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Samenvatting statistiek voor pedagogen deel 3

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Course
Statistiek voor pedagogen (P0L17B)

Institution
Katholieke Universiteit Leuven (KU Leuven)

Dit vak werd sinds dit jaar in het Engels gegeven. De lessen tot en met enkelvoudige lineaire regressie volgde ik in het Engels (slides en notities tijdens college) en heb ik vertaald naar het Nederlands. Hierna werden de opnames van vorig academiejaar online geplaatst op vraag van studenten. Ik be...

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Uploaded on July 8, 2024
Number of pages 121
Written in 2023/2024
Type Summary

anova
ancova
speciale predictoren
repeated measures
contrastanalyse
mediatie
enkelvoudige lineaire regressie
meervoudige lineaire regressie

Institution
Katholieke Universiteit Leuven (KU Leuven)
Education
Pedagogische Wetenschappen
Course
Statistiek voor pedagogen (P0L17B)

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Statistiek voor pedagogen, deel 3

Hoofdstuk 1: Data-analytisch proces ............................................................................................................... 1
1. Voorbeeld.................................................................................................................................................... 1
2. Data analytische workflow ......................................................................................................................... 1
2.1 Voorbereidingen................................................................................................................................. 1
2.2 Exploratieve data analyse................................................................................................................... 1
2.3 Statistische interferentie .................................................................................................................... 2
2.4 Interpretatie ....................................................................................................................................... 6
2.5 Opmerkingen ...................................................................................................................................... 8

Hoofdstuk 2: Variantie-analyse met één factor (ANOVA 1).............................................................................. 9
1. Voorbeeld.................................................................................................................................................... 9
2. Notatie en introductie tot one-way ANOVA (structuur van data) .............................................................. 9
3. Exploratieve data analyse ......................................................................................................................... 10
4. Statistische inferentie ............................................................................................................................... 10
4.1 Formuleer modellen en hypothesen ................................................................................................ 10
4.2 Toetsstatistiek: keuze en waarde ..................................................................................................... 11
.4.2.1 Hoe goed past model bij de data (fit)?..................................................................................... 11
.4.2.2 Complexiteit van de modellen? ............................................................................................... 12
.4.2.3 F-statistiek ................................................................................................................................ 12
4.3 Leid de steekproefverdeling af, bepaal de p-waarde en neem (optioneel) een beslissing .............. 14
.4.3.1 ANOVA-tabel ............................................................................................................................ 14
5. Effectgrootte berekening en interpretatie ................................................................................................ 15
5.1 Verschilmaten .................................................................................................................................. 15
5.2 Associatiematen ............................................................................................................................... 16
.5.2.1 Opmerkingen over effectgrootte ............................................................................................. 16
5.3 Interpretatie ..................................................................................................................................... 17
6. Assumpties van ANOVA-modellen ............................................................................................................ 17
6.1 Schending van assumpties ............................................................................................................... 17
.6.1.1 Gelijke populatie standaarddeviaties ~ homoscedasticiteit .................................................... 18
.6.1.2 Normaliteit ............................................................................................................................... 18
.6.1.3 Onafhankelijkheid .................................................................................................................... 19
6.2 Robuustheid tegen uitbijters ............................................................................................................ 20
6.3 Opmerkingen .................................................................................................................................... 20

Hoofdstuk 3: Contrastanalyse ....................................................................................................................... 21
1. Één gepland contrast ................................................................................................................................ 23
1.1 Statistische inferentie....................................................................................................................... 24
1.2 Interpretatie ..................................................................................................................................... 25
2. Meerdere geplande contrasten ................................................................................................................ 26
3. Complex post hoc contrasten.................................................................................................................... 28
4. Paarsgewijze contrasten ........................................................................................................................... 30

,Hoofdstuk 4: ANOVA2................................................................................................................................... 32
1. Voorbeeld.................................................................................................................................................. 32
2. Exploratieve data-analyse ........................................................................................................................ 32
3. Notatie en voorstelling van de gegevens .................................................................................................. 33
4. Hoofdeffecten en interactie ...................................................................................................................... 34
5. Effectparameters ...................................................................................................................................... 36
5.1 Variantieanalyse met één factor ...................................................................................................... 36
5.2 Variantieanalyse met twee factoren ................................................................................................ 37
6. Statistische inferentie ............................................................................................................................... 39
6.1 Hoofdeffect van factor A? ................................................................................................................ 39
6.2 Hoofdeffect van factor B? ................................................................................................................ 42
6.3 Interactie-effect? .............................................................................................................................. 44
6.4 Opmerkingen .................................................................................................................................... 47
7. Assumpties ................................................................................................................................................ 47
8. Contrastanalyse ........................................................................................................................................ 47

Hoofdstuk 5: ANOVA – repeated measures ................................................................................................... 48
1. Voorbeeld.................................................................................................................................................. 48
2. Exploratieve data-analyse ........................................................................................................................ 48
3. Notatie en structuur van data .................................................................................................................. 48
4. Één binnen-subject factor ......................................................................................................................... 48
4.1 Data structuur en notatie ................................................................................................................. 48
4.2 Hoofdeffect van WS factor B? .......................................................................................................... 49
.4.2.1 Statistische inferentie .............................................................................................................. 50
5. Één binnen-subject factor en één tussen-subject factor ........................................................................... 51
5.1 Data structuur en notatie ................................................................................................................. 51
5.2 Hoofdeffect van BS factor A ............................................................................................................. 53
5.3 Hoofdeffect van WS factor B ............................................................................................................ 53
5.4 Interactie-effect................................................................................................................................ 53
5.5 Effectmaat ........................................................................................................................................ 53
5.6 Voorbeeld van ANOVA-tabel van repeated measures ..................................................................... 53
6. Assumpties ................................................................................................................................................ 54

