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Samenvatting Statistiek 2
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Samenvatting Statistiek 2
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Samenvatting Statistiek 2Inhoud
Inleiding en herhaling .............................................................................................................................. 6
o Statistiek en statistische gegevens ................................................................................ 6
o Steekproef en onderzoekspopulatie ............................................................................. 6
o Beschrijvende en inferentiële statistiek ........................................................................ 6
o Variabelen: operationalisering en meetniveaus ........................................................... 8
Tekstuele VS. Numerieke variabelen............................................................................................... 8
Operationalisering ........................................................................................................................... 8
Kwalitatieve VS. Kwantitatieve variabelen ...................................................................................... 8
Meetniveau’s ................................................................................................................................... 9
o Frequentieverdelingen en grafische weergaven ......................................................... 11
Grafische weergaven ..................................................................................................................... 11
o Maten van centraliteit................................................................................................. 12
Modus............................................................................................................................................ 13
Mediaan......................................................................................................................................... 13
Kwartielen, decielen en percentielen............................................................................................ 13
Gemiddelde ................................................................................................................................... 13
o Maten van spreiding.................................................................................................... 14
Variatiebreedte ............................................................................................................................. 14
Interkwartielafstand ...................................................................................................................... 14
Variatie/Kwadratensom ................................................................................................................ 15
Variantie ........................................................................................................................................ 15
Standaardafwijking ........................................................................................................................ 15
o Outliers ........................................................................................................................ 16
Kansrekenen .......................................................................................................................................... 17
o Basisconcepten kansrekenen ...................................................................................... 17
Drie soorten kansen ...................................................................................................................... 18
Uitkomstenruimte ......................................................................................................................... 18
Boomdiagram ................................................................................................................................ 18
Kans op een gebeurtenis ............................................................................................................... 19
Doorsnede van gebeurtenissen..................................................................................................... 20
Disjuncte gebeurtenissen .............................................................................................................. 20
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, Unie van gebeurtenissen ............................................................................................................... 21
o Rekenregels voor kansen ............................................................................................ 21
Complementregel .......................................................................................................................... 21
Somregel........................................................................................................................................ 22
Productregel .................................................................................................................................. 22
o Voorwaardelijke kansen .............................................................................................. 23
Onafhankelijke gebeurtenissen ..................................................................................................... 23
Afhankelijke gebeurtenissen ......................................................................................................... 24
Productregel .................................................................................................................................. 24
Controleren voor onafhankelijkheid ............................................................................................. 25
Onafhankelijke gebeurtenissen ..................................................................................................... 25
Voorwaardelijke kans .................................................................................................................... 25
Totale kans op basis van voorwaardelijke kans ............................................................................ 25
Regel van Bayes ............................................................................................................................. 26
Statistische kansverdelingen ................................................................................................................. 28
o Variabelen ................................................................................................................... 28
Toevalsvariabele ............................................................................................................................ 28
Kansverdeling ................................................................................................................................ 28
Kansverdeling vs. Frequentieverdelingen ..................................................................................... 28
Verschillende kansverdelingen ...................................................................................................... 29
Discrete kansverdeling .................................................................................................................. 29
Continue kansverdeling ................................................................................................................. 32
o Normaalverdeling ........................................................................................................ 33
Empirische regel ............................................................................................................................ 34
Standaardnormaalverdeling .......................................................................................................... 35
Van kans naar x.............................................................................................................................. 37
Normaalverdeling vs. binomiaalverdeling..................................................................................... 38
Steekproevenverdeling & centrale limietstelling .................................................................................. 39
o Steekproevenverdeling & centrale limietstelling ........................................................ 39
Twee categorieën van statistiek .................................................................................................... 39
Variatie tussen steekproefverdelingen ......................................................................................... 39
Betrouwbaarheid en geldigheid .................................................................................................... 40
Steekproevenverdeling ................................................................................................................. 40
Centrale limietstelling ................................................................................................................... 40
o Steekproevenverdeling voor een proportie ................................................................ 41
