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Samenvatting Statistiek: Theorie
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Samenvatting Statistiek: Theorie
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STATISTIEK - THEORIESamenvatting
Brysse Yme
UGent
,1
,Inhoud
1. Inleiding .............................................................................................................................. 6
1.1. Soorten onderzoeksvormen ........................................................................................ 6
1.2. Soorten variabelen ...................................................................................................... 7
1.3. Soorten statistiek ......................................................................................................... 9
2. Beschrijvende statistiek.................................................................................................... 10
2.1. Grafische weergave van onderzoeksgegevens.......................................................... 11
2.2. Numerieke weergave van onderzoeksgegevens ....................................................... 12
2.2.1. Frequentietabel .................................................................................................. 12
2.2.2. Centrummaten ................................................................................................... 12
2.2.3. Spreidingsmaten................................................................................................. 16
3. Verklarende statistiek ...................................................................................................... 20
3.1. Toetsen van hypothesen ........................................................................................... 20
3.2. Statistisch toetsen ..................................................................................................... 22
3.3. Kansen en kansverdelingen ....................................................................................... 23
3.3.1. Binominale kansverdeling .................................................................................. 23
3.3.2. Normale kansverdeling ...................................................................................... 24
3.4. Toetsen en schatten van steekproefgemiddelden .................................................... 27
3.4.1. Toetsen ............................................................................................................... 27
3.4.2. Tweezijdig vs. eenzijdig toetsen ........................................................................ 29
3.5. Schatten ..................................................................................................................... 30
3.6. Toetsen vs schatten ................................................................................................... 31
3.7. Centrale limietstelling................................................................................................ 31
3.8. T-verdeling of student-verdeling ............................................................................... 32
4. Analyse van continue uitkomstvariabelen ....................................................................... 34
4.1. Het vergelijken van twee metingen bij dezelfde personen....................................... 38
4.1.1. Paired samples t test .......................................................................................... 38
4.1.2. One sample t-test ............................................................................................... 42
4.1.3. Wilcoxon signed rank test .................................................................................. 44
4.1.4. Sign test .............................................................................................................. 46
4.2. Het vergelijken van twee onafhankelijke groepen .................................................... 47
4.2.1. Independent Samples t test ............................................................................... 47
2
, 4.2.2. Mann-Whitney U test ......................................................................................... 51
4.3. Het vergelijken van meer dan twee groepen ............................................................ 53
4.3.1. Analysis of Variance - ANOVA ............................................................................ 53
4.3.2. Kruskal-Wallis-toets............................................................................................ 56
4.4. Analyseren van de relatie tussen twee continue variabele ...................................... 57
4.4.1. Pearson correlatiecoëfficiënt ............................................................................. 57
4.4.2. Spearman correlatiecoëfficiënt .......................................................................... 60
4.5. Analyseren van de relatie tussen continue variabele en andere variabele .............. 61
4.5.1. Lineaire regressieanalyse met continue determinant ....................................... 61
4.5.2. Lineaire regressieanalyse met dichotome determinant .................................... 65
4.5.3. Lineaire regressieanalyse met categoriale determinant.................................... 67
4.5.4. Verklaarde variantie R²....................................................................................... 69
4.5.5. Lineaire regressieanalyse met niet-normaal verdeelde uitkomstvariabele ...... 70
4.6. Meervoudige lineaire regressie ................................................................................. 71
4.6.1. Confounding ....................................................................................................... 72
4.6.2. Effectmodificatie ................................................................................................ 74
5. Analyse van dichotome uitkomstvariabelen .................................................................... 78
5.1. Het vergelijken van twee metingen bij dezelfde personen....................................... 79
5.1.1. McNemar-toets .................................................................................................. 79
5.1.2. Z-toets voor proportie ........................................................................................ 81
5.2. Het vergelijken van twee onafhankelijke groepen .................................................... 83
5.2.1. Schatten van onzekerheid .................................................................................. 84
5.2.2. Chikwadraattoets ............................................................................................... 85
5.3. Het vergelijken van meer dan twee groepen ............................................................ 89
5.3.1. Chikwadraattoets ............................................................................................... 89
5.3.2. De oddsratio ....................................................................................................... 93
5.4. Analyseren van de relatie tussen continue variabele en andere variabele .............. 94
5.4.1. Logistische regressie........................................................................................... 94
5.4.2. Logistische regressieanalyse met een dichotome determinant ........................ 94
5.4.3. Maximum likelihood ........................................................................................... 96
5.4.4. Logistische regressieanalyse met een categoriale determinant ........................ 98
5.4.5. Logistische regressieanalyse met een continue determinant ......................... 103
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