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Samenvatting Statistiek 2: Kansrekening en inductieve statistiek
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Dit is een samenvatting van het vak Statistiek 2 (vroeger inleiding statistiek).
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Inleiding tot statistiekvoor de
gedragswetenschappen
1
,Inhoudsopgave
H.1 Meetschalen...................................................................................................................................... 5
1.1 Inleiding ......................................................................................................................................... 5
1.1.1 Meten is gebaseerd op 4 eigenschappen ............................................................................... 5
1.1.2 Soorten meetschalen ............................................................................................................. 5
1.1.3 Hoe bepaal ik mijn meetschalen? .......................................................................................... 5
1.1.4 Kwalitatief vs kwantitatief ...................................................................................................... 6
H.2 Kijken naar gegevens: verdelingen ................................................................................................... 7
2.1 Frequentietabellen ........................................................................................................................ 7
2.1.1 Formules ................................................................................................................................. 7
2.2 Indelen in klassen .......................................................................................................................... 7
2.2.1 Klassegrenzen ......................................................................................................................... 7
2.2.2 Klassemiddens ........................................................................................................................ 8
2.2.3 Absolute Histogrammen......................................................................................................... 9
2.2.4 Absolute Cumulatieve frequentiefunctie ............................................................................. 10
2.3 Karakteristieken om de spreiding te bepalen ............................................................................. 11
2.3.1 Centrale tendens: centrummaten ........................................................................................ 11
2.3.2 Spreiding: maten van spreiding ............................................................................................ 13
2.3.3 Centrummaten en maten van spreiding formules ............................................................... 16
2.3.4 Centrummaten en maten van spreiding: In klassen gegroepeerde gegevens ..................... 16
2.3.5 Kiezen van centrum- en spreidingsmaten ............................................................................ 17
2.4 Verdelingen beschrijven .............................................................................................................. 18
2.4.1 Maten van vorm: Symmetrie................................................................................................ 18
2.4.2 Maten van vorm: Gepiektheid ............................................................................................. 19
2.5 De normale verdelingen: De techniek van standaardiseren ....................................................... 20
2.5.1 Z-scores................................................................................................................................ 20
H.3 Kijken naar gegevens: relaties ........................................................................................................ 24
3.1 Covariantie .................................................................................................................................. 24
3.2 Correlatiecoëfficiënt Vanaf intervalschaal .................................................................................. 24
3.3 Determinatiecoëfficiënt Vanaf intervalschaal ............................................................................. 26
3.4 Rangcorrelatiecoëfficiënten Vanaf ordinaal niveau .................................................................... 29
3.4.1 Rangcorrelatiecoëfficiënt van Spearman (rs) ....................................................................... 29
3.4.2 Rangcorrelatiecoëfficiënt van Kendall.................................................................................. 30
H.4 Integralen ........................................................................................................................................ 31
4.1 Inleiding ....................................................................................................................................... 31
2
, 4.2 Rekenregels integralen ................................................................................................................ 32
4.3 Bepaalde integralen .................................................................................................................... 33
4.4 Stappenplan................................................................................................................................. 34
H.5 Combinatieleer................................................................................................................................ 35
5.1 Faculteit ....................................................................................................................................... 35
5.2 Variaties ....................................................................................................................................... 35
5.3 Permutaties ................................................................................................................................. 36
5.4 Combinaties ................................................................................................................................. 37
5.5 Overzicht...................................................................................................................................... 38
H.6 Kansrekenen ................................................................................................................................... 40
6.1 Unie en doorsnede ...................................................................................................................... 40
6.2 Verschil ........................................................................................................................................ 41
6.3 Complement ................................................................................................................................ 41
6.4 Definitie van kans ........................................................................................................................ 42
6.4.1 Klassieke definitie ................................................................................................................. 42
6.4.2 Frequentiële definitie ........................................................................................................... 42
6.5 Somregel...................................................................................................................................... 43
6.5.1 Disjuncte gebeurtenissen ..................................................................................................... 43
6.5.2 Niet-disjuncte gebeurtenissen ............................................................................................. 43
6.5.3 3 niet-disjuncte gebeurtenissen ........................................................................................... 43
6.6 Basisregels voor kansen .............................................................................................................. 44
6.7 Voorwaardelijke kans .................................................................................................................. 44
6.8 Productregel ................................................................................................................................ 45
6.8.1 2 gebeurtenissen .................................................................................................................. 45
6.8.2 3 gebeurtenissen .................................................................................................................. 45
6.9 Stochastische onafhankelijkheid ................................................................................................. 46
6.10 Overzicht ................................................................................................................................... 47
6.11 Regel van Bayes ......................................................................................................................... 47
H.7 Stochastische variabelen ................................................................................................................ 49
7.1 Discrete stochastische variabelen ............................................................................................... 49
7.1.1 Algemeen.............................................................................................................................. 49
7.1.2 Verwachting.......................................................................................................................... 50
7.1.3 Variantie ............................................................................................................................... 50
7.2 Continue stochastische variabelen.............................................................................................. 50
7.2.1 Algemeen.............................................................................................................................. 50
7.2.2 Verwachting.......................................................................................................................... 51
3
, 7.2.3 Variantie ............................................................................................................................... 52
7.3 Regels voor (wiskundige) verwachtingen .................................................................................... 53
7.4 Regels voor varianties ................................................................................................................. 54
H.8 Steekproevenverdelingen ............................................................................................................... 55
8.1 Inleiding ....................................................................................................................................... 55
8.2 Binomiale verdelingen van steekproefaantallen......................................................................... 56
8.2.1 Inleiding ................................................................................................................................ 56
8.2.2 4 voorwaarden van een binomiale situatie .......................................................................... 56
8.2.3 Speciale gevallen .................................................................................................................. 57
8.2.4 Binomiaalcoëfficiënt ............................................................................................................. 58
8.2.5 Binomiale verdelingen .......................................................................................................... 58
8.3 Binomiale verdelingen in steekproeven ...................................................................................... 59
8.4 Binomiale kansen bepalen .......................................................................................................... 59
8.5 Verwachting en standaardafwijking van een binomiale verdeling ............................................. 60
8.6 Normale benadering van de binomiale verdeling van aantallen ................................................ 60
8.7 Continuïteitscorrectie.................................................................................................................. 61
8.8 Normale benadering van de binomiale verdeling van proporties .............................................. 62
8.9 Centrale limietstelling ................................................................................................................. 62
8.10 Schema benaderingen ............................................................................................................... 63
H.9 Inleiding tot inferentie .................................................................................................................... 64
9.1 Inferentiemethoden .................................................................................................................... 64
9.2 Schatten....................................................................................................................................... 64
9.2.1 Puntschatting........................................................................................................................ 64
9.2.2 Intervalschatting ................................................................................................................... 65
9.3 Significantietoetsen ..................................................................................................................... 66
9.4 Z-toets.......................................................................................................................................... 68
9.5 Overschrijdingskansen (p-waarden) vs vast significantieniveau α.............................................. 68
4
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