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, In Inferentiële statistiek ................................................................................................................ 41
Binomiaalverdeling ........................................................................................................................ 41
Kenmerken van een steekproevenverdeling................................................................................. 43
o De steekproevenverdeling voor een gemiddelde ....................................................... 44
Kenmerken van de steekproevenverdeling................................................................................... 44
Betrouwbaarheidsintervallen ................................................................................................................ 46
Statistische inferentie.................................................................................................................... 46
Steekproevenverdeling ................................................................................................................. 46
Drie verdelingen ............................................................................................................................ 46
o Punt- en intervalschatting ........................................................................................... 46
Puntschatting................................................................................................................................. 47
Intervalschatting ............................................................................................................................ 47
o Betrouwbaarheidsinterval voor proportie .................................................................. 47
Z-score opzoeken voor een betrouwbaarheidsinterval ................................................................ 48
Invloed van de steekproefgrootte ................................................................................................. 49
Invloed van het betrouwbaarheidsniveau .................................................................................... 49
o Betrouwbaarheidsinterval voor gemiddelde .............................................................. 50
t-verdeling ..................................................................................................................................... 50
Hypothesetoetsen ................................................................................................................................. 51
Steekproevenverdeling ................................................................................................................. 51
Betrouwbaarheidsinterval ............................................................................................................. 51
o Hypothesetoetsen: opbouw en logica ........................................................................ 52
o Hypthesetoetsen voor een proportie.......................................................................... 52
o Hypothesetoets voor een gemiddelde ........................................................................ 57
o Type I- en Type II-fouten ............................................................................................. 61
Type I-fout ..................................................................................................................................... 61
Type II-fout .................................................................................................................................... 61
Power............................................................................................................................................. 61
o Beperkingen van hypothesetoetsen ........................................................................... 64
P-waarde en significantieniveau ................................................................................................... 64
Statistische significantie ≠ praktische significantie ....................................................................... 64
Significantietoetsen vs. betrouwbaarheidsintervallen.................................................................. 64
Opgelet bij interpretatie van de significantietoetsen ................................................................... 64
Vergelijken van twee groepen............................................................................................................... 65
Tweezijdige hypothesetoetsen vs. Betrouwbaarheidsintervallen ................................................ 67
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, Standaardfout voor verschil van steekproefstatistieken .............................................................. 68
o Vergelijken van twee groepen: proporties.................................................................. 69
Betrouwbaarheidsinterval ............................................................................................................. 70
Hypothesetoets ............................................................................................................................. 71
o Vergelijken van twee groepen: gemiddelden ............................................................. 74
Chi-kwadraattoets en variantieanalyse................................................................................................. 78
o Onafhankelijkheid categorische variabelen ................................................................ 78
Chi-kwadraatverdeling (x2) ............................................................................................................ 78
Chi-kwadraattest 2x2 vs. vergelijking van twee proporties .......................................................... 87
Sterkte van het verband ................................................................................................................ 87
o Groepsgemiddelden vergelijken ................................................................................. 89
o T-test ........................................................................................................................... 91
t-test voor verschil tussen 2 gemiddelden .................................................................................... 91
o Variantie-analyse (ANOVA) ......................................................................................... 93
Eta-kwadraat 𝜂2 ............................................................................................................................ 98
o Post-hoc testen ........................................................................................................... 99
Bivariate regressieanalyse: herhaling en dummycodering ................................................................. 101
o Het lineair regressiemodel ........................................................................................ 101
Lineaire regressie......................................................................................................................... 102
Lineaire regressie: regressievergelijking ..................................................................................... 103
Bivariate lineaire regressie .......................................................................................................... 104
o Goodness of fit: R2 ..................................................................................................... 104
Residueel (RESIDUAL) .................................................................................................................. 106
o Centreren van de onafhankelijke variabele .............................................................. 109
o Dummyregressie ....................................................................................................... 111
Categorische onafhankelijke variabele (x)?................................................................................. 111
Dichotome onafhankelijke variabele........................................................................................... 111
Polytome onafhankelijke variabele ............................................................................................. 113
Meervoudige regressieanalyse............................................................................................................ 116
Lineaire regressie......................................................................................................................... 116
o Inferentie voor het regressiemodel .......................................................................... 116
o Inferentie voor regressiecoëfficiënten ...................................................................... 120
Hypothesetoets regressiecoëfficiënt........................................................................................... 120
Betrouwbaarheidsinterval regressiecoëfficiënt β1 ..................................................................... 122
o Waarom multivariate regressie? ............................................................................... 122
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