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Samenvatting - Statistiek I voor de sociale wetenschappen (000363)
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Haalde het direct bij het eerste examen. Alles zit erin, samen met powerpoints. bevat vooral theorie
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Inhoud1 Waarom doen wij aan statistiek? ................................................................................................... 10
2 Soorten statistiek: ........................................................................................................................... 11
2.1 Beschrijvende statistiek: ......................................................................................................... 11
2.2 Inferentiële statistiek .............................................................................................................. 12
2.3 Verklarende statistiek of statistische analyse ......................................................................... 12
3 Misleiding door statistiek ............................................................................................................... 13
4 Statistiek: oorsprong? ..................................................................................................................... 13
4.1 Ontstaan midden de 18de eeuw ............................................................................................ 13
4.2 Midden 19de eeuw................................................................................................................. 13
4.2.1 Adolphe Quetelet ........................................................................................................... 13
1 Terminologie en kernbegrippen ..................................................................................................... 14
2 Waarom meten?............................................................................................................................. 15
3 Wat is meten? ................................................................................................................................ 16
3.1 Operationalisatie .................................................................................................................... 16
3.2 Afhankelijke en onafhankelijke variabelen ............................................................................. 16
3.3 Het meten ............................................................................................................................... 16
3.4 Meten en meetschalen........................................................................................................... 17
3.5 Kwantitatieve versus kwalitatieve waarden? ......................................................................... 17
4 Eigenschappen van variabelen ....................................................................................................... 18
4.1 Meetniveau............................................................................................................................. 18
4.1.1 Nominale variabelen....................................................................................................... 18
4.1.2 Ordinale variabelen ........................................................................................................ 18
4.1.3 Intervalvariabelen ........................................................................................................... 18
4.1.4 Ratiovariabelen ............................................................................................................... 19
4.1.5 Soorten variabelen ......................................................................................................... 19
4.2 Eigenschappen van variabelen ............................................................................................... 20
4.2.1 Kwalitatieve of categorische variabelen en kwantitatieve ............................................. 20
4.2.2 Discrete en continue variabelen ..................................................................................... 20
4.2.3 Dummy variabelen.......................................................................................................... 20
5 Examenvragen ................................................................................................................................ 20
1 Inleiding .......................................................................................................................................... 21
1.1 Bos door de getallenbomen?.................................................................................................. 21
2 Frequentieverdelingen en – tabellen en grafieken......................................................................... 21
2.1 Voorbeeld uit European Sociale Survey .................................................................................. 21
, 2.2 Frequentieverdelingen en –tabellen: Waarom?..................................................................... 22
2.3 Grafieken: waarom? ............................................................................................................... 22
3 Definities en notatie ....................................................................................................................... 22
4 Absolute en relatieve frequenties .................................................................................................. 23
5 Frequentieverdeling en grafische voorstelling ............................................................................... 23
5.1 Grafische voorstelling van frequentieverdelingen .................................................................. 23
5.2 Nominale gegevens ................................................................................................................ 23
Schikking van gegevens op nominale schaal................................................................................... 23
5.2.1 Schikking van gegevens op nominale schaal: balkdiagram ............................................. 23
5.2.2 Grafische voorstelling van nominale schaal: balkdiagram .............................................. 24
5.2.3 Grafische voorstelling van nominale schaal: cirkeldiagram/taartdiagram ..................... 24
5.2.4 Grafische voorstelling van nominale schaal: pictogram (symboolverzameling) ............. 24
5.3 Ordinale gegevens .................................................................................................................. 24
Schikking van gegevens op ordinale schaal .................................................................................... 24
5.3.1 Grafische voorstelling van ordinale schaal: balkdiagram................................................ 25
5.3.2 Grafische voorstelling ordinale schaal: cumulatieve frequentiefunctie ......................... 25
5.4 Interval- en ratiogegevens ...................................................................................................... 25
Niet in klassen gegroepeerde gegevens ......................................................................................... 25
5.4.1 Niet in klassen gegroepeerde gegevens ......................................................................... 26
5.4.2 Niet in klassen gegroepeerde gegevens: staafdiagram .................................................. 26
5.4.3 Niet in klassen gegroepeerde gegevens: histogram ....................................................... 26
5.4.4 Niet in klassen gegroepeerde gegevens: frequentiepolygoon ....................................... 26
5.4.5 Niet in klassen gegroepeerde gegevens: cumulatieve frequentiefunctie ...................... 27
5.4.6 In klassen gegroepeerde gegevens: frequentietabel...................................................... 28
5.4.7 In klassen gegroepeerde gegevens: histogram .............................................................. 29
5.4.8 In klassen gegroepeerde gegevens: frequentieveelhoek ............................................... 29
5.4.9 In klassen gegroepeerde gegevens: diagram cumulatieve frequentie ........................... 29
6 Frequentieverdeling en grafische voorstelling: synthese ............................................................... 30
1 Waarom statistische maten? .......................................................................................................... 31
1.1 Statistische maten .................................................................................................................. 31
2 Soorten statistische maten ............................................................................................................. 31
2.1 Statistische maten van ligging (van positie) ............................................................................ 31
2.1.1 Statistische maten van centrale tendens of centrummaten .......................................... 31
2.2 Statistische maten van spreiding ............................................................................................ 31
2.3 Statistische maten van vorm .................................................................................................. 31
3 Statistische maten van ligging ........................................................................................................ 32
, 3.1 Centrummaten: modus .......................................................................................................... 32
