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Samenvatting Statistiek voor de gezondheidswetenschappen: Schakeljaar
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Volledige samenvatting statistiek met voorbeeldoefeningen. Haalde hiermee 17/20
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Statistiek voor de gezondheidswetenschappen: theorieInhoudstafel
H1: INLEIDING ................................................................................................................................................ 6
1.1 INLEIDING ........................................................................................................................................................ 6
1.2 ONDERZOEKSVORMEN........................................................................................................................................ 6
1.3 VARIABELEN ..................................................................................................................................................... 6
1.3.1 Terminologie......................................................................................................................................... 6
1.3.2 Soorten variabelen ............................................................................................................................... 6
1.3.2.1 Categorische/categoriale/kwalitatieve variabelen ....................................................................................... 6
1.3.2.2 Numerieke/kwantitatieve variabelen ........................................................................................................... 6
1.4 SOORTEN STATISTIEK .......................................................................................................................................... 7
1.4.1 Beschrijvende statistiek ....................................................................................................................... 7
1.4.2.Verklarende/inferentiële statistiek ..................................................................................................... 7
H2: BESCHRIJVENDE STATISTIEK ..................................................................................................................... 8
2.1 GRAFISCHE WEERGAVE ....................................................................................................................................... 8
2.1.1 Categorische variabelen ...................................................................................................................... 8
2.1.1.1 Staafdiagram/bar chart ................................................................................................................................... 8
2.1.1.2 Taartdiagram/pie chart ................................................................................................................................... 8
2.1.1.3 Geclusterd staafdiagram/clustered bar chart of gesegmenteerd staafdiagram/segmented bar chart .......... 8
2.1.2 Continue variabelen ............................................................................................................................ 9
2.1.2.1 Histogram ........................................................................................................................................................ 9
2.2 NUMERIEKE WEERGAVE .................................................................................................................................... 10
2.2.1 Categorische variabelen .................................................................................................................... 10
2.2.1.1 Frequentietabel ............................................................................................................................................. 10
2.2.2 Continue variabelen .......................................................................................................................... 10
2.2.2.1 Centrummaten .............................................................................................................................................. 10
Soorten ................................................................................................................................................................ 10
Modus............................................................................................................................................................. 10
Rekenkundig gemiddelde/mean (𝒙).............................................................................................................. 10
Mediaan ......................................................................................................................................................... 10
Geometrisch gemiddelde ............................................................................................................................... 10
Voor- en nadelen van centrummaten .................................................................................................................. 11
2.2.2.2 Spreidingsmaten ........................................................................................................................................... 11
Soorten ................................................................................................................................................................ 11
Variantie (s2) & standaarddeviatie (sd) ......................................................................................................... 11
Range .............................................................................................................................................................. 11
Interkwartiel-range ........................................................................................................................................ 11
Voor- en nadelen van spreidingsmaten ............................................................................................................... 12
2.3 GRAFISCHE ÉN NUMMERIEKE WEERGAVE .............................................................................................................. 12
2.3.1 Continue variabelen .......................................................................................................................... 12
2.2.1.1 Box-and-whisker plot/box-plot ..................................................................................................................... 12
2.4 NORMALE VERDELING VAN CONTINUE VARIABELEN................................................................................................. 12
2.4.1 Kenmerken.......................................................................................................................................... 12
2.4.1.1 Symmetrisch .................................................................................................................................................. 12
2.4.1.2 Klokvorm ....................................................................................................................................................... 13
2.5 NIET-NORMALE VERDELING ............................................................................................................................... 13
2.5.1 Scheef naar rechtse verdeling/skewed to the right/positive skew ..................................................... 13
2.5.2 Scheef naar linkse verdeling/skewed to the left/negative skew......................................................... 13
2.6 SAMENVATTEND OVERZICHT .............................................................................................................................. 14
H3: PRINCIPES VAN DE VERKLARENDE/INFERENTIËLE STATISTIEK................................................................. 15
3.1 INLEIDING ...................................................................................................................................................... 15
3.1.1 Terminologie....................................................................................................................................... 15
Doelpopulatie ............................................................................................................................................................ 15
