ............................................................................................................................................................... 98
Flexibele smooth regressielijn .............................................................................................................................. 99
Uitschieters .......................................................................................................................................................... 99
Chapter 9: Simple lineair regression ....................................................................................................................103
Chapter 9: Simple lineair regression: Advanced simple linear regression .............................................................104
Datavoorbeeld: Mathematics of forgetting .........................................................................................................104
Doel ....................................................................................................................................................................105
Een verkeerd ingestelde poging: een lineaire relatie............................................................................................106
Betere/ sterkere modellen ..................................................................................................................................106
Model 1: exponentiële functie ........................................................................................................................... 108
Model 2: power functie ...................................................................................................................................... 109
Statistische interferentie .....................................................................................................................................109
Chapter 10: Multiple lineair regression ................................................................................................................111
Chapter 10: Multiple lineair regression................................................................................................................112
Datavoorbeeld: Burnout bij verpleegkundigen ....................................................................................................112
Doel ....................................................................................................................................................................113
Exploratieve data analyse....................................................................................................................................113
Multiple lineaire regressie model ........................................................................................................................114
Statistische inferentie .........................................................................................................................................116
Schatting van de regressiecoëfficiënten en de onzekerheid .................................................................................... 116
Formule voor .1 ................................................................................................................................................ 117
Effectgrootte ........................................................................................................................................................... 118
02 gerelateerde meting ..................................................................................................................................... 118
Hypothese tests ....................................................................................................................................................... 120
Er kunnen vreemde dingen gebeuren in het regressie-analyse ............................................................................122
Case 1: 23(5 ∙ -)5 is kleiner dan 2355 .................................................................................................................. 122
Case 2: 23(5 ∙ -)5 is groter dan 2355 ................................................................................................................... 123
Case 3: multicollineariteit........................................................................................................................................ 124
4
,Interpretatie van regressiegewichten ..................................................................................................................125
Assumpties checken in multiple lineaire regressie ...............................................................................................126
Chapter 11: Speciale predictoren.........................................................................................................................127
Chapter 11: Speciale predictoren.........................................................................................................................128
Doel ....................................................................................................................................................................129
Categorische predictors .......................................................................................................................................129
Hoofdeffecten model............................................................................................................................................... 131
Interactie model ...................................................................................................................................................... 133
Squared predictoren (kwadraat van predictoren) ................................................................................................135
Het toevoegen van categorische hoofdeffecten aan het kwadratische model ................................................. 137
Putting it all together ..........................................................................................................................................137
Interpretatie ............................................................................................................................................................ 138
Chapter 13: Get Validated ...................................................................................................................................139
Chapter 13: Get validated : Validatie van regressiemodellen ...............................................................................140
Data voorbeeld: Salarisgegevens .........................................................................................................................140
Big Data, maar ernstige beperkingen ................................................................................................................. 143
Doel ....................................................................................................................................................................144
Modelselectie, generaliseerbaarheid en predictieve accuraatheid.......................................................................144
Methoden ...........................................................................................................................................................148
Cross-validatie ......................................................................................................................................................... 148
Andere methoden.................................................................................................................................................... 150
Interpretatie .......................................................................................................................................................151
5
, Chapters 1 (Introduction) + 2 (one-way ANOVA)
francis tuerlinckx
gaten
24 september 2019
Table of contents
Overview of the course
Overview
• See Toledo
– syllabus
– schedule
Overview – team
• Instructor: Francis Tuerlinckx
• Teaching assistants:
– Maja Fischer, Febe Brackx, and Sara Herrebosch (statistiek vier)
– Tim Loossens, Sigert Ariens, and Sara Herrebosch (statistics four)
Overview – Goal + content
• introduction to the most common data-analytical methods in psychology
• passive insight (what, how, . . .) and elementary active insight (apply to simple data sets)
• content:
– one-way ANOVA – contrasts – sample size planning – assumptions – multiway anova – repeated
measures
– simple linear regression – mathematical models – multiple linear regression – special predictors –
design matrices – cross validation
Overview – Prerequisites
