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Samenvatting Statistiek voor Humane Wetenschappen 2023 - Dirk Speelman
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Statistiek voor Humane Wetenschappen 2023 - gegeven door D. Speelman
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STATISTIEK VOOR HUMANEWETENSCHAPPEN
Linn Rademaekers
Schakeljaar Bedrijfscommunicatie
,1. Introductie van de datasets ........................................................................................................ 4
Kolomtypes in de datasets .................................................................................................................................... 4
Meten en meetniveaus .......................................................................................................................................... 4
Categoriaal meetniveau ..................................................................................................................................................... 4
1. Nominaal meetniveau ....................................................................................................................................... 4
2. Ordinaal meetniveau ......................................................................................................................................... 4
Numerisch meetniveau ........................................................................................................................................................ 5
3. Interval niveau ..................................................................................................................................................... 5
4. Ratio niveau......................................................................................................................................................... 5
5. Discreet niveau ................................................................................................................................................... 5
6. Continu niveau .................................................................................................................................................... 5
2. Introductie RStudio ....................................................................................................................... 6
3. Descriptieve of beschrijvende statistiek.................................................................................. 15
Centrummaten (measures of central tendency) .............................................................................................. 16
Gemiddelde (mean) .......................................................................................................................................................... 16
Standaard gemiddelde ............................................................................................................................................... 16
Gewogen gemiddelde ................................................................................................................................................ 16
Wegingscoëfficiënten .................................................................................................................................................. 17
Mediaan (median) ............................................................................................................................................................. 18
Gemiddelde versus mediaan ...................................................................................................................................... 18
Modus (mode) .................................................................................................................................................................... 19
Modus bij categoriale variabelen ............................................................................................................................... 19
Modus bij numerische variabelen ............................................................................................................................... 19
Spreidingsmaten (measures of dispersion)........................................................................................................ 21
Bereik (range)...................................................................................................................................................................... 21
Variantie (variance) ........................................................................................................................................................... 21
Standaarddeviatie (standard deviation) ......................................................................................................................... 23
Variantiecoëfficiënt (coëfficient of variation) ................................................................................................................. 23
Interkwartielbereik (interquartile range) ........................................................................................................................... 24
Covariantie (covariance) .................................................................................................................................................. 25
Correlatie (pearson product-moment correlation)......................................................................................................... 27
4. Visualisatie van data ................................................................................................................. 31
Staafdiagram (bar plot) voor categorische data ............................................................................................. 31
Histogram en dichtheidsgrafiek (density plot) .................................................................................................. 31
Histogram in R (frequentie- en dichtheidshistogram)...................................................................................................... 32
Frequentiehistogram in R .............................................................................................................................................. 34
Dichtheidshistogram in R .............................................................................................................................................. 35
Toevoegen tapijt (rug plot) .......................................................................................................................................... 36
Rijk dichtheidshistogram in R ........................................................................................................................................ 37
Cumulatieve frequentiegrafiek ........................................................................................................................... 38
,Boxplot ................................................................................................................................................................... 39
Smooth lines toevoegen aan scatter plots ........................................................................................................ 42
5. Kansverdelingen (probability distributions) ............................................................................ 44
Stochastisch/willekeurige proeven (random experiment) .............................................................................. 44
Kansen (probability) ............................................................................................................................................. 45
Basic probability axioms and rules (kanswetten)............................................................................................................. 47
Kanskomen (probability trees)........................................................................................................................................... 48
Regel van Bayes voor gestratificeerde data ................................................................................................................... 50
Kansverdeling (probability distribution) ............................................................................................................. 51
1. Dichtheidsfunctie (desity function) ......................................................................................................................... 52
2. Verdelingsfunctie (cumulative distribution function)............................................................................................. 53
3. Kwantielfunctie (quantile function) ......................................................................................................................... 54
Populatie-parameters .......................................................................................................................................... 54
Populatiegemiddelde μ ..................................................................................................................................................... 55
