STATISTIEK
Statistiek.................................................................................................................................................................. 1
Inleiding les 1: Inzichten vanuit statistiek 1 ........................................................................................................ 6
Waarom statistiek in psychologie? ..................................................................................................................... 8
Hoofdstuk 1: wat is inductieve statistiek en wat is het nut ervan? .................................................................... 9
1.1 Inductieve statistiek .................................................................................................................................. 9
1.2 De empirische cyclus ............................................................................................................................... 10
1.3 Hypothesetoetsing .................................................................................................................................. 10
1.4 Kansberekening ....................................................................................................................................... 11
1.5 Inductieve statistiek ................................................................................................................................ 11
1.6 Toetsen .................................................................................................................................................... 11
1.7 Misbruik van statistiek ............................................................................................................................ 12
1.8 Interne validiteit ...................................................................................................................................... 12
1.9 Externe validiteit ..................................................................................................................................... 14
Samenvatting .................................................................................................................................................... 15
De basis: wat moet je nog kennen/kunnen om statistiek 2 goed te starten? .................................................. 15
Opdracht ....................................................................................................................................................... 15
Statistiek 1 in vogelvlucht ................................................................................................................................. 16
Variabelen operationaliseren en meten ....................................................................................................... 16
Steekproeven ................................................................................................................................................ 16
Soorten steekproeven ............................................................................................................................... 17
Frequentieverdelingen .................................................................................................................................. 19
Centrummaten .............................................................................................................................................. 19
Spreidingsmaten ........................................................................................................................................... 20
De normale verdeling .................................................................................................................................... 20
Transformaties van verdelingen ................................................................................................................... 21
Kruistabellen ................................................................................................................................................. 21
Correlatie ...................................................................................................................................................... 21
Lineaire regressie .......................................................................................................................................... 22
Hoofdstuk 2: kansverdelingen en kansberekening ........................................................................................... 22
Previously on statistiek 2 .............................................................................................................................. 22
Waarom kansen? .......................................................................................................................................... 22
Frequentieverdeling ...................................................................................................................................... 23
Kansen ........................................................................................................................................................... 24
Kansverdeling ................................................................................................................................................ 24
De steekproevenverdeling ............................................................................................................................ 25
1
,Opfrissing: normale verdeling en kansen berekenen ....................................................................................... 30
Normale verdeling ......................................................................................................................................... 30
Standaardnormale verdeling ......................................................................................................................... 31
Terug naar de steekproevenverdeling .............................................................................................................. 32
Samenvatting .................................................................................................................................................... 34
Herhalingsoefeningen: kansen berekenen in de normale verdeling. ............................................................... 34
Scenario 1: ..................................................................................................................................................... 34
Scenario 2: ..................................................................................................................................................... 34
Scenario 3: ..................................................................................................................................................... 36
Scenario 4: ..................................................................................................................................................... 36
Hoofdstuk 3: betrouwbaarheidsintervallen en hypothesetoetsing .................................................................. 39
Previously on statistiek 2 .............................................................................................................................. 39
Betrouwbaarheidsintervallen ....................................................................................................................... 40
Hypothesetoetsing ........................................................................................................................................ 45
Nulhypothese ................................................................................................................................................ 46
Hypothesetoetsing: dataverzameling ........................................................................................................... 47
Hypothesetoetsing: toetsing ......................................................................................................................... 48
Huiswerk ....................................................................................................................................................... 50
Samenvatting .................................................................................................................................................... 50
Previously on statistiek 2 .............................................................................................................................. 51
Hypothesetoetsing: mogelijke fouten, kritieke waarden, één- of tweezijdig toetsen .................................. 51
Één- of tweezijdig? ........................................................................................................................................ 53
