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Statistiek deel 3
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STATISTIEK DEEL 3Statistiek deel 3 ....................................................................................................................................................... 1
Les 1: Illustratie data-analytische proces ............................................................................................................ 5
Overzicht ......................................................................................................................................................... 5
1.Voorbeeld ................................................................................................................................................. 6
2.Flowchart van het data-analytische proces ............................................................................................. 7
2.1Voorbereidingen ................................................................................................................................ 7
2.2 Exploratieve data-analyse ................................................................................................................. 8
2.3 Statistische inferentie...................................................................................................................... 10
stap 1: formuleer modellen en hypothesen ...................................................................................... 11
stap 2: toetsstatiestiek: keuze en waarde ......................................................................................... 13
stap 3: leid steekproevenverdeling af en bepaal p-waarde, en (optioneel) neem een beslissing .... 16
stap 4: bepaal effectgrootte .............................................................................................................. 19
2.4 Presentatie ...................................................................................................................................... 21
2.5 Opmerking ....................................................................................................................................... 23
Hoofdstuk 2: Variantie-analyse met één factor ................................................................................................ 23
Overzicht ....................................................................................................................................................... 23
2.1 Voorbeeld ............................................................................................................................................ 24
2.2 Notatie en voorstelling van de gegevens ............................................................................................ 24
2.3 Exploratieve data-analyse ................................................................................................................... 25
2.4 Statistische inferentie ......................................................................................................................... 26
stap 1: Formuleer modellen en hypothesen ......................................................................................... 26
stap 2: Toetsstatistiek: keuze en waarde .............................................................................................. 27
fit van beide modellen ...................................................................................................................... 27
complexiteit van beide modellen ...................................................................................................... 29
f-statistiek.......................................................................................................................................... 30
stap 3: steekproefverdeling van F onder H0 en bepalen van p-waarde ............................................... 35
stap 3: Bepaal p-waarde ........................................................................................................................ 36
2.5 Evaluatie van de effectgrootte en presentatie.................................................................................... 37
2.5.1 Verschilmaten (evaluatie van de effectgrootte) .......................................................................... 38
2.5.2 Associatiematen ........................................................................................................................... 40
2.5.3 Opmerkingen ................................................................................................................................ 43
2.5 Presentatie .......................................................................................................................................... 43
2.6 Assumpties van ANOVA-modellen ...................................................................................................... 44
2.6.1 Schendingen van de assumpties .................................................................................................. 44
2.6.2 Robuustheid tegen uitbijters ........................................................................................................ 48
1
, 2.6.3 Opmerking .................................................................................................................................... 48
H3: contrastanalyse........................................................................................................................................... 48
Contrasten..................................................................................................................................................... 48
1.Eén gepland contrast ............................................................................................................................. 52
1.Eén gepland contrast: Statistische inferentie ..................................................................................... 53
1.Eén gepland contrast: Presentatie ..................................................................................................... 55
2.Meerdere geplande contrasten ............................................................................................................. 55
3.Complexe posthoc contrasten ............................................................................................................... 59
4.Paarsgewijze contrasten ........................................................................................................................ 62
H4: variantie-analyse met twee factoren .......................................................................................................... 65
1.voorbeeld ................................................................................................................................................... 65
2.exploratieve data-analyse .......................................................................................................................... 67
3.notatie en voorstelling van de gegevens ................................................................................................... 67
4.hoofdeffecten en interactie ....................................................................................................................... 70
5.effectparameters ....................................................................................................................................... 74
1.variantieanalyse met één factor ............................................................................................................ 74
2.variantieanalyse met twee factoren ...................................................................................................... 76
6.statistische inferentie ................................................................................................................................. 80
6.1 Hoofdeffect van factor A? ................................................................................................................... 81
6.2 Hoofdeffect van factor B? ................................................................................................................... 88
6.3 Interactie-effect?................................................................................................................................. 93
7.Assumpties ............................................................................................................................................... 100
8.Contrastanalyse........................................................................................................................................ 100
9.Hogere orde proefopzetten ..................................................................................................................... 100
Hoofdstuk 5: enkelvoudige regressie-analyse ................................................................................................ 100
Overzicht ..................................................................................................................................................... 100
1.voorbeeld ................................................................................................................................................. 101
2.notatie en voorstelling van de gegevens ................................................................................................. 101
3. exploratieve data-analyse ....................................................................................................................... 102
4. Het enkelvoudige lineaire regressiemodel, assumpties en interpretatie ............................................... 103
5. statistische inferentie .............................................................................................................................. 107
Stap 1: formuleer modellen en hypothesen ........................................................................................... 107
Stap 2: toetsstatistiek: keuze en waarde ................................................................................................ 113
Stap 3: bepaal de steekproevenverdeling en p-waarde.......................................................................... 114
Stap 2: toetsstatistiek: keuze en waarde ................................................................................................ 115
Stap 3: bepaal steekproevenverdeling en p-waarde............................................................................... 116
6. Effectgrootte ........................................................................................................................................... 118
2
