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Samenvatting statistiek 2
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STATISTIEK 2Inhoudsopgave
INTRODUCTIE ............................................................................................................................................. 5
HOOFDSTUK 1 INDUCTIEVE STATISTIEK ....................................................................................................... 5
Welke plaats heeft statistiek in onderzoek en wat is het kernprobleem van de inductieve statistiek? .............. 5
De empirische cyclus ....................................................................................................................................... 5
Wat is de rol van kansberekening en toetsen in de statistiek?............................................................................ 5
Hoe kan statistiek misbruikt worden en wat doen we daaraan? ........................................................................ 6
Experimenteel onderzoek ............................................................................................................................... 6
HOOFDSTUK 2 KANSVERDELINGEN.............................................................................................................. 7
Wat is kansverdeling en hoe kunnen we haar kenmerken berekenen? .............................................................. 7
Wat is de steekproevenverdeling van het gemiddelde en hoe kunnen we de vorm van deze verdeling kennen?
............................................................................................................................................................................. 8
Steekproefverdeling van het gemiddelde....................................................................................................... 8
Kenmerk 1: De vorm van die steekproefverdeling ......................................................................................... 8
Kenmerk 2: standaardfout van het gemiddelde ............................................................................................. 9
Hoe bereken je de kans op het voorkomen van een specifieke steekproefgemiddelde? .................................... 9
HOOFDSTUK 3 HYPOTHESETOETSING ........................................................................................................ 10
Inleiding.............................................................................................................................................................. 10
Wat is een betrouwbaarheidsinterval en hoe bereken je dit? ........................................................................... 10
Wat is hypothesetoetsing? ................................................................................................................................ 11
Wat is het verschil tussen eenzijdig en tweezijdig toetsen? .............................................................................. 12
Hoe kan je kritieke waarden gebruiken in plaats van kansen om te toetsen? .................................................. 13
Met welke onzekerheden kampen we bij hypothesetoetsing en wat hebben power en effectgrootte daarmee
te maken? .......................................................................................................................................................... 14
Wat is het verschil tussen parametrisch en non-parametrisch toetsen? .......................................................... 15
HOOFDSTUK 4 TREKKEN 1 STEEKPROEF UIT 1 POPULATIE ........................................................................... 16
T-toets voor het gemiddelde .............................................................................................................................. 16
Toetsingssituatie ........................................................................................................................................... 16
Voorwaarden ................................................................................................................................................ 16
Hypothesen ................................................................................................................................................... 16
Toetsingsgrootheid ....................................................................................................................................... 16
Beslissingsregels ............................................................................................................................................ 16
Effectgrootte ................................................................................................................................................. 18
Rapporteren .................................................................................................................................................. 18
De X2-toets voor frequenties .............................................................................................................................. 18
Toetsingssituatie ........................................................................................................................................... 18
Voorwaarden ................................................................................................................................................ 18
Hypothesen ................................................................................................................................................... 18
Toetsingsgrootheid ....................................................................................................................................... 18
Beslissingsregels ............................................................................................................................................ 18
Effectgrootte ................................................................................................................................................. 19
1
, Rapportering ................................................................................................................................................. 19
HOOFDSTUK 5 TOETSEN VOOR TREKKEN VAN 2 ONAFHANKELIJKE STEEKPROEVEN ..................................... 20
T-toets voor onafhankelijke steekproeven......................................................................................................... 20
Toetsingssituatie ........................................................................................................................................... 20
Voorwaarden ................................................................................................................................................ 20
Hypothesen ................................................................................................................................................... 20
Toetsingsgrootheid ....................................................................................................................................... 20
Beslissingsregels ............................................................................................................................................ 20
F-toets voor twee varianties .............................................................................................................................. 21
Toetsingssituatie ........................................................................................................................................... 21
Voorwaarden ................................................................................................................................................ 21
Hypotheses.................................................................................................................................................... 21
Toetsingsgrootheid ....................................................................................................................................... 21
Beslissingsregels ............................................................................................................................................ 21
Effectgrootte ................................................................................................................................................. 23
Rapportering ................................................................................................................................................. 23
Wilcoxon RANK-SUM/ MANN-Whitney toets .................................................................................................... 23
Toetsingssituatie ........................................................................................................................................... 23
Voorwaarden ................................................................................................................................................ 23
Hypothesen ................................................................................................................................................... 23
Toetsingsgrootheid ....................................................................................................................................... 23
Beslissingsregel ............................................................................................................................................. 23
Effectgrootte ................................................................................................................................................. 24
Rapportering ................................................................................................................................................. 24
HOOFDSTUK 6 TOETSEN VOOR 2 AFHANKELIJKE STEEKPROEVEN ................................................................ 25
T-toets voor afhankelijke steekproeven ............................................................................................................. 25
Toetsingssituatie ........................................................................................................................................... 25
Voorwaarden ................................................................................................................................................ 25
Hypothesen ................................................................................................................................................... 25
Toetsingsgrootheid ....................................................................................................................................... 25
Beslissingsregels ............................................................................................................................................ 25
Effectgrootte ................................................................................................................................................. 26
Rapportering ................................................................................................................................................. 26
Wilcoxon Signed-rank toets ............................................................................................................................... 26
Toetsingssituatie ........................................................................................................................................... 26
Voorwaarden ................................................................................................................................................ 26
Hypothesen ................................................................................................................................................... 27
Toetsingsgrootheid ....................................................................................................................................... 27
Beslissingsregels ............................................................................................................................................ 27
Effectgrootte ................................................................................................................................................. 28
Rapportering ................................................................................................................................................. 28
HOOFDSTUK 7 TOETSEN BIJ MEER DAN TWEE ONAFH STEEKPROEVEN ....................................................... 28