Kritieke waarden ........................................................................................................................................... 55
Onzekerheden bij hypothesetoetsing ........................................................................................................... 58
Effectgrootte ................................................................................................................................................. 60
Parametrisch vs. Non-parametrisch .............................................................................................................. 61
Huiswerk ....................................................................................................................................................... 61
Samenvatting .................................................................................................................................................... 62
Hoofdstuk 4: toetsen voor één populatie ......................................................................................................... 62
Previously on statistiek 2 .............................................................................................................................. 62
Toetsen voor één populatie: T-toets, X²-toets .............................................................................................. 63
4.1 Stramien toetsen: T-toets voor het gemiddelde ..................................................................................... 63
4.1.1 Toetsingssituatie (onderzoeksvraag: variabelen) ............................................................................. 63
4.1.2 Voorwaarden .................................................................................................................................... 63
4.1.3 Hypothesen (nulhypothese, alternatieve hypothese)...................................................................... 63
4.1.4 Toetsingsgrootheid .......................................................................................................................... 64
4.1.5 Beslissingsregels ............................................................................................................................... 65
2
, 4.1.6 Effectgrootte .................................................................................................................................... 68
4.1.7 Rapporteren ..................................................................................................................................... 68
4.2 X²-toets voor frequenties ........................................................................................................................ 68
4.2.1 Toetsingssituatie .............................................................................................................................. 69
4.2.2 Voorwaarden .................................................................................................................................... 69
4.2.3 Hypothesen ...................................................................................................................................... 69
4.2.4 Toetsingsgrootheid .......................................................................................................................... 69
4.2.5 Beslissingsregels ............................................................................................................................... 70
4.2.6 Effectgrootte (phi - interpreteerbaar zoals r)................................................................................... 71
4.2.7 Rapporteren ..................................................................................................................................... 71
Hoofdstuk 5: toetsen voor twee populaties van onafhankelijke steekproeven ............................................... 72
Previously on statistiek 2 .............................................................................................................................. 72
Toetsen voor twee populaties: T-toets voor 2 gemiddelden, Wilcoxon Rank sum toets ............................. 73
5.1 Steekproeven .......................................................................................................................................... 73
5.2 T-toets voor verschil tussen 2 gemiddelden ........................................................................................... 73
5.2.1 Toetsingssituatie .............................................................................................................................. 73
5.2.2 Voorwaarden .................................................................................................................................... 73
5.2.3 Hypothesen ...................................................................................................................................... 73
5.2.4 Toetsingsgrootheid .......................................................................................................................... 74
5.2.5 Beslissingsregels ............................................................................................................................... 75
5.3 T-toets: F-toets voor 2 varianties ............................................................................................................ 75
5.3.1 Toetsingssituatie .............................................................................................................................. 75
5.3.2 Voorwaarden .................................................................................................................................... 75
5.3.3 Hypothesen ...................................................................................................................................... 76
5.3.4 Toetsingsgrootheid .......................................................................................................................... 76
5.3.5 Beslissingsregels ............................................................................................................................... 77
5.3.6 Effectgrootte .................................................................................................................................... 80
5.3.7 Rapporteren ..................................................................................................................................... 80
5.4 Wilcoxon Rank-sum/ Mann-whitney toets ............................................................................................. 80
5.4.1 Toetsingssituatie .............................................................................................................................. 80
5.4.2 Voorwaarden .................................................................................................................................... 80
5.4.3 Hypotheses ....................................................................................................................................... 80
5.4.4 Toetsingsgrootheid .......................................................................................................................... 80
5.4.5 Beslissingsregel ................................................................................................................................ 81
5.4.6 Effectgrootte .................................................................................................................................... 82
5.4.7 Rapportering .................................................................................................................................... 82
Hoofdstuk 6: toetsen voor 2 populaties bij afhankelijke steekproeven ........................................................... 83
3
, 6.1 T-toets voor verschil tussen 2 gemiddelden – afhankelijke steekproeven ............................................. 83
6.1.1 Toetsingssituatie .............................................................................................................................. 83
6.1.2 Voorwaarden .................................................................................................................................... 83
6.1.3 Hypothesen ...................................................................................................................................... 83
6.1.4 Toetsingsgrootheid .......................................................................................................................... 84
6.1.5 Beslissingsregels ............................................................................................................................... 84
6.1.6 Effectgrootte .................................................................................................................................... 86