• basics of descriptive and inductive statistics
• no advanced math
Overview – Lectures times
• Statistiek vier
– Tuesday 2pm-4pm (VHI 01.29)
– Friday 2pm-4pm (VHI 01.29)
• Statistics four
– Wednesday 9:30am-11am (VHI 01.40)
– Friday 4pm-6pm (PSI 01.90)
• but check schedule on Toledo for details
1
Francis Tuerlinckx
Inhoudsopgave
Chapter 3 contrasten: Wees specifieker! ................................................................................................................ 2
Gegevens voorbeeld MDD: Again treatment of depression .................................................................................... 2
Gegevensvoorbeeld MDD: beperkingen ...................................................................................................................... 3
Doel (van dit hoofdstuk) ......................................................................................................................................... 3
Terminologie .......................................................................................................................................................... 3
1 gepland contrast.................................................................................................................................................. 6
Afleiding van de SP-verdeling van ! ........................................................................................................................... 6
Statistische inferentie voor " ...................................................................................................................................... 8
Statistische inferentie voor ": CI ................................................................................................................................. 8
Statistische inferentie voor ": hypothese test ............................................................................................................. 9
Statistische inferentie voor ": Effectgrootte ............................................................................................................. 10
Statistische inferentie voor ": Street fighting statistics ............................................................................................ 11
Het veelvuldig testen van vele geplande contrasten ............................................................................................. 12
Multiple testing: many planned contrasts ................................................................................................................ 12
Paarsgewijze contrasten....................................................................................................................................... 15
Posthoc contrasten en fishing expeditions............................................................................................................ 18
Enkele bijkomende zoektochten naar contrasten ................................................................................................. 19
Class project ......................................................................................................................................................... 21
Chapter 4: sample size planning ........................................................................................................................... 23
Datavoorbeeld: Moral self-licensing ..................................................................................................................... 24
Doel ..................................................................................................................................................................... 25
Basisbegrippen van het statistical power/ onderscheidingsvermogen .................................................................. 25
De centrale en niet-centrale #-distributie ................................................................................................................. 26
De waarschijnlijkheid van $% verwerpen als dat waar is? ....................................................................................... 29
De waarschijnlijkheid van $% verwerpen als dat niet waar is? ................................................................................ 29
Power is afhankelijk van &, ( en effectgrootte ......................................................................................................... 30
Berekeningen van de steekproefomvang .................................................................................................................. 32
Discussie .............................................................................................................................................................. 34
1
,Chapter 5: Assumptions: There is no free lunch .................................................................................................... 35
Datavoorbeeld: Moral self-licensing ..................................................................................................................... 36
Doel ..................................................................................................................................................................... 36
Assumpties en uitschieters ................................................................................................................................... 37
Robuustheid tegen schendingen van assumpties...................................................................................................... 37
Homoscedasticiteit .................................................................................................................................................... 38
Normaliteit ................................................................................................................................................................ 39
Onafhankelijkheid ..................................................................................................................................................... 39
Uitschieters ............................................................................................................................................................... 39
Checken van de assumpties .................................................................................................................................. 39
Hoe om te gaan met geschonden assumpties en uitschieters?.............................................................................. 41
Transformaties .......................................................................................................................................................... 42
ANOVA op rangorde .................................................................................................................................................. 42
Simulatie gebaseerde methoden............................................................................................................................... 43
Gerandomizeerde tests ........................................................................................................................................ 43
Bootstrap .............................................................................................................................................................. 44
Hoe vermijdt u “the garden of forken paths”? ...................................................................................................... 45
Chapter 6: Multifactoriële ANOVA........................................................................................................................ 46
Datavoorbeeld: vruchtbaarheid, relaties en religiositeit ....................................................................................... 47
Doel ..................................................................................................................................................................... 48
Exploratieve analyse ............................................................................................................................................ 48
Introductie & notatie ........................................................................................................................................... 49
Gebalanceerd design ................................................................................................................................................. 50
Gebalanceerd design: illustratie ........................................................................................................................... 50
Gebalanceerd design: Vruchtbaarheidsgegevens ................................................................................................ 50