Onderzoekspopulatie/steekproef ............................................................................................................................. 15
3.1.2 Toetsen van hypothesen ..................................................................................................................... 15
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,Statistiek voor de gezondheidswetenschappen: theorie
3.2 MATE VAN ONZEKERHEID .................................................................................................................................. 15
3.1.1 Mate van onzekerheid kwantificeren ................................................................................................. 15
3.1.1.1 Statistisch toetsen ........................................................................................................................................ 15
Theoretische kansverdelingen ............................................................................................................................ 16
(1) Binomiale verdeling voor dichotome uitkomstvariabelen ......................................................................... 16
(2) Standaardnormale kansverdeling voor continue uitkomstvariabelen = z-verdeling → voor schatten van
gemiddelden ................................................................................................................................................... 16
Toetsingsgrootheid z ................................................................................................................................. 16
Kenmerken standaardnormale kansverdeling .......................................................................................... 16
Overschrijdingskans p................................................................................................................................ 17
Principes van de toetsingstheorie ............................................................................................................. 17
(3) Afgeleide Student’s t-verdeling ................................................................................................................. 17
Éénzijdig toetsen vs. tweezijdig toetsen............................................................................................................. 17
3.1.1.2 Schatten van onzekerheid ............................................................................................................................ 18
3.1.1.3 Toetsen vs. schatten ..................................................................................................................................... 18
3.1.1.4 Voorbeeld ...................................................................................................................................................... 19
3.1.2 Mate van onzekerheid afhankelijk van… ............................................................................................ 19
(1) Grootte steekproef (N)........................................................................................................................................ 19
(2) Spreiding/heterogeniteit van de observaties in de steekproef ......................................................................... 19
(3) Standaardfout van het gemiddelde/standard error of the mean (sem) ........................................................... 19
3.5 CENTRALE LIMIETSTELLING (CLS) ........................................................................................................................ 19
3.5.1 Definitie .............................................................................................................................................. 19
3.5.2 Voorbeeld ........................................................................................................................................... 20
3.6 T-VERDELING VS. Z-VERDELING........................................................................................................................... 20
3.6.1 T-verdeling .......................................................................................................................................... 20
3.6.2 Z-verdeling .......................................................................................................................................... 20
H4: ANALYSE VAN CONTINUE UITKOMSTVARIABELEN .................................................................................. 21
4.1 VERGELIJKEN .................................................................................................................................................. 21
4.1.1 Paired samples t test = gepaarde t-toets............................................................................................ 22
4.1.1.1 Beschrijvende statistiek ............................................................................................................................... 22
4.1.1.2 Toetsen ......................................................................................................................................................... 22
4.1.1.3 Schatten ........................................................................................................................................................ 22
4.1.2 One Sample t test ............................................................................................................................... 24
4.1.2.1 Beschrijvende statistiek ............................................................................................................................... 24
4.1.2.2 Toetsen ......................................................................................................................................................... 24
Optie 1: H0: 𝜇𝛥 = 0............................................................................................................................................... 24
Optie 2: H0: 𝜇 = 𝜇0 ............................................................................................................................................... 24
4.1.2.3 Schatten ........................................................................................................................................................ 25
Optie 1: H0: 𝜇𝛥 = 0............................................................................................................................................... 25
Optie 2: H0: 𝜇 = 𝜇0 ............................................................................................................................................... 25
4.1.3 Independent Samples t test ................................................................................................................ 26
4.1.3.1 Beschrijvende statistiek ............................................................................................................................... 26
4.1.3.2 Toetsen ......................................................................................................................................................... 26
4.1.3.3 Schatten ........................................................................................................................................................ 26
4.1.3.4 Levene’s test ................................................................................................................................................. 27
4.1.4 ANOVA ................................................................................................................................................ 28
4.1.4.1 Beschrijvende statistiek ............................................................................................................................... 28
4.1.4.2 Voorwaarden check ...................................................................................................................................... 28
A.d.h.v. beschrijvende statistiek .......................................................................................................................... 28
A.d.h.v. Levene’s test ........................................................................................................................................... 28
4.1.4.3 ANOVA .......................................................................................................................................................... 28
