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Samenvatting basisbegrippen statistiek voor criminologen
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INHOUDSOPGAVEHoofdstuk 1: Doel van de statistiek .................................................................................................................. 5
1.1 inleiding ................................................................................................................................................... 5
1.2 verzamelen van gegevens ....................................................................................................................... 7
verzamelen van gegevens ............................................................................................................................... 8
1.3 classificatie van gegevens ....................................................................................................................... 9
OEFENINGen ................................................................................................................................................. 10
1.4. van steekproef naar populatie ................................................................................................................... 11
Hoofstuk 2: beschrijvende statistiek .............................................................................................................. 13
Inleiding ............................................................................................................................................................. 13
2.1. absolute en relatieve frequenties ............................................................................................................... 14
2.2. vormen van verdelingen .......................................................................................................................... 21
Symetrische verdeling ....................................................................................................................................... 21
normale verdelingsvorm ................................................................................................................................... 21
andere verdelingsvormen (scheve verdelingen) ................................................................................................ 22
andere verdelingsvormen (bimodale verdelingen) ............................................................................................ 23
uitschieters ........................................................................................................................................................ 23
2.3. cumulatieve frequenties en kwantielen ..................................................................................................... 24
kwantielfunctie ................................................................................................................................................. 27
2.4. centrumkenmerken .................................................................................................................................... 29
Modus ........................................................................................................................................................... 30
Mediaan ........................................................................................................................................................ 30
Steekproefgemiddelde .................................................................................................................................. 31
Steekproefgemiddelde versus mediaan ........................................................................................................ 32
Centrummaten: opmerkingen ...................................................................................................................... 32
2.5. spreidingskenmerken ................................................................................................................................. 33
Bereik ............................................................................................................................................................ 34
Standaardafwijking en variantie ................................................................................................................... 35
Standaardafwijking en variantie berekenen stappenplan ............................................................................ 36
Interpretatie van standaardafwijking en variantie ....................................................................................... 38
Z-scores ......................................................................................................................................................... 38
Interkwartielafstand...................................................................................................................................... 41
2.6. BOXPLOT .................................................................................................................................................... 41
UITSCHIETERS ................................................................................................................................................ 42
soorten verdelingen in een boxplot .............................................................................................................. 43
2.8. verbanden tussen twee variabelen ............................................................................................................ 45
twee kwalitatieve variabelen: kruistabel ...................................................................................................... 45
twee kwalitatieve variabelen: staafdiagram ................................................................................................. 46
, twee kwalitatieve variabelen: staafdiagrammen voorwaardelijke relatieve frequenties ............................ 48
een kwantitatieve en kwalitatieve variabele: boxplot per groep ................................................................. 48
een kwantitatieve en kwalitatieve variabele: heatmap ................................................................................ 48
twee kwantitatieve variabelen: scatterplot .................................................................................................. 49
covariantie en correlatiecoëfficiënt .............................................................................................................. 50
twee kwantitatieve variabelen: correlatiecoëfficiënt ................................................................................... 52
hoofdstuk 3: kansen en toevalsvariabelen ..................................................................................................... 55
3.1. kansen en kansregels ............................................................................................................................ 55
kanstheorie ................................................................................................................................................... 55
kansregels ..................................................................................................................................................... 56
3.2. voorwaardelijke kansen ........................................................................................................................ 58
onafhankelijkheid van gebeurtenissen ......................................................................................................... 59
3.3. toevalsvariabelen .................................................................................................................................. 60
Kansen op gebeurtenissen met betrekking tot toevalsvariabelen ............................................................... 62
3.4. dichtheidsfunctie ................................................................................................................................... 62
discrete toevalsvariabele vs continue toevalsvariabele ................................................................................ 62
discrete toevalsvariabele .............................................................................................................................. 62
continue toevalsvariabele ............................................................................................................................. 65
3.5. verdelings- en kwantielfunctie .............................................................................................................. 67
definitie verdelingsfunctie ............................................................................................................................ 67
3.6. centrum- en spredingskenmerken ......................................................................................................... 72
centrumkenmerken....................................................................................................................................... 72
spreidingskenmerken .................................................................................................................................... 75
3.7. transformaties ....................................................................................................................................... 76
lineaire transformaties .................................................................................................................................. 77
3.8. covariantie, correlatie en onafhankelijkheid van twee variabelen........................................................ 80
Covariantie en correlatie ............................................................................................................................... 80
Onafhankelijkheid van toevalsvariabelen ..................................................................................................... 80