Gebalanceerd design: SP gemiddelden ................................................................................................................ 50
Interactie & hoofdeffect ....................................................................................................................................... 51
Geen interactie .......................................................................................................................................................... 51
Effect parameters ................................................................................................................................................. 54
Analyse van een gebalanceerd two-way factorieel design .................................................................................... 56
Interactie tussen A en B............................................................................................................................................. 56
Stap 1: Modellen en hypothesen ......................................................................................................................... 56
Stap 2: Keuze van de toetsstatistiek..................................................................................................................... 58
Stap 3: de steekproefverdeling van ) onder *0 .................................................................................................. 59
Stap 4: Bepaal de grootte van uw effect .............................................................................................................. 59
Hoofdeffect van A ..................................................................................................................................................... 60
Stap 1: Modellen en hypotheses .......................................................................................................................... 60
2
, Stap 2: Keuze van de toetsstatistiek..................................................................................................................... 61
Stap 3: de steekproefverdeling van ) onder *0 .................................................................................................. 61
Stap 4: Bepaal de grootte van uw effect .............................................................................................................. 61
Wat te doen als het design ongebalanceerd is? .................................................................................................... 62
The data multiverse ............................................................................................................................................. 64
Enkele verschillende topics .................................................................................................................................. 65
Chapter 7: Repeated measures ............................................................................................................................. 66
Datavoorbeeld: E-cigarettes en craving ................................................................................................................ 67
Doel ..................................................................................................................................................................... 68
Terminologie en dataformaten ............................................................................................................................. 69
De eenvoudigste repeated metingen design ......................................................................................................... 69
Meer complexe designs ........................................................................................................................................ 71
1 within-subject factor .............................................................................................................................................. 71
1 between-subject en 1 within-subject factor ........................................................................................................... 74
Statistische interferentie ...................................................................................................................................... 75
1 within-subject factor .............................................................................................................................................. 76
1 between-subject en 1 within-subject factor ........................................................................................................... 78
Diverse topics....................................................................................................................................................... 80
Effectgrootte ............................................................................................................................................................. 80
Assumpties ................................................................................................................................................................ 80
Steekproefgrootte berekenen ................................................................................................................................... 82
Chapter 8: Simple lineair regression ..................................................................................................................... 83
Chapter 8: Eenvoudige lineaire regressie: Simple but powerful ............................................................................ 83
Datavoorbeeld: Predicatie van 100 m in 2020....................................................................................................... 84
Doel ..................................................................................................................................................................... 85
Exploratieve (of verkennende) dataanalyse .......................................................................................................... 85
Notatie & interpretatie ........................................................................................................................................ 86
Populatie model ........................................................................................................................................................ 86
Interpretatie van ,- ................................................................................................................................................. 87
Interpretatie van ,% ................................................................................................................................................. 88
Statistische inferentie .......................................................................................................................................... 90
Schatting van de regressiecoëfficiënten .................................................................................................................... 90
Onzekerheid van ,% en ,- ....................................................................................................................................... 91
3
, Betrouwbaarheidsinterval......................................................................................................................................... 93
Hypothesetests .......................................................................................................................................................... 93
Effectgrootte ............................................................................................................................................................. 95
Effectgrootte: Associatie sterkte .......................................................................................................................... 95
Effectgrootte: ruw regressiegewicht en bijbehorend CI ...................................................................................... 95
Effectgrootte: gestandaardiseerd regressiegewicht ............................................................................................ 96
Predictie ............................................................................................................................................................... 96
Assumpties .......................................................................................................................................................... 97
Assumpties: ............................................................................................................................................................... 98
Flexibele smooth regressielijn .............................................................................................................................. 99
