Dit is een samenvatting van het vak Statistiek voor humane wetenschappen. Het bevat alle theorie uit de lessen (slides) en de cursus van Dirk Speelman.
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STATISTIEK VOOR HUMANE WETENSCHAPPEN
Inhoud
Doel en inhoud.................................................................................................................... 5
Inleiding........................................................................................................................... 6
Inhoud en opbouw........................................................................................................ 6
Examen........................................................................................................................ 6
Hoofdstuk 1: Eerste verkenning van de datasets................................................................7
Structuur van data........................................................................................................... 7
Archeologische dataset: oxford-pots................................................................................7
Ecologische dataset: pollution.........................................................................................8
Meetniveaus (levels of measurement)...........................................................................10
Conventies voor aanmaak............................................................................................. 11
Tekstbestanden............................................................................................................. 11
Toepassing.................................................................................................................... 11
Video 1....................................................................................................................... 11
Video 2....................................................................................................................... 12
Hoofdstuk 2: Eerste verkenning van de software (RStudio)..............................................14
Inleiding......................................................................................................................... 14
Openen van bestand C02-session.R in RStudio..........................................................14
Over bestanden zoals C02-session.R..........................................................................14
Instellen van working directory......................................................................................14
Uitvoeren R-instructies............................................................................................... 15
Laden van packages...................................................................................................... 15
Beschikbaar maken van een package........................................................................15
Packages gebruikt in de sessie C02-session.R............................................................16
Meldingen die je krijgt bij activeren van tidyverse packages......................................16
Importeren data............................................................................................................. 16
Importeren van een tvs-bestand.................................................................................16
Inspecteren van dataset student.cvs (of student.txt).................................................16
Importeren van dataset students.csv.........................................................................17
Opvragen van documentatie......................................................................................18
Inspecteren van een object........................................................................................18
Inspecteren van eigenschappen van data frame........................................................19
Aanpassen van data frames.......................................................................................... 19
Nieuwe kolommen maken.......................................................................................... 19
Inspectie resultaat met frequentietabel......................................................................20
Inspectie resultaat met staafdiagram.........................................................................21
Inspectie structuur van object met str().....................................................................21
1
, Omzetting van character data naar factor..................................................................21
Veranderen van volgorde van levels met fct_relevel()................................................22
Verwijderen van een kolom met select ()...................................................................22
Hernoemen van levels met fct_recode().....................................................................23
Levels samenklappen met fct_recode()......................................................................23
Liever factor dan numerische codes voor categoriale variabelen...............................23
Liever logical variable dan numerische codes voor ja-nee-variabelen........................24
Verwijderen van verschillende kolommen met select()..............................................25
Aanmaken van vectoren met c()................................................................................25
Bewaren van data frame als tsv-bestand...................................................................25
Sorteren van een data frame met arrange()...............................................................26
Grafieken....................................................................................................................... 27
Spreidingsdiagram van languages tegenover statistics..............................................27
Staafdiagram voor math............................................................................................. 28
Staafdiagram voor sex................................................................................................ 28
Samenvatting................................................................................................................ 28
R afsluiten...................................................................................................................... 29
Hoofdstuk 3: Beschrijvende statistieken...........................................................................30
Inleiding......................................................................................................................... 30
Centraliteit..................................................................................................................... 30
Modus (mode)............................................................................................................. 31
Gemiddelde (mean).................................................................................................... 32
Mediaan (median)....................................................................................................... 33
Spreiding....................................................................................................................... 34
Bereik (range)............................................................................................................. 35
Variantie (variance).................................................................................................... 35
Standaarddeviatie (standard deviation).....................................................................35
Variatiecoëfficiënt (coefficient of variation)................................................................36
Interkwartielbereik (interquartile range).....................................................................36
Vorm.............................................................................................................................. 36
Correlatie....................................................................................................................... 36
Covariantie (covariance)............................................................................................. 36
Correlatie (correlation)............................................................................................... 37
Hoofdstuk 4: Datavisualisatie........................................................................................... 39