One-way ANOVA ................................................................................................................................................ 28
Toetsingssituatie ........................................................................................................................................... 28
Voorwaarden ................................................................................................................................................ 28
Hypothesen ................................................................................................................................................... 28
Toetsingsgrootheid ....................................................................................................................................... 29
Beslissingsregels ............................................................................................................................................ 30
Effectgrootte ................................................................................................................................................. 31
Rapportering ................................................................................................................................................. 31
2
, Two-way ANOVA................................................................................................................................................ 31
Toetsingssituatie ........................................................................................................................................... 31
Voorwaarden ................................................................................................................................................ 31
Hypothesen ................................................................................................................................................... 32
Toetsingsgrootheid ....................................................................................................................................... 32
Beslissingsregels ............................................................................................................................................ 32
Effectgrootte ................................................................................................................................................. 33
Rapportering ................................................................................................................................................. 33
Kruskal-Wallis .................................................................................................................................................... 33
Toetsingssituatie ........................................................................................................................................... 33
Voorwaarden ................................................................................................................................................ 33
Hypothesen ................................................................................................................................................... 33
Toetsingsgrootheid ....................................................................................................................................... 33
Beslissingsregels ............................................................................................................................................ 33
Effectgrootte ................................................................................................................................................. 33
Rapportering ................................................................................................................................................. 34
HOOFDSTUK 8 TOETSEN BIJ MEER DAN TWEE AFH STEEKPROEVEN ............................................................ 34
Repeated measures ANOVA............................................................................................................................... 34
Toetsingssituatie ........................................................................................................................................... 34
Voorwaarden ................................................................................................................................................ 34
Hypothesen ................................................................................................................................................... 34
Toetsingsgrootheid ....................................................................................................................................... 34
Beslissingsregels ............................................................................................................................................ 35
Effectgrootte ................................................................................................................................................. 35
Rapportering ................................................................................................................................................. 36
Friedmans’s ANOVA ........................................................................................................................................... 36
Toetsingssituatie ........................................................................................................................................... 36
Voorwaarden ................................................................................................................................................ 36
Hypothesen ................................................................................................................................................... 36
Toetsingsgrootheid ....................................................................................................................................... 36
Beslissingsregels ............................................................................................................................................ 36
Effectgrootte ................................................................................................................................................. 37
Rapportering ................................................................................................................................................. 37
HOOFDSTUK 9 TOETSEN VOOR VERBAND TUSSEN 2 VARIABELEN MET GELIJK MEETNIVEAU ....................... 37
Pearson correlation ............................................................................................................................................ 37
Toetsingssituatie ........................................................................................................................................... 38
Voorwaarden ................................................................................................................................................ 38
Hypothesen ................................................................................................................................................... 38
Toetsingsgrootheid ....................................................................................................................................... 38
Beslissingsregels ............................................................................................................................................ 40
Determinatiecoëfficiënt R2 ................................................................................................................................. 40
(Partiële) correlatie berekenen met SPSS ..................................................................................................... 40
Effectgrootte ................................................................................................................................................. 40
Rapporteren .................................................................................................................................................. 40
Spearman correlation ........................................................................................................................................ 40
Toetsingssituatie ........................................................................................................................................... 40
Voorwaarden ................................................................................................................................................ 40
Hypothesen ................................................................................................................................................... 40
Beslissingsregels ............................................................................................................................................ 41
Effectgrootte ................................................................................................................................................. 41
Raportering ................................................................................................................................................... 41
3
, Chi-kwadraat...................................................................................................................................................... 41
Toetsingssituatie ........................................................................................................................................... 41
Voorwaarden ................................................................................................................................................ 41
Hypothesen ................................................................................................................................................... 42
Toetsingsgrootheid ....................................................................................................................................... 42
Beslissingsregels ............................................................................................................................................ 42
Effectgrootte ................................................................................................................................................. 42
Rapportering ................................................................................................................................................. 42
HOOFDSTUK 10 TOETSEN ALS WE EEN SCORE OP DE AV WILLEN VOORSPELLEN ADHV 1 OF MEER OV ......... 42
Enkelvoudige regressieanalyse .......................................................................................................................... 42
Toetsingssituatie ........................................................................................................................................... 42
Voorwaarden ................................................................................................................................................ 42
Hypothesen ................................................................................................................................................... 43
Beslissingsregels ............................................................................................................................................ 44
Hoe checken we de voorwaarden in verband met residuen en outliers?.................................................... 44
Effectgrootte ................................................................................................................................................. 45
Regressievergelijking..................................................................................................................................... 45
Rapportering ................................................................................................................................................. 45
Meervoudige regressieanalyse .......................................................................................................................... 45
HOOFDSTUK 11 TOETSKEUZE .................................................................................................................... 46
4
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