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Analyse 1_Volledige samenvatting van hoorcolleges, PowerPoints en Grasple
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12 hoorcolleges volledig aangevuld met informatie van Grasple en PowerPoints.
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2022-2023Inhoudsopgave
1 Hoorcollege 1 – Meten en frequen1everdeling ....................................................................................... 6
1.1 Meetniveaus .......................................................................................................................................... 6
1.1.1 Categoriale variabele/kwalita2eve variabele .................................................................................... 6
1.1.1.1 Nominaal .................................................................................................................................. 6
1.1.1.2 Ordinaal .................................................................................................................................... 6
1.1.2 Kwan2ta2eve variabele ..................................................................................................................... 6
1.1.2.1 Interval ..................................................................................................................................... 6
1.1.2.2 Ra2o: ........................................................................................................................................ 7
1.1.3 Discrete en con2nu variabele ............................................................................................................ 7
1.1.3.1 Discreet..................................................................................................................................... 7
1.1.3.2 Con2nu ..................................................................................................................................... 7
1.2 Frequen2everdelingen ........................................................................................................................... 8
1.2.1 Absolute frequen2e (fi) ..................................................................................................................... 8
1.2.2 Rela2eve frequen2everdeling ........................................................................................................... 8
1.2.3 Cumula2eve frequen2e..................................................................................................................... 8
1.2.3.1 Cumula2eve absolute frequen2e (cfi)/somfrequen2e ............................................................. 8
1.2.3.2 Cumula2eve rela1eve frequen2e............................................................................................. 8
1.2.3.3 Percen2elen zijn op twee manieren te gebruiken .................................................................... 8
1.2.3.4 Valid percentage ....................................................................................................................... 9
1.2.3.5 Cumula2eve percentage ........................................................................................................... 9
2 Hoorcollege 2 – Centrum- en spreidingsmaten ....................................................................................... 9
2.1 Centrummaten....................................................................................................................................... 9
2.1.1 Modus ............................................................................................................................................... 9
2.1.1.1 Nadelen .................................................................................................................................. 10
2.1.2 Mediaan .......................................................................................................................................... 10
2.1.2.1 Voordelen ............................................................................................................................... 10
2.1.2.2 Nadelen .................................................................................................................................. 10
2.1.3 Gemiddelde (M à van Mean) ........................................................................................................ 10
2.1.3.1 Voordelen ............................................................................................................................... 10
2.1.3.2 Nadelen .................................................................................................................................. 11
2.1.3.3 Popula2egemiddelde (µ) ........................................................................................................ 11
2.1.3.4 Gewogen gemiddelde............................................................................................................. 11
2.1.3.5 Omgekeerd ............................................................................................................................. 11
2.1.4 Wanneer welke centrummaat ......................................................................................................... 11
2.1.5 ScheeYeid ....................................................................................................................................... 11
2.1.5.1 Soorten scheeYeid ................................................................................................................. 12
2.1.5.2 Wat als er sprake is van scheeYeid ........................................................................................ 12
2.2 Spreidingsmaten .................................................................................................................................. 12
2.2.1 Range = bereik = varia2ebreedte = spreidingsbreedte ................................................................... 12
2.2.2 Kwar2elen ....................................................................................................................................... 13
2.2.2.1 Even of oneven ....................................................................................................................... 13
2.2.3 Interkwar2elafstand ........................................................................................................................ 14
2.2.4 Varian2e en standaarddevia2e (SD)/standaardafwijking ................................................................ 14
2.2.4.1 Formule standaarddevia2e in de popula2e (𝜎) ...................................................................... 14
2.2.4.2 Formule voor de varian2e in de popula2e (𝜎2) ..................................................................... 14
2.2.4.3 Formule voor de standaarddevia2e (s) in de steekproef ........................................................ 14
2.2.4.4 Formule voor de varian2e (s2) in de steekproef ..................................................................... 14
2.2.4.5 Standaarddevia2e in vier stappen .......................................................................................... 15
2.2.4.6 Steekproefcorrec2e ................................................................................................................ 16
,2022-2023
2.2.4.7 (Zuivere) scha^er.................................................................................................................... 17
3 Hoorcollege 3 – Grafische weergave en scoretransforma1es................................................................. 17
3.1 (Score)transforma2es .......................................................................................................................... 17
3.1.1 Lineaire transforma2es ................................................................................................................... 18
3.1.2 Percen2elscores .............................................................................................................................. 18
3.1.3 Z-scores/standaardscore: ................................................................................................................ 18
3.1.3.1 Formule Z-score voor een steekproefscore ............................................................................ 18
3.1.3.2 Formule Z-score voor een popula2escore .............................................................................. 18
3.1.3.3 Eigenschappen van Z-score .................................................................................................... 18