4.1.4.3 Post-hoc test ................................................................................................................................................. 29
4.1.5 Vergelijken van scheef verdeelde continue variabelen ....................................................................... 30
4.1.5.1 Transformeren .............................................................................................................................................. 30
Voorwaarden check ............................................................................................................................................. 30
Normale verdeling .......................................................................................................................................... 30
Homoscedasticiteit ......................................................................................................................................... 30
Stappenplan ......................................................................................................................................................... 30
1. Natuurlijk logaritme nemen........................................................................................................................ 30
2. Gemiddelde nemen van de getransformeerde variabele ........................................................................... 30
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,Statistiek voor de gezondheidswetenschappen: theorie
3. Nagaan of men nu wel een normale verdeling/spreiding bekomen heeft? ............................................... 30
4. Test uitvoeren op deze getransformeerde variabele ................................................................................. 30
5. Resultaat terug transformeren ................................................................................................................... 31
4.1.5.2 Non-parametrische testen ........................................................................................................................... 31
Mann-Whitney U test .......................................................................................................................................... 31
Wilcoxon signed rank test .................................................................................................................................... 32
Kruskal-Wallis test................................................................................................................................................ 32
4.2 RELATIES ....................................................................................................................................................... 33
4.2.1 Correlatie ............................................................................................................................................ 35
4.2.1.1 Beschrijvende statistiek ............................................................................................................................... 35
4.2.1.2 Pearson correlatie (parametrisch) ............................................................................................................... 35
4.2.1.3 Spearman’s correlatie (niet-parametrisch).................................................................................................. 35
4.2.1.3 Vergelijking beide testen.............................................................................................................................. 35
4.2.2 Lineaire regressie................................................................................................................................ 36
4.2.2.1 Voorbeeld ..................................................................................................................................................... 36
Verklaarde variantie R2 ........................................................................................................................................ 37
Lineaire regressie ≈ variantieanalyse (ANOVA) ................................................................................................... 37
Voorwaarden voor lineaire regressie ................................................................................................................... 37
Lineariteit relatie nagaan ................................................................................................................................ 37
Normailteit residuen nagaan .......................................................................................................................... 38
4.2.2.2 Extra ter illustratie: verschil en overeenkomst tussen lineaire regressieanalyse en correlatiecoeffiënt .. 38
4.2.2.3 Meervoudige lineaire regressie ................................................................................................................... 39
Confounding......................................................................................................................................................... 39
Effectmodificatie/interactie ................................................................................................................................. 39
Indien we besluiten tot effectmodificatie/interactie: .................................................................................... 39
Indien we besluiten tot GEEN effectmodificatie/interactie: .......................................................................... 40
Confounding nagaan ................................................................................................................................. 40
Effectmodificatie nagaan met continue variabele .................................................................................... 40
Voorbeeld: opbouw van associatiemodel tussen BMI en cholesterol ................................................................. 41
Ruwe associatie (altijd eerste stap!) ............................................................................................................... 41
(Uitgebreide) procedure om effectmodificatie met (alle) mogelijke covariaten na te gaan .......................... 41
O.a. interactie met categorische variabele................................................................................................ 41
Één significante interactieterm uitkiezen (diegene met laagste p-waarde) ................................................... 42
Interactievariabele stratificeren ..................................................................................................................... 42
Mogelijke volgende stap: binnen deze subgroepen verdere mogeljke effectmodificaties testen en eventueel
stratificeren .................................................................................................................................................... 42
Volgende stap na testen effectmodificaties: confounding nagaan ................................................................ 43
Meest eenvoudige: alle mogelijke covariaten tegelijkertijd toevoegen aan model .................................. 43
Alternatieve procedure: stapsgewijs, corrigeren voor verschillende inhoudelijke groepen confounders .. 43
Uitgebreide procedure: one by one testen van covariaten en bij 10% verandering in effectmaat:
toevoegen aan model als confounder ....................................................................................................... 44
Alternatieve uitwerking van uitgebreide procedure: eenmalig one by one testen van covariaten en bij
10% verandering in effectmaat tegelijkertijd toevoegen aan het finaal model (meer realistische
uitvoering) ................................................................................................................................................. 45
Voorbeeld: opbouw van predictiemodel ............................................................................................................. 46
Backward procedure ...................................................................................................................................... 46
H5: ANALYSE VAN DICHOTOME UITKOMSTVARIABELEN............................................................................... 48
5.1 DICHOTOME UITKOMSTVARIABELEN .................................................................................................................... 48