Populatievariantie σ2.......................................................................................................................................................... 56
Populatiestandaarddeviatie σ .......................................................................................................................................... 56
Statistische modellen voor kansverdeling ......................................................................................................... 56
Modellen voor discrete variabelen ................................................................................................................................... 56
1. Binaire verdeling................................................................................................................................................ 56
2. Binomiale verdeling .......................................................................................................................................... 58
3. Poissonverdeling................................................................................................................................................ 59
Modellen voor continue variabelen ................................................................................................................................. 60
4. Exponentiële verdeling ..................................................................................................................................... 60
5. Normale verdeling ............................................................................................................................................ 62
Centrale Limiet Stelling ......................................................................................................................................... 64
CLT voor een som ............................................................................................................................................................... 64
CLT voor een gemiddelde ................................................................................................................................................. 64
6. Normaliteitstoetsen .................................................................................................................... 74
Normaal kwantieldiagram (normal QQ plot) .................................................................................................... 74
Shapiro-Wilktoets .................................................................................................................................................. 79
Lilliefors-toets ......................................................................................................................................................... 80
7. Betrouwbaarheidsintervallen .................................................................................................... 81
Steekproefverdeling van X en zijn standaardiseringen ................................................................................... 83
Betrouwbaarheidsinterval met T-verdeling........................................................................................................ 85
Betrouwbaarheidsniveau, foutenniveau, foutmarge en standaardfout ......................................................... 86
Betrouwbaarheidsinterval met Z-verdeling ....................................................................................................... 87
Betrouwbaarheidsinterval voor een proportie .................................................................................................. 88
Vereiste steekproefomvang voor een specifieke foutenmarge ..................................................................... 89
Voor gemiddelde ............................................................................................................................................................... 89
Voor proportie..................................................................................................................................................................... 89
, 8. Hypotheses.................................................................................................................................. 90
Tweezijdige t-toets voor het gemiddelde .......................................................................................................... 90
Een ‘wat als’-redenering.................................................................................................................................................... 91
P-waarde ............................................................................................................................................................................. 94
Eenzijdige t-toets voor gemiddelde (rechterstaart) ......................................................................................... 96
Eenzijdige t-toets voor gemiddelde (linkerstaart) ............................................................................................ 98
Relatie tussen tweezijdige t-toets en betrouwbaarheidsinterval .................................................................... 99
De z-toets voor het gemiddelde ....................................................................................................................... 100
Maten voor effecten ........................................................................................................................................... 102
Effectgrootte ..................................................................................................................................................................... 102
Parametrische en niet-parametrische toetsen................................................................................................ 104
Parametrische toetsen ..................................................................................................................................................... 104
Niet-parametrische toetsen ............................................................................................................................................. 104
9. Statistische testen in de praktijk ............................................................................................. 105
Testen van de centrale tendens van een numerieke variabele ................................................................... 105
1. T-toets voor populatiegemiddelde voor één groep ........................................................................................... 105
2. Wilcoxon-toetsen voor één groep ........................................................................................................................ 109
3. T-toets voor gemiddelde voor twee gepaarde groepen ................................................................................... 111
4. Wilcoxon test voor twee gepaarde groepen ...................................................................................................... 112
5. T-toets voor gemiddelde voor twee onafhankelijke groepen met gelijke variantie ........................................ 112
6. T-toets voor gemiddelde voor twee onafhankelijke groepen met ongelijke variantie ................................... 114
7. Wilcoxontoets voor twee onafhankelijke groepen ............................................................................................. 115
Toetsen voor frequentietabellen ....................................................................................................................... 117
X2-test voor goodness of fit .............................................................................................................................................. 117
X2 -toets voor onafhankelijkheid...................................................................................................................................... 121
X2-toets voor homogeniteit bij onafhankelijke groepen ............................................................................................... 124
Toetsen voor proporties ...................................................................................................................................... 125
t-toets voor proportie ....................................................................................................................................................... 125
Binomiale toets voor proportie ........................................................................................................................................ 126
Toetsen voor correlatie....................................................................................................................................... 127
Pearson-correlatietoets .................................................................................................................................................... 127
Spearman-rangcorrelatietoets ........................................................................................................................................ 128
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