Hoofdstuk 6: enkelvoudige lineaire regressie ................................................................................................ 55
1. Voorbeeld Boets et al. (2010): .................................................................................................................. 55
2. Notatie en voorstelling van de gegevens .................................................................................................. 55
3. Exploratieve data-analyse ........................................................................................................................ 55
4. Het enkelvoudige lineaire regressiemodel: assumpties en interpretatie .................................................. 56
4.1 Achterliggende assumpties: ............................................................................................................. 56
4.2 Interpretatie van parameters of regressiecoëfficiënten: ................................................................. 56
5. Statistische inferentie ............................................................................................................................... 57
6. Effectgrootte ............................................................................................................................................. 61

, 6.1 Associatiesterkte: Proportie verklaarde variantie: R² ...................................................................... 61
6.2 Regressiecoëfficiënt (en corresponderend BI) ................................................................................. 62
6.3 Gestandaardiseerde regressiecoëfficiënt ......................................................................................... 62
7. Centreren .................................................................................................................................................. 63
8. Assumpties ................................................................................................................................................ 64
9. Grafische hulpmiddelen voor checken assumpties ................................................................................... 64
9.1 Spreidingsdiagrammen (Y vs. X) ....................................................................................................... 65
9.2 Residuenplots (𝑌 − 𝑌 vs. 𝑌) ............................................................................................................. 65
9.3 Boxplots van residuen 𝑌 − 𝑌 ............................................................................................................ 66

Hoofdstuk 6: meervoudige lineaire regressie ................................................................................................ 67
1. Voorbeeld: “Pace of life- data” ................................................................................................................. 67
2. Exploratieve data-analyse ........................................................................................................................ 67
2.1 Correlatiematrix ............................................................................................................................... 67
2.2 Venn-diagram ................................................................................................................................... 67
2.3 Draftman’s plot of matrix van spreidingsdiagrammen..................................................................... 67
3. Notatie ...................................................................................................................................................... 68
4. Het meervoudige lineaire regressiemodel ................................................................................................ 68
4.1 Interpretatie regressiegewichten β .................................................................................................. 68
4.2 Achterliggende assumpties .............................................................................................................. 69
5. Statistische inferentie met betrekking tot één gewicht (β1)...................................................................... 69

6. Effectgrootte ............................................................................................................................................. 73
6.1 Associatiesterkte (= voor hele model) .............................................................................................. 73
6.2 Gekwadrateerde partcorrelatie (voor een predictor) ...................................................................... 74
6.3 Regressiecoëfficiënt (en corresponderend BI) ................................................................................. 75
6.4 Gestandaardiseerde regressiecoëfficiënt ......................................................................................... 76
6.5 Conclusie over effectgrootte ............................................................................................................ 76
7. Correlaties tussen predictoren .................................................................................................................. 76
7.1 Onechte correlatie / spurious correlation ........................................................................................ 77
7.2 Supressie .......................................................................................................................................... 77
7.3 (Multi)collineariteit .......................................................................................................................... 78
8. Statistische inferentie met betrekking tot meerdere gewichten / meerdere predictoren ........................ 79
8.1 Inferentie .......................................................................................................................................... 79

Hoofdstuk 7: speciale predictoren bij MLR .................................................................................................... 81
1. Categorische predictoren en indicatorvariabelen (dummy-variabelen) ................................................... 81
1.1 Dummycodering ............................................................................................................................... 81
1.2 Populatiemodel bij indicatorvariabele met 2 categorieën ............................................................... 82
1.3 Populatiemodel indicatorvariabelen met c>2 .................................................................................. 84
1.4 Statistische inferentie c=2 ................................................................................................................ 85
1.5 Statistische inferentie: c>2 ............................................................................................................... 85
2. Productterm voor interactie tussen een kwantitatieve en categorische predictor ................................... 87
2.1 Statistische inferentie interactie kwant. & cat. predictor ................................................................ 89
2.2 Voorbeeld ......................................................................................................................................... 89

, 3. Productterm voor interactie tussen twee kwantitatieve predictoren ....................................................... 91
3.1 Statistische inferentie....................................................................................................................... 91
.3.1.1 Zonder interactie...................................................................................................................... 92
.3.1.2 Met interactie .......................................................................................................................... 92
.3.1.3 Wel interactie + centreren ....................................................................................................... 94
4. Modelconstructie ...................................................................................................................................... 96
4.1 Principes ........................................................................................................................................... 96
4.2 Opmerkingen .................................................................................................................................... 97

Hoofdstuk 8: ANCOVA en het algemeen lineair model .................................................................................. 99
1. ANCOVA .................................................................................................................................................... 99
1.1 Voorbeeld ......................................................................................................................................... 99
1.2 Exploratieve data-analyse .............................................................................................................. 100
.1.2.1 Gecodeerd spreidingsdiagram ............................................................................................... 100
1.3 Statistische inferentie..................................................................................................................... 100
1.4 Aangepaste gemiddelden ............................................................................................................... 104
1.5 Assumpties ..................................................................................................................................... 106
2. Algemeen lineair model .......................................................................................................................... 108
2.1 ANOVA ............................................................................................................................................ 108
2.2 ANCOVA.......................................................................................................................................... 110

Hoofdstuk 9: Mediatie ................................................................................................................................ 112

1. Wat is mediatie? ..................................................................................................................................... 113
1.1 3 modellen in aanpak van Baron & Kenny...................................................................................... 113
1.2 Verschillende types van effecten ................................................................................................... 113
1.3 Belangrijke inferentievragen .......................................................................................................... 114
1.4 Opmerkingen .................................................................................................................................. 116
2. Assumpties en schendingen .................................................................................................................... 116
3. Kritiek op mediatie-onderzoek ................................................................................................................ 117

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