5.1.1 Vergelijken .......................................................................................................................................... 51
5.1.1.1 McNemar toets ............................................................................................................................................. 51
5.1.1.2 Z-toets voor proportie ................................................................................................................................... 51
Toetsen ................................................................................................................................................................ 52
Schatten ............................................................................................................................................................... 52
1e manier: 95% BI rond geschatte proportie .................................................................................................. 52
2e manier: 95% BI rond verschil in proportie .................................................................................................. 52
5.1.1.3 Chikwadraattoets (2 groepen) ...................................................................................................................... 53
Toetsen ................................................................................................................................................................ 53
Fisher’s exact en continuïteitscorrectie........................................................................................................... 54
Voorbeeld........................................................................................................................................................ 54
Schatten ............................................................................................................................................................... 55
5.1.1.4 Chikwadraattoets (> 2 groepen).................................................................................................................... 55
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,Statistiek voor de gezondheidswetenschappen: theorie
Linear-by-Linear Association ........................................................................................................................... 56
5.1.2 Relaties ............................................................................................................................................... 56
5.1.2.1 Logistische regressie...................................................................................................................................... 56
5.1.2.1.1 Enkelvoudige logistische regressie........................................................................................................ 56
Dichtome determinant ................................................................................................................................... 56
Maximum likelihood .................................................................................................................................. 57
Likelihoodratio-toets ................................................................................................................................. 57
Categorische determinant (≥ 3 groepen) ..................................................................................................... 58
1e mogelijke codering: niet-drinkers als referentie .................................................................................. 58
2e mogelijke codering: zware drinkers als referentie ............................................................................... 59
Likelihood ratio-toets ........................................................................................................................... 59
Continue determinant .................................................................................................................................... 60
Lineariteit .................................................................................................................................................. 60
5.1.2.1.2 Meervoudige logistische regressie........................................................................................................ 61
Associatiemodellen......................................................................................................................................... 61
Confounding .............................................................................................................................................. 61
Effectmodificatie ....................................................................................................................................... 61
Predictiemodellen .......................................................................................................................................... 62
Backward selectieprocedure...................................................................................................................... 62
Kwaliteit van multiple logistisch regressiemodel ........................................................................................... 66
Classificatietabel........................................................................................................................................ 66
Hosmer-Lemeshow-toets = goodness-of-fit test ........................................................................................ 67
H6: ANALYSE VAN OVERLEVINGSDATA ......................................................................................................... 68
6.1 OVERZICHT VAN VERSCHILLENDE TECHNIEKEN ....................................................................................................... 68
6.1.1 Kaplan-Meier-overlevingscurve + log-ranktoets................................................................................. 70
Vergelijken van overlevingsdata tussen twee groepen ............................................................................................. 70
Vergelijken van overlevingsdata tussen meer dan twee groepen ............................................................................. 70
6.1.2 Cox-regressieanalyse .......................................................................................................................... 71
Dichotome determinant ............................................................................................................................................ 71
Categorische determinant ......................................................................................................................................... 72
Continue determinant ............................................................................................................................................... 73
Confounding en effectmodificatie ............................................................................................................................. 74
Confounding ........................................................................................................................................................ 74
Effectmodificatie ................................................................................................................................................. 74
H8: SAMPLE-SIZE BEREKENINGEN ................................................................................................................. 75
8.1 TYPES ERROR .................................................................................................................................................. 75
8.2 SAMPLE SIZE BEREKENEN ................................................................................................................................... 75
H9: EEN STAP VERDER .................................................................................................................................. 76
9.1 NORMALITEIT VAN CONTINUE VARIABELEN ........................................................................................................... 76
9.1.1 Eenvoudig nagaan .............................................................................................................................. 76