6.1.7 Rapporteren ..................................................................................................................................... 86
6.2 Wilcoxon signed-rank toets: rangtekentoets .......................................................................................... 86
6.2.1 Toetsingssituatie .............................................................................................................................. 86
6.2.2 Voorwaarden .................................................................................................................................... 86
6.2.3 Hypotheses ....................................................................................................................................... 86
6.2.4 Toetsingsgrootheid .......................................................................................................................... 87
6.2.5 Beslissingsregel ................................................................................................................................ 87
6.2.6 Effectgrootte .................................................................................................................................... 88
6.2.7 Rapporteren ..................................................................................................................................... 88
Hoofdstuk 7: welke toets gebruiken we bij meer dan 2 onafhankelijke steekproeven? (variantieanalyse) .... 89
7.1 One way anova: variantieanalyse ........................................................................................................... 89
7.1.1 Toetsingssituatie .............................................................................................................................. 90
7.1.2 Voorwaarden .................................................................................................................................... 90
7.1.3 Hypothesen ...................................................................................................................................... 90
7.1.4 Toetsingsgrootheid .......................................................................................................................... 92
7.1.5 Beslissingsregels ............................................................................................................................... 93
7.1.6 Effectgrootte .................................................................................................................................... 94
7.1.7 Rapportering .................................................................................................................................... 95
7.2 Two way anova: tweewegs-variantieanalyse .......................................................................................... 95
7.2.1 Toetsingssituatie .............................................................................................................................. 96
7.2.2 voorwaarden .................................................................................................................................... 96
7.2.3 Hypothesen (gelijk aan de one way anova)...................................................................................... 97
7.2.4 Toetsingsgrootheid .......................................................................................................................... 98
7.2.4.1 F toets voor hoofdeffect van A .................................................................................................. 98
7.2.4.2 F toets voor hoofdeffect B ........................................................................................................ 98
7.2.4.3 F toets voor interactie-effect van AxB ....................................................................................... 98
7.2.5 Beslissingsregels ............................................................................................................................... 98
7.2.6 Effectgrootte .................................................................................................................................. 100
7.2.7 Rapportering .................................................................................................................................. 101
7.3 Kruskal-Wallis toets voor verschil tussen k populaties ......................................................................... 101
4
Statistiek.................................................................................................................................................................. 1
Inleiding les 1: Inzichten vanuit statistiek 1 ........................................................................................................ 6
Waarom statistiek in psychologie? ..................................................................................................................... 8
Hoofdstuk 1: wat is inductieve statistiek en wat is het nut ervan? .................................................................... 9
1.1 Inductieve statistiek .................................................................................................................................. 9
1.2 De empirische cyclus ............................................................................................................................... 10
1.3 Hypothesetoetsing .................................................................................................................................. 10
1.4 Kansberekening ....................................................................................................................................... 11
1.5 Inductieve statistiek ................................................................................................................................ 11
1.6 Toetsen .................................................................................................................................................... 11
1.7 Misbruik van statistiek ............................................................................................................................ 12
1.8 Interne validiteit ...................................................................................................................................... 12
1.9 Externe validiteit ..................................................................................................................................... 14
Samenvatting .................................................................................................................................................... 15
De basis: wat moet je nog kennen/kunnen om statistiek 2 goed te starten? .................................................. 15
Opdracht ....................................................................................................................................................... 15
Statistiek 1 in vogelvlucht ................................................................................................................................. 16
Variabelen operationaliseren en meten ....................................................................................................... 16
Steekproeven ................................................................................................................................................ 16
Soorten steekproeven ............................................................................................................................... 17
Frequentieverdelingen .................................................................................................................................. 19
Centrummaten .............................................................................................................................................. 19
Spreidingsmaten ........................................................................................................................................... 20
De normale verdeling .................................................................................................................................... 20
Transformaties van verdelingen ................................................................................................................... 21
Kruistabellen ................................................................................................................................................. 21
Correlatie ...................................................................................................................................................... 21
Lineaire regressie .......................................................................................................................................... 22