3.1.1 In klassen gegroepeerde gegevens................................................................................. 32
3.2 Centrummaten: mediaan ....................................................................................................... 33
3.2.1 Mediaan in klassen gegroepeerde gegevens .................................................................. 33
3.2.2 Mediaan: eigenschappen ............................................................................................... 34
3.3 Centrummaten: rekenkundige gemiddelde............................................................................ 35
3.3.1 Rekenkundig gemiddelde (intervalschaal) ...................................................................... 35
3.3.2 Eigenschappen gemiddelde ............................................................................................ 36
3.3.3 Overzicht......................................................................................................................... 36
4 Statistische maten van ligging: kwantielen ..................................................................................... 37
4.1 Kwantielen: kwartielen ........................................................................................................... 37
4.2 Kwantielen: decielen .............................................................................................................. 38
4.3 Kwantielen: percentielen........................................................................................................ 38
4.4 Kwantielen: oefening .............................................................................................................. 39
5 Momenten ...................................................................................................................................... 40
5.1 Karl Pearson (1857-1936) ....................................................................................................... 40
5.2 Momenten rond de oorsprong (c = 0) .................................................................................... 41
5.3 Momenten rond een constante (c = c) ................................................................................... 41
5.4 Momenten rond gemiddelde (c = gemiddelde)...................................................................... 41
5.5 Momenten: oefening.............................................................................................................. 42
1 Statistische maten van spreiding .................................................................................................... 43
1.1 Variatie is de werkelijkheid ..................................................................................................... 43
1.2 Begrip spreiding ...................................................................................................................... 43
1.3 Spreidingsmaten ..................................................................................................................... 44
1.4 Variatiebreedte of range ........................................................................................................ 44
1.5 Interkwartielafstand ............................................................................................................... 44
1.5.1 Oefening interkwartielafstand ........................................................................................ 45
1.6 Interdecielafstand................................................................................................................... 45
1.6.1 Oefening interdecielafstand ........................................................................................... 45
2 De Boxplot: 5 kengetallen in één grafiek ........................................................................................ 45
2.1 De Boxplot: outliers ................................................................................................................ 46
2.2 De Boxplot: 5 kengetallen in één grafiek ................................................................................ 46
3 Spreiding ......................................................................................................................................... 47
3.1 Maten voor spreiding bij interval- en ratiovariabelen ............................................................ 47
3.1.1 Centraal moment van rang 1: gemiddelde afwijking van het gemiddelde ..................... 47
3.2 Gemiddelde absolute afwijking .............................................................................................. 48
, 3.3 Variatie: sum of squares (SS) .................................................................................................. 48
4 Variantie ......................................................................................................................................... 49
4.1 Even centrale momenten ....................................................................................................... 49
4.1.1 Kenmerken van de variantie ........................................................................................... 49
4.1.2 Standaardafwijking ......................................................................................................... 50
5 Variatiecoëfficiënt .......................................................................................................................... 50
6 Overzicht van spreidingsmaten ...................................................................................................... 51
Oefening spreidingsmaten PW Statistiek I...................................................................................... 51
7 Toepassing standaardafwijking: normaalverdeling ........................................................................ 52
7.1 Toepassing 1: oppervlakte onder normale verdeling ............................................................. 52
8 Toepassingen standaardafwijking: z-scores.................................................................................... 53
8.1 Toepassing 2: gestandaardiseerde scores .............................................................................. 53
8.1.1 Standaard normaal verdeling ......................................................................................... 53
9 Statistische maten van vorm .......................................................................................................... 54
9.1 Maten voor symmetrie van een verdeling.............................................................................. 54
9.1.1 De empirische coëfficiënt van Pearson S........................................................................ 55
9.1.2 Coëfficiënt van Yule en Kendall ...................................................................................... 56
9.2 Oneven centrale momenten .................................................................................................. 57
9.2.1 Coëfficiënt van Fisher (𝑔1) ............................................................................................. 57
9.2.2 Coëfficiënt van Pearson (𝑏1) .......................................................................................... 57
9.3 Maten voor afplatting van een verdeling ............................................................................... 58
9.3.1 De coëfficiënt van Pearson (𝑏2) ..................................................................................... 58
9.3.2 De coëfficiënt van Fisher (𝑔2) ........................................................................................ 58
10 Overzicht momenten (brutogegevens) ...................................................................................... 59
1 Introductie ...................................................................................................................................... 60
1.1 Wat is de samenhang? ........................................................................................................... 60
1.1.1 Samenhang: waarom? .................................................................................................... 60
Voorbeelden ................................................................................................................................... 60
1.2 Hoe onderzoeken we de samenhang? ................................................................................... 61
1.2.1 Samenhang: hoe onderzoeken? ..................................................................................... 61
1.3 Samenhang en causaliteit? ..................................................................................................... 61
2 Samenhang tussen twee categorische variabelen .......................................................................... 62
Tweedimensionale kruistabellen ........................................................................................................ 62
2.1 Aard en richting van een relatie ............................................................................................. 62
2.1.1 Anatomie ........................................................................................................................ 62
Anatomie: kolommen, rijen en cellen............................................................................................. 63
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