, 6.1 associatiesterkte ............................................................................................................................... 119
6.2 regressiegewicht (en BI) .................................................................................................................... 121
6.3 gestandaardiseerde regressiegewichten .......................................................................................... 121
Formuleer conclusie ................................................................................................................................ 123
7. Centreren ................................................................................................................................................ 124
8. assumpties van enkelvoudige lineaire regressie ..................................................................................... 127
8.1 lineariteit ........................................................................................................................................... 127
8.2 gelijke varianties-onafhankelijkheid-normaliteit .............................................................................. 128
9. grafische hulpmiddelen voor checken modelassumpties ....................................................................... 128
9.1 spreidingsdiagrammen ...................................................................................................................... 129
9.2 residuenplots..................................................................................................................................... 130
9.3 boxplots ............................................................................................................................................. 133
Hoofdstuk 6: meervoudige lineaire regressie (meerdere predictoren) .......................................................... 133
1.Voorbeeld ................................................................................................................................................. 134
2.Exploratieve data-analyse ........................................................................................................................ 135
3.Notatie ..................................................................................................................................................... 138
4.Het meervoudige lineaire regressiemodel ............................................................................................... 139
5.Statistische inferentie met betrekking tot één regressiegewicht ............................................................ 141
Stap 1: formuleer modellen en hypothesen (statistische inferentie m.b.t 1......................................... 141
Stap 2: toetsstatistiek: keuze en waarde ................................................................................................ 145
Stap 3: bepaal steekproevenverdeling en p-waarde............................................................................... 147
6.Effectgrootte ............................................................................................................................................ 148
6.1 Associatiesterkte ............................................................................................................................... 149
6.2 gekwadrateerde partcorrelatie ......................................................................................................... 152
6.3 regressiegewicht (en corresponderend BI) ....................................................................................... 156
6.4 gestandaardiseerde regressiegewichten .......................................................................................... 157
Formuleer conclusie ................................................................................................................................ 158
7.Correlaties tussen predictoren ................................................................................................................. 158
7.1 Onechte correlatie ............................................................................................................................ 159
7.2 Suppressie ......................................................................................................................................... 160
7.3 (Multi) collineariteit .......................................................................................................................... 161
8.Statische inferentie met betrekking tot meerdere gewichten/toets voor meerdere predictoren .......... 165
Inferentie ................................................................................................................................................. 165
Hoofdstuk 7: speciale predictoren bij meervoudige lineaire regressie ........................................................... 168
Overzicht ..................................................................................................................................................... 168
1.Categorische predictoren en dummy-variabelen .................................................................................... 169
1.Voorbeelden ......................................................................................................................................... 169
3
, 2.Exploratieve data-analyse .................................................................................................................... 170
3.Dummycodering ................................................................................................................................... 171
4.Populatiemodel: c=2 ............................................................................................................................ 174
4.Populatiemodel: c>2 ............................................................................................................................ 176
5.Statistische inferentie: c=2 ................................................................................................................... 178
5.Statistische inferentie: c>2 ................................................................................................................... 179
6.Opmerkingen........................................................................................................................................ 181
2.Productterm voor een interactie tussen een kwantitatieve en categorische predictor .......................... 182
Voorbeeld ................................................................................................................................................ 188
3.Productterm voor een interactie tussen twee kwantitatieve predictoren .............................................. 190
3.1 Interactie tussen 2 kwantitatieve variabelen: zonder interactie ...................................................... 193
3.2 Interactie tussen 2 kwantitatieve variabelen: wel interactie............................................................ 195
3.3 Interactie tussen 2 kwantitatieve variabelen: wel interactie + centreren ....................................... 199
4.Modelconstructie ..................................................................................................................................... 203
Hoofdstuk 8: ANCOVA en het algemeen lineair model ................................................................................... 206
Overzicht ..................................................................................................................................................... 206
Even opfrissen…ANOVA .............................................................................................................................. 206
1.ANCOVA ................................................................................................................................................... 207
1.1 voorbeeld .................................................................................................................................. 207
1.2 Exploratieve data-analyse ......................................................................................................... 208
1.3 statistische inferentie ............................................................................................................... 209
1.3.1 statistische inferentie: stap 1 ............................................................................................... 209
1.3.2 Statistische inferentie: stap 2 ............................................................................................... 213
1.3.3 Statistische inferentie: stap 3 ............................................................................................... 213
1.3.4 Statistische inferentie: stap 4 ............................................................................................... 214
1.3.5 Statistische inferentie: conclusie .......................................................................................... 214
1.3 statistische inferentie ............................................................................................................... 215
1.4 Aangepaste gemiddelden ......................................................................................................... 218
1.5 Assumpties ................................................................................................................................ 221
2. algemeen lineair model (ALM) ................................................................................................................ 222
2.1 ANOVA............................................................................................................................................... 223
2.2 ANCOVA ............................................................................................................................................ 226
2.3 algemeen lineair model ..................................................................................................................... 227
Hoofdstuk 9: mediatie ..................................................................................................................................... 229
overzicht ...................................................................................................................................................... 229
4.Mediatie ................................................................................................................................................... 229
4.1Wat is het? ......................................................................................................................................... 230
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