Hoofdstuk 2: kansverdelingen en kansberekening ........................................................................................... 22
Previously on statistiek 2 .............................................................................................................................. 22
Waarom kansen? .......................................................................................................................................... 22
Frequentieverdeling ...................................................................................................................................... 23
Kansen ........................................................................................................................................................... 24
Kansverdeling ................................................................................................................................................ 24
De steekproevenverdeling ............................................................................................................................ 25
1
,Opfrissing: normale verdeling en kansen berekenen ....................................................................................... 30
Normale verdeling ......................................................................................................................................... 30
Standaardnormale verdeling ......................................................................................................................... 31
Terug naar de steekproevenverdeling .............................................................................................................. 32
Samenvatting .................................................................................................................................................... 34
Herhalingsoefeningen: kansen berekenen in de normale verdeling. ............................................................... 34
Scenario 1: ..................................................................................................................................................... 34
Scenario 2: ..................................................................................................................................................... 34
Scenario 3: ..................................................................................................................................................... 36
Scenario 4: ..................................................................................................................................................... 36
Hoofdstuk 3: betrouwbaarheidsintervallen en hypothesetoetsing .................................................................. 39
Previously on statistiek 2 .............................................................................................................................. 39
Betrouwbaarheidsintervallen ....................................................................................................................... 40
Hypothesetoetsing ........................................................................................................................................ 45
Nulhypothese ................................................................................................................................................ 46
Hypothesetoetsing: dataverzameling ........................................................................................................... 47
Hypothesetoetsing: toetsing ......................................................................................................................... 48
Huiswerk ....................................................................................................................................................... 50
Samenvatting .................................................................................................................................................... 50
Previously on statistiek 2 .............................................................................................................................. 51
Hypothesetoetsing: mogelijke fouten, kritieke waarden, één- of tweezijdig toetsen .................................. 51
Één- of tweezijdig? ........................................................................................................................................ 53
Kritieke waarden ........................................................................................................................................... 55
Onzekerheden bij hypothesetoetsing ........................................................................................................... 58
Effectgrootte ................................................................................................................................................. 60
Parametrisch vs. Non-parametrisch .............................................................................................................. 61
Huiswerk ....................................................................................................................................................... 61
Samenvatting .................................................................................................................................................... 62
Hoofdstuk 4: toetsen voor één populatie ......................................................................................................... 62
Previously on statistiek 2 .............................................................................................................................. 62
Toetsen voor één populatie: T-toets, X²-toets .............................................................................................. 63
4.1 Stramien toetsen: T-toets voor het gemiddelde ..................................................................................... 63
4.1.1 Toetsingssituatie (onderzoeksvraag: variabelen) ............................................................................. 63
4.1.2 Voorwaarden .................................................................................................................................... 63
4.1.3 Hypothesen (nulhypothese, alternatieve hypothese)...................................................................... 63
4.1.4 Toetsingsgrootheid .......................................................................................................................... 64
4.1.5 Beslissingsregels ............................................................................................................................... 65
2
, 4.1.6 Effectgrootte .................................................................................................................................... 68
4.1.7 Rapporteren ..................................................................................................................................... 68
4.2 X²-toets voor frequenties ........................................................................................................................ 68
4.2.1 Toetsingssituatie .............................................................................................................................. 69
4.2.2 Voorwaarden .................................................................................................................................... 69
4.2.3 Hypothesen ...................................................................................................................................... 69
4.2.4 Toetsingsgrootheid .......................................................................................................................... 69
4.2.5 Beslissingsregels ............................................................................................................................... 70
4.2.6 Effectgrootte (phi - interpreteerbaar zoals r)................................................................................... 71
4.2.7 Rapporteren ..................................................................................................................................... 71
Hoofdstuk 5: toetsen voor twee populaties van onafhankelijke steekproeven ............................................... 72
Previously on statistiek 2 .............................................................................................................................. 72
Toetsen voor twee populaties: T-toets voor 2 gemiddelden, Wilcoxon Rank sum toets ............................. 73
5.1 Steekproeven .......................................................................................................................................... 73
5.2 T-toets voor verschil tussen 2 gemiddelden ........................................................................................... 73