3.9. lineaire combinaties van toevalsvariabelen .......................................................................................... 81
lineaire combinaties van steekproefgegevens .............................................................................................. 81
Lineaire combinaties van toevalsvariabelen ................................................................................................. 81
hoofdstuk 4: univariate kansmodellen ........................................................................................................... 83
4.1. bernoulli verdeling ...................................................................................................................................... 83
variantie Bernoulli verdeling ......................................................................................................................... 85
4.2. binomiaalverdeling ..................................................................................................................................... 85
kansen onder een binomiaalverdeling .......................................................................................................... 87
binomiaalverdeling: kansverdeling ............................................................................................................... 89
intermezzo: rekenen met faculteit (!) ........................................................................................................... 90
kenmerken van een binomiaalverdeling ....................................................................................................... 90
4.3. poisson verdeling ........................................................................................................................................ 92
4.4. normale verdeling ...................................................................................................................................... 92
standaardnormale verdeling ......................................................................................................................... 94
, standaardnormale verdeling: kansen............................................................................................................ 96
Standaardnormale verdeling: 68-95-99.7 regel ............................................................................................ 99
Standaardnormale verdeling: kwantielen ..................................................................................................... 99
Kansen en kwantielen onder een willekeurige normale verdeling ............................................................. 100
Willekeurige normale verdeling: kansen..................................................................................................... 101
4.6. toepassingen ............................................................................................................................................ 104
toepassing: sociaal-economische wetenschap ........................................................................................... 104
hoofdstuk 5: schatters en hun verdeling ...................................................................................................... 105
5.1. steekproefgemiddelde als toevalsvariabele ........................................................................................ 105
parameter, schatter en schatting ................................................................................................................ 107
5.2. verdeling van het steekproefgemiddelde ............................................................................................ 108
verdeling van het gemiddelde van een normale variabele ......................................................................... 110
5.3. centrale limietstelling .......................................................................................................................... 111
5.4. normale benadering voor binomiaalkansen ....................................................................................... 115
percentage als toevalsvariabele .................................................................................................................. 115
binomiaalverdeling...................................................................................................................................... 116
normale benadering voor binomiaalkansen ............................................................................................... 117
normale benadering voor binomiale kansen: continuïteitscorrectie .......................................................... 120
Hoofdstuk 6: univariate inferentie ............................................................................................................... 122
van steekproef naar populatie .................................................................................................................... 122
puntschatters en puntschattingen .............................................................................................................. 123
betrouwbaarheidsinterval: definitie ........................................................................................................... 125
6.1. betrouwbaarheidsinterval voor het gemiddelde van een normale variabele .......................................... 126
intermezzo: kwantielen met kleine staartkans ........................................................................................... 127
betrouwbaarheidsinterval: foutmarge........................................................................................................ 128
betrouwbaarheidsinterval voor het gemiddelde van een normale variabele ............................................ 129
6.2. testen omtrent het gemiddelde van een normale variabele .................................................................... 138
hypothesetest ............................................................................................................................................. 138
EENZIJDIGE TEST VOOR MET ONBEKEND ............................................................................................. 150
hypothesetest voor het gemiddelde van een variabele, onbekend: overzicht ....................................... 154
aanvaardings- en verwerpingsgebied = geen leerstof ................................................................................ 155
type 1 en type 2 fout ................................................................................................................................... 156
6.3. inferrentie omtrent een proportie ............................................................................................................ 161
betrouwbaarheidsinterval voor een proportie ........................................................................................... 161
testen omtrent een proportie: n voldoende groot ..................................................................................... 163
Hoofdstuk 7: bivariate inferentie ................................................................................................................. 167
respons- en verklarende variabele .............................................................................................................. 167
7.1. twee kwalitatieve variabelen ................................................................................................................... 169
7.1.1. inferfentie omtrent twee proporties ................................................................................................ 169
betrouwbaarheidsinterval voor verschil in proporties: interpretatie ......................................................... 171
7.1.2. onafhankelijkheid van twee variabelen testen ................................................................................. 176
7.2. een kwantitatieve en een kwalitatieve variabele ..................................................................................... 187
, 7.2.1. het gemiddelde van een variabele vergelijken voor twee groepen .................................................. 187
7.3. twee kwantitatieve variabelen ................................................................................................................. 198
7.3.1. het verschil van twee variabelen vergelijken .................................................................................... 198
7.3.2. de correlatie tussen twee variabelen testen ..................................................................................... 205
causaal en associatief verband ................................................................................................................... 208
hypothesetesten: overzicht ........................................................................................................................ 209
sectie 2.9: Lineaire regressie ........................................................................................................................... 209
2.9.1. kleinste-kwadratenmethode ............................................................................................................. 209
Hoofdstuk 8: lineaire regressie ..................................................................................................................... 214
8.1. het enkelvoudige lineaire regressiemodel ................................................................................................ 214
8.3. nagaan van de modelveronderstellingen ................................................................................................. 215
2.9.2. determinatiecoëfficiënt .................................................................................................................... 216
8.2. anova-tabel .............................................................................................................................................. 219
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