Observeren van histogram ........................................................................................................................................ 76
Vergelijken van gemiddelde en mediaan .................................................................................................................. 76
Vergelijken van gemiddelde en standaarddeviatie ................................................................................................... 76
9.1.2 Meer formele indicatoren ................................................................................................................... 76
Skewness en kurtosis ................................................................................................................................................ 76
Kolmogorov-Smirnov en Shapiro-Wilks toets ........................................................................................................... 77
QQ-plot...................................................................................................................................................................... 77
9.2 VALKUILEN IN STATISTISCHE ANALYSES ................................................................................................................. 78
9.2.1 Multi-collineariteit / collineariteit ...................................................................................................... 78
Voorbeelden van collineariteit bij lineaire regressie ........................................................................................... 78
Voorbeeld van collineariteit bij logistische regressie .......................................................................................... 78
9.2.1.1 Ontplofte modellen ....................................................................................................................................... 79
Redenen ............................................................................................................................................................... 79
9.3 MEER GEVORDERDE ANALYSES ........................................................................................................................... 79
9.3.1 Categorische uitkomstvariabelen ≥ 3 groepen .................................................................................. 79
Voorbeeld 1 ............................................................................................................................................................... 79
Voorbeeld 2 ............................................................................................................................................................... 80
Voorbeeld 3 ............................................................................................................................................................... 80
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,Statistiek voor de gezondheidswetenschappen: theorie
9.3.2 Two-way ANOVA ................................................................................................................................ 80
9.3.3 Repeated measures analyse ............................................................................................................... 80
9.3.4 Multilevel analyse............................................................................................................................... 81
H10: BETROUWBAARHEID VAN MEETINSTRUMENTEN ................................................................................. 82
10.1 MATE VAN OVEREENKOMST BIJ CATEGORISCHE VARIABELEN .................................................................................. 82
10.1.1 Kappa ............................................................................................................................................... 82
Voorbeeld .................................................................................................................................................................. 82
10.2 MATE VAN OVEREENKOMST BIJ CONTINUE VARIABELEN......................................................................................... 83
10.2.1 Pearson correlatiecoëfficiënt ............................................................................................................ 83
Voorbeeld .................................................................................................................................................................. 83
Visuele weergave ...................................................................................................................................................... 83
Scatterplot ........................................................................................................................................................... 83
Band-Altman-plot................................................................................................................................................. 83
Nadeel ....................................................................................................................................................................... 84
10.2.2 Intra-class correlatiecoëfficiënt (ICC)................................................................................................ 84
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,Statistiek voor de gezondheidswetenschappen: theorie
H1: Inleiding
1.1 Inleiding
Toegepaste statistiek: analyseren van data (= waarnemingen op variabelen) om een
wetenschappelijke vraag te beantwoorden
Steekproef (= onderzoekspopulatie) van de doelpopulatie (daar willen we uitspraken over
doen)
1.2 Onderzoeksvormen
1.3 Variabelen
1.3.1 Terminologie
Uitkomstvariabele (= outcome of afhankelijke/dependent variabele) → willen we
voorspellen, verklaren
Onafhankelijke variabele (= verklarende/independent variabele of determinant of
voorspeller of predictor of covariate)
1.3.2 Soorten variabelen
1.3.2.1 Categorische/categoriale/kwalitatieve variabelen
• Nominaal: niet geordend (bv. provincies, bloedgroep)
• Ordinaal: geordend (bv. ziekte-ernst, opleidingsniveau)
• Dichotoom: 2 categorieën (bv. geslacht) → dummy codering (1 vs. 0)
1.3.2.2 Numerieke/kwantitatieve variabelen
• Discreet: gehele getallen/aantallen (bv. aantal tandarts bezoeken per jaar)
• Continu: in theorie oneindig aantal mogelijke waarden (bv. lengte, gewicht)
o Interval-schaal
o Ratio-schaal
6
,Statistiek voor de gezondheidswetenschappen: theorie
1.4 Soorten statistiek
1.4.1 Beschrijvende statistiek
Overzichtelijk samenvatten van data: grafische/numerieke weergave
1.4.2.Verklarende/inferentiële statistiek
Schatten van effecten/relaties
→ Betrouwbaarheid van de onderzoeksresultaten
→ Hypothese testen
7
,Statistiek voor de gezondheidswetenschappen: theorie
H2: Beschrijvende statistiek
2.1 Grafische weergave
2.1.1 Categorische variabelen
2.1.1.1 Staafdiagram/bar chart
2.1.1.2 Taartdiagram/pie chart
2.1.1.3 Geclusterd staafdiagram/clustered bar chart of gesegmenteerd
staafdiagram/segmented bar chart
→ Bij 2 categorische variabelen
8
,Statistiek voor de gezondheidswetenschappen: theorie
2.1.2 Continue variabelen
2.1.2.1 Histogram
2.1.2.2 Tak-en-blad diagram/stem-and-leaf plot
Stengel/stem bevat tientallen
Blad/leaf bevat eenheden
2 proefpersonen van 19 jaar
2 proefpersonen van 21 jaar, 3 proefpersonen van 22 jaar,
1 proefpersoon van 23 jaar en 3 proefpersonen van 24 jaar
2.1.2.3 Puntenwolk/scatterplot
→ Bij 2 continue variabelen
9
, Statistiek voor de gezondheidswetenschappen: theorie
2.2 Numerieke weergave
2.2.1 Categorische variabelen
2.2.1.1 Frequentietabel
→ Al dan niet met missende waarden
2.2.2 Continue variabelen
2.2.2.1 Centrummaten
Soorten
Modus
Meest voorkomende waarde in de dataset
→ ook voor categorische variabelen
→ weinig informatief
Rekenkundig gemiddelde/mean (𝒙 $)
→ alleen een goede indicator bij normaal verdeelde variabelen
Mediaan
Alle observaties ordenen → middelste waarde = P50 (percentielpunten)
Geometrisch gemiddelde
Transformatie van niet-normaal verdeelde (rechts scheve) variabelen
1. Natuurlijk logaritme nemen van elke waarde (= nieuwe variabele)
2. Gemiddelde nemen van de getransformeerde variabele
3. Terug transformeren: inverse van natuurlijk logaritme (om opnieuw in
oorspronkelijke eenheid uit te drukken)
10
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