5.2.1 Toetsingssituatie .............................................................................................................................. 73
5.2.2 Voorwaarden .................................................................................................................................... 73
5.2.3 Hypothesen ...................................................................................................................................... 73
5.2.4 Toetsingsgrootheid .......................................................................................................................... 74
5.2.5 Beslissingsregels ............................................................................................................................... 75
5.3 T-toets: F-toets voor 2 varianties ............................................................................................................ 75
5.3.1 Toetsingssituatie .............................................................................................................................. 75
5.3.2 Voorwaarden .................................................................................................................................... 75
5.3.3 Hypothesen ...................................................................................................................................... 76
5.3.4 Toetsingsgrootheid .......................................................................................................................... 76
5.3.5 Beslissingsregels ............................................................................................................................... 77
5.3.6 Effectgrootte .................................................................................................................................... 80
5.3.7 Rapporteren ..................................................................................................................................... 80
5.4 Wilcoxon Rank-sum/ Mann-whitney toets ............................................................................................. 80
5.4.1 Toetsingssituatie .............................................................................................................................. 80
5.4.2 Voorwaarden .................................................................................................................................... 80
5.4.3 Hypotheses ....................................................................................................................................... 80
5.4.4 Toetsingsgrootheid .......................................................................................................................... 80
5.4.5 Beslissingsregel ................................................................................................................................ 81
5.4.6 Effectgrootte .................................................................................................................................... 82
5.4.7 Rapportering .................................................................................................................................... 82
Hoofdstuk 6: toetsen voor 2 populaties bij afhankelijke steekproeven ........................................................... 83
3
, 6.1 T-toets voor verschil tussen 2 gemiddelden – afhankelijke steekproeven ............................................. 83
6.1.1 Toetsingssituatie .............................................................................................................................. 83
6.1.2 Voorwaarden .................................................................................................................................... 83
6.1.3 Hypothesen ...................................................................................................................................... 83
6.1.4 Toetsingsgrootheid .......................................................................................................................... 84
6.1.5 Beslissingsregels ............................................................................................................................... 84
6.1.6 Effectgrootte .................................................................................................................................... 86
6.1.7 Rapporteren ..................................................................................................................................... 86
6.2 Wilcoxon signed-rank toets: rangtekentoets .......................................................................................... 86
6.2.1 Toetsingssituatie .............................................................................................................................. 86
6.2.2 Voorwaarden .................................................................................................................................... 86
6.2.3 Hypotheses ....................................................................................................................................... 86
6.2.4 Toetsingsgrootheid .......................................................................................................................... 87
6.2.5 Beslissingsregel ................................................................................................................................ 87
6.2.6 Effectgrootte .................................................................................................................................... 88
6.2.7 Rapporteren ..................................................................................................................................... 88
Hoofdstuk 7: welke toets gebruiken we bij meer dan 2 onafhankelijke steekproeven? (variantieanalyse) .... 89
7.1 One way anova: variantieanalyse ........................................................................................................... 89
7.1.1 Toetsingssituatie .............................................................................................................................. 90
7.1.2 Voorwaarden .................................................................................................................................... 90
7.1.3 Hypothesen ...................................................................................................................................... 90
7.1.4 Toetsingsgrootheid .......................................................................................................................... 92
7.1.5 Beslissingsregels ............................................................................................................................... 93
7.1.6 Effectgrootte .................................................................................................................................... 94
7.1.7 Rapportering .................................................................................................................................... 95
7.2 Two way anova: tweewegs-variantieanalyse .......................................................................................... 95
7.2.1 Toetsingssituatie .............................................................................................................................. 96
7.2.2 voorwaarden .................................................................................................................................... 96
7.2.3 Hypothesen (gelijk aan de one way anova)...................................................................................... 97
7.2.4 Toetsingsgrootheid .......................................................................................................................... 98
7.2.4.1 F toets voor hoofdeffect van A .................................................................................................. 98
7.2.4.2 F toets voor hoofdeffect B ........................................................................................................ 98
7.2.4.3 F toets voor interactie-effect van AxB ....................................................................................... 98
7.2.5 Beslissingsregels ............................................................................................................................... 98
7.2.6 Effectgrootte .................................................................................................................................. 100
7.2.7 Rapportering .................................................................................................................................. 101
7.3 Kruskal-Wallis toets voor verschil tussen k populaties ......................................................................... 101
4