Inleiding......................................................................................................................... 39
Staafdiagram (bar plot)................................................................................................. 39
Histogram...................................................................................................................... 39
Cumulatieve frequentiegrafiek......................................................................................41
Boxplot.......................................................................................................................... 41
Smooth lines scatter plot............................................................................................... 42
2
,Hoofdstuk 5: Kansverdelingen.......................................................................................... 43
Inleiding......................................................................................................................... 43
Stochastisch experiment............................................................................................... 43
Kans (probability).......................................................................................................... 44
Kanswetten................................................................................................................. 46
Regel van Bayes (gestratificeerde data):....................................................................47
Kansverdeling (probability distribution).........................................................................48
Dichtheidsfunctie........................................................................................................ 48
Verdelingsfunctie........................................................................................................ 49
Kwantielfunctie........................................................................................................... 50
Populatieparameters.................................................................................................. 51
Modellen........................................................................................................................ 53
Binaire verdeling........................................................................................................ 53
Binomiale verdeling.................................................................................................... 55
Poissonverdeling......................................................................................................... 56
Exponentiële verdeling............................................................................................... 57
Normale verdeling...................................................................................................... 58
Andere verdelingen.................................................................................................... 60
Centrale limietstelling (CLT).......................................................................................... 60
Hoofdstuk 6: Normaliteitstoetsen.....................................................................................62
Inleiding......................................................................................................................... 62
Normaal kwantieldiagram.............................................................................................. 62
Shapiro-Wilktoets........................................................................................................... 66
Lilliefors-toets................................................................................................................ 66
Hoofdstuk 7: Betrouwbaarheidsintervallen.......................................................................68
Inleiding......................................................................................................................... 68
Met t-verdeling.............................................................................................................. 69
Met z-verdeling.............................................................................................................. 70
Voor proportie................................................................................................................ 70
Voor proportie, met t-verdeling..................................................................................71
Vereisten n voor bepaalde ε.......................................................................................... 71
Parameters σ en p invullen?.......................................................................................71
Hoofdstuk 8: Toetsen van hypotheses..............................................................................73
Inleiding......................................................................................................................... 73
Tweezijdige t-toets........................................................................................................ 73
Een ‘wat als’-redenering............................................................................................. 74
Eenzijdige t-toets........................................................................................................... 76
Eenzijdige t-toets, rechterstaart.................................................................................76
Eenzijdige t-toets, linkerstaart....................................................................................77
Eenzijdige versus tweezijdige t-toetsen......................................................................78
3
, CI................................................................................................................................... 78
De z-toets...................................................................................................................... 78
Stappen bij inferentiële toetsen.....................................................................................79
Kwaliteitsmaten............................................................................................................. 79
Effectgrootte.................................................................................................................. 80
Niet-parametrische toetsen........................................................................................... 81
Hoofdstuk 9: Toetsen in de praktijk..................................................................................82
Inleiding......................................................................................................................... 82
Centraliteit..................................................................................................................... 82
t-toets voor gemiddelde voor één groep....................................................................82
Rangtekentoets van Wilcoxon voor één groep...........................................................84
t-toets voor gemiddelde voor twee gepaarde groepen...............................................85
Rangtekentoets van Wilcoxon voor twee gepaarde groepen......................................87
Rangtekentoets van Wicoxon voor één groep............................................................87
t-toets voor gemiddelde voor twee onafhankelijke groepen.......................................87
Mann-Whitney-Wilcoxontoets voor twee onafhankelijke groepen...............................88
Frequentietabellen......................................................................................................... 89
Toetsen voor frequentietabellen.................................................................................89
Toetsen voor proporties................................................................................................. 96
t-toets voor een proportie........................................................................................... 96
Binominiale toets voor een proportie..........................................................................96
Toetsen voor correlatie.................................................................................................. 97
Pearson-correlatietoets............................................................................................... 97
Spearman-correlatietoets........................................................................................... 98
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