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Samenvatting/aantekeningen van het vak 'Methodologie en Statistiek' (alleen onderdeel statistiek)

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Bevat de volgende onderwerpen: Multiple regressie Covariantie analyse Logistische regressie Sample size Survival analyse Factor analyse Longitudinaal

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  • February 4, 2024
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  • 2023/2024
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Samenvatting statistiek M&S


Onderwerpen:
- Mul'ple regressie
- Covarian'e analyse
- Logis'sche regressie
- Sample size
- Survival analyse
- Factoranalyse
- Longitudinaal




1

,Inhoudsopgave

Mul$ple regressie ........................................................................................................................................... 4
Aannames ...................................................................................................................................................... 7
Regressie uitvoer SPSS enkelvoudige regressie ............................................................................................. 9
Verklaarde varian9e (R2) .............................................................................................................................. 10
SPSS uitvoer mul9ple regressie ................................................................................................................... 11
Mul9ple regressie interpreta9e SPSS voorbeeld ‘’burden’’ ......................................................................... 12
Forward methode ........................................................................................................................................ 14
Backward methode ...................................................................................................................................... 14
Interpreta9e ANOVA en F-waarden ............................................................................................................. 15
Stel dat 2 variabelen alleen samen iets doen? ............................................................................................ 15
Voorwaarden mul9ple regressie .................................................................................................................. 18
Multi collineariteit ....................................................................................................................................... 19
Normal probability plot ............................................................................................................................... 20
Residuenplot ................................................................................................................................................ 20
“Dummy-codering” ...................................................................................................................................... 21
“Indicator” codering .................................................................................................................................... 22
Interac9e wel/niet ‘’flowchart’’ ................................................................................................................... 23

Covarian$e analyse (ANCOVA) ...................................................................................................................... 27
Confounding binnen covarian9e.................................................................................................................. 28
Toets op interac9e ....................................................................................................................................... 30
ANCOVA model ............................................................................................................................................ 31
Aannames ANCOVA ..................................................................................................................................... 33
Wanneer zinvol om ANCOVA te gebruiken .................................................................................................. 33
Indicator codering ........................................................................................................................................ 37

Logis$sche regressieanalyse deel 1 ............................................................................................................... 39
Dichotomiseren ........................................................................................................................................... 41
Verschil odds en RR ...................................................................................................................................... 42
Formules associa9ematen ........................................................................................................................... 43
Waarom logis9sche regressie & geen Chi-kwadraat? .................................................................................. 45
Interpreta9e ‘’variables in the equa9on’’ .................................................................................................... 52
Toelich9ng odds ........................................................................................................................................... 52

Logis$sche regressieanalyse deel 2 ............................................................................................................... 53
Cut value ...................................................................................................................................................... 57
Uiteindelijk model forward & backward ...................................................................................................... 59
Indicator dummy coding .............................................................................................................................. 62

Sample size ................................................................................................................................................... 66
Factoren die de sample size beïnvloeden .................................................................................................... 66
Steekproefgemiddelde: variabiliteit ............................................................................................................ 69
Sensi9viteitsanalyse..................................................................................................................................... 78
Wat gebeurt er met mijn sample size als ik… .............................................................................................. 81

Survival analyse ............................................................................................................................................ 83
Algemene inleiding survival analyse ............................................................................................................ 89
Survival en Hazard Func9es ......................................................................................................................... 90
Kaplan-Meier methode ................................................................................................................................ 92
Opmerkingen bij en aannames van de Kaplan-Meier curve ........................................................................ 96
Aannames van Kaplan-Meier ....................................................................................................................... 98



2

, Log-Rank Test ............................................................................................................................................... 99
Karnofsky ................................................................................................................................................... 102
Alterna9even voor Log-Rank Test .............................................................................................................. 103

Factoranalyse .............................................................................................................................................. 104
Item correla9es .......................................................................................................................................... 107
KMO en Bartleh’s test ............................................................................................................................... 108
Construc9e van factoren............................................................................................................................ 113
Selec9e van factoren ................................................................................................................................. 113
Selec9e van factoren in voorbeeld ............................................................................................................ 114
(Ongeroteerde) factorladingen .................................................................................................................. 115
Berekening communaliteiten..................................................................................................................... 116
Correla9es.................................................................................................................................................. 117
Berekening reproduced correla9ons ......................................................................................................... 117
Rota9e ....................................................................................................................................................... 119
Cronbach’s alpha........................................................................................................................................ 121

Longitudinaal .............................................................................................................................................. 125
Repeated measures ANOVA....................................................................................................................... 128
Twee soorten analyse binnen repeated measures binnen RM ANOVA ..................................................... 129
RM ANOVA, mul9variate ........................................................................................................................... 129
RM ANOVA, Mauchley’s test ...................................................................................................................... 130
Within Subjects test inclusief epsilon. ....................................................................................................... 130
Invloed df op power/significan9e .............................................................................................................. 131
Verschil within subjects & between subjects............................................................................................. 133
Nadelen RM ANOVA .................................................................................................................................. 134
Modernere methode: Linear Mixed Models.............................................................................................. 135
SPSS uitvoer: Linear Mixed Models ........................................................................................................... 135
Voordelen Linear Mixed Models ................................................................................................................ 136
Voorbeeld missing data ............................................................................................................................. 137

Soorten toetsen .......................................................................................................................................... 145




3

, Mul$ple regressie
Voorbeeld hoorcollege




Plaatje hierboven sluit aan op waar we mee aan de slag gaan met multiple regressie.
Intercept en helling op plaatje zijn direct af te lezen. Correlatie coëfficiënt inschatten is lastig
à wel duidelijk positief (stijgende lijn). Best positief verband, correlatie is niet al te klein.
Correlatie = 0.725 op plaatje. Interpretatie: correlatie doe je met de R2 die vertelt je hoeveel
variatie in je uitkomst (in dit geval) vetpercentage verklaard kan worden door je (in dit geval)
BMI. Je kan dus voor een groot deel vetpercentage verklaren door je BMI, maar niet
helemaal (blijft 47,4% over; niet iedereen met zelfde BMI zal niet zelfde vetpercentage
hebben, er is variabiliteit in de Y-richting voor de gegeven X-waarde; dit noem je het residu).

Correlatiematen worden gebruikt om samenhang tussen variabelen te bestuderen. Pearson
correlatie coëfficiënt wordt hiervoor gebruikt.

Pearson’s correlatiecoëfficiënt heeft een aantal eigenschappen:

• Kwantificeert lineair verband
• Geeft zowel richting als sterkte aan
Dichtbij 0; geen verband, dichtbij 1 zeer sterk verband.
• -1 ≤ r ≤ +1
• Dimensie loos (betekent dat niet uitmaakt welke eenheden je x en y variabelen
uitdrukt; bijv. lengte in meters/centimeters, gewicht in kilo’s/grammen, correlatie
blijft hetzelfde).
• Als x en y onafhankelijk zijn, dan is r gelijk aan 0; als r gelijk is aan 0, dan zijn x en y
niet altijd onafhankelijk. Kwadratisch verband kan ook (maak een plaatje om
correlatie coëfficiënt uit te rekenen om te kijken of het verband lineair is).
• Toets op correlatie (ρ=0) gaat uit van normaal verdeelde data.



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