Uitschieters .......................................................................................................................................................... 99
Chapter 9: Simple lineair regression ....................................................................................................................103
Chapter 9: Simple lineair regression: Advanced simple linear regression .............................................................104
Datavoorbeeld: Mathematics of forgetting .........................................................................................................104
Doel ....................................................................................................................................................................105
Een verkeerd ingestelde poging: een lineaire relatie............................................................................................106
Betere/ sterkere modellen ..................................................................................................................................106
Model 1: exponentiële functie ........................................................................................................................... 108
Model 2: power functie ...................................................................................................................................... 109
Statistische interferentie .....................................................................................................................................109
Chapter 10: Multiple lineair regression ................................................................................................................111
Chapter 10: Multiple lineair regression................................................................................................................112
Datavoorbeeld: Burnout bij verpleegkundigen ....................................................................................................112
Doel ....................................................................................................................................................................113
Exploratieve data analyse....................................................................................................................................113
Multiple lineaire regressie model ........................................................................................................................114
Statistische inferentie .........................................................................................................................................116
Schatting van de regressiecoëfficiënten en de onzekerheid .................................................................................... 116
Formule voor .1 ................................................................................................................................................ 117
Effectgrootte ........................................................................................................................................................... 118
02 gerelateerde meting ..................................................................................................................................... 118
Hypothese tests ....................................................................................................................................................... 120
Er kunnen vreemde dingen gebeuren in het regressie-analyse ............................................................................122
Case 1: 23(5 ∙ -)5 is kleiner dan 2355 .................................................................................................................. 122
Case 2: 23(5 ∙ -)5 is groter dan 2355 ................................................................................................................... 123
Case 3: multicollineariteit........................................................................................................................................ 124
4
,Interpretatie van regressiegewichten ..................................................................................................................125
Assumpties checken in multiple lineaire regressie ...............................................................................................126
Chapter 11: Speciale predictoren.........................................................................................................................127
Chapter 11: Speciale predictoren.........................................................................................................................128
Doel ....................................................................................................................................................................129
Categorische predictors .......................................................................................................................................129
Hoofdeffecten model............................................................................................................................................... 131
Interactie model ...................................................................................................................................................... 133
Squared predictoren (kwadraat van predictoren) ................................................................................................135
Het toevoegen van categorische hoofdeffecten aan het kwadratische model ................................................. 137
Putting it all together ..........................................................................................................................................137
Interpretatie ............................................................................................................................................................ 138
Chapter 13: Get Validated ...................................................................................................................................139
Chapter 13: Get validated : Validatie van regressiemodellen ...............................................................................140
Data voorbeeld: Salarisgegevens .........................................................................................................................140
Big Data, maar ernstige beperkingen ................................................................................................................. 143
Doel ....................................................................................................................................................................144
Modelselectie, generaliseerbaarheid en predictieve accuraatheid.......................................................................144
Methoden ...........................................................................................................................................................148
Cross-validatie ......................................................................................................................................................... 148
Andere methoden.................................................................................................................................................... 150
Interpretatie .......................................................................................................................................................151
5
, Chapters 1 (Introduction) + 2 (one-way ANOVA)
francis tuerlinckx
gaten
24 september 2019
Table of contents
Overview of the course
Overview
• See Toledo
– syllabus
– schedule
Overview – team
• Instructor: Francis Tuerlinckx
• Teaching assistants:
– Maja Fischer, Febe Brackx, and Sara Herrebosch (statistiek vier)
– Tim Loossens, Sigert Ariens, and Sara Herrebosch (statistics four)
Overview – Goal + content
• introduction to the most common data-analytical methods in psychology
• passive insight (what, how, . . .) and elementary active insight (apply to simple data sets)
• content:
– one-way ANOVA – contrasts – sample size planning – assumptions – multiway anova – repeated
measures
– simple linear regression – mathematical models – multiple linear regression – special predictors –
design matrices – cross validation
Overview – Prerequisites
• basics of descriptive and inductive statistics
• no advanced math
Overview – Lectures times
• Statistiek vier
– Tuesday 2pm-4pm (VHI 01.29)
– Friday 2pm-4pm (VHI 01.29)
• Statistics four
– Wednesday 9:30am-11am (VHI 01.40)
– Friday 4pm-6pm (PSI 01.90)
• but check schedule on Toledo for details
1