3.1.3.4 Oorspronkelijke score herleiden vanuit een Z-score .............................................................. 18
3.1.3.5 Voordelen Z-score ................................................................................................................... 18
3.1.3.6 “Normale” verdeling ............................................................................................................... 19
3.1.3.7 Hoe Z-scores interpreteren als scores normaal verdeeld? ..................................................... 19
3.2 Datavisualisa2es .................................................................................................................................. 20
3.2.1 Staafdiagram ................................................................................................................................... 20
3.2.1.1 Geclusterde staafdiagram ....................................................................................................... 20
3.2.1.2 Gestapelde staafdiagram (stacked bar chart) ......................................................................... 20
3.2.2 Taartdiagram/cirkeldiagram ............................................................................................................ 20
3.2.3 Histogram: ....................................................................................................................................... 21
3.2.3.1 Klassen .................................................................................................................................... 21
3.2.4 Lijngrafiek/frequen2epolygoon....................................................................................................... 22
3.2.5 Boxplot: ........................................................................................................................................... 22
3.2.5.1 Boxplot versus histogram ....................................................................................................... 22
3.3 Outliers en extremes ............................................................................................................................ 23
4 Hoorcollege 4 – Correla1e .................................................................................................................... 23
4.1 Spreidingsdiagram en samenhang ...................................................................................................... 23
4.1.1 Soorten rela2es ............................................................................................................................... 24
4.1.1.1 Lineaire rela2e/samenhang .................................................................................................... 24
4.2 Kruisproductensom en covarian2e ...................................................................................................... 25
4.2.1 Pearson correla2ecoëfficiënt........................................................................................................... 25
4.2.1.1 Kruisproduct ........................................................................................................................... 25
4.2.1.2 Kruisproductensom ................................................................................................................ 26
4.2.2 Covarian2e ...................................................................................................................................... 26
4.3 Pearson correla2ecoëfficiënt ............................................................................................................... 28
4.3.1.1 = Correla2e ............................................................................................................................. 28
4.3.2 Interpreta2e .................................................................................................................................... 29
4.3.3 Assump2es/voorwaarden voor Pearson's r .................................................................................... 30
4.3.4 Causaliteit........................................................................................................................................ 30
4.4 Spearman’s rho/Spearmans rangcorrela2e ......................................................................................... 30
4.4.1 monotoniciteit................................................................................................................................. 31
4.4.2 Spearman’s rho berekenen ............................................................................................................. 31
4.4.3 Spearman's rho versus Pearson's r .................................................................................................. 32
5 Hoorcollege 5 – Enkelvoudige regressieanalyse (ERA) ........................................................................... 32
5.1 Voorwaarde ......................................................................................................................................... 32
5.2 Regressielijn ......................................................................................................................................... 33
5.2.1 Regressievergelijking ....................................................................................................................... 33
5.2.1.1 Intercept (b0) .......................................................................................................................... 34
5.2.1.2 Berekenen regressiecoëfficiënten .......................................................................................... 34
5.3 Varia2e in scores.................................................................................................................................. 35
,2022-2023
5.3.1 𝑆𝑆𝑟𝑒𝑠𝑖𝑑𝑢 ......................................................................................................................................... 35
5.3.2 𝑆𝑆𝑟𝑒𝑔𝑟𝑒𝑠𝑠𝑖𝑒 ................................................................................................................................... 36
5.3.3 𝑆𝑆𝑡𝑜𝑡𝑎𝑎𝑙 ......................................................................................................................................... 36
5.3.4 𝑅2 .................................................................................................................................................... 36
5.3.4.1 Interpreta2e 𝑅2 ...................................................................................................................... 37
5.3.5 Dus: ................................................................................................................................................. 37
6 Hoorcollege 6 – Meervoudige regressieanalyse (MRA) ......................................................................... 37
6.1 Formule MRA/ Berekenen .................................................................................................................... 38
6.2 Visualiseren ......................................................................................................................................... 39
6.3 Verklaarde en onverklaarde varian2e MRA à aanvullend op ERA ..................................................... 40
6.4 Beta’s ................................................................................................................................................... 40
6.5 Modera2e ............................................................................................................................................ 41
6.5.1 Formule modera2e.......................................................................................................................... 42
6.6 Media2e .............................................................................................................................................. 42
7 Hoorcollege 7 – Categorische variabele ................................................................................................ 43
7.1 Kruistabellen ........................................................................................................................................ 43
7.2 Percenteren.......................................................................................................................................... 44
7.3 Samenhang kwan2ficeren ................................................................................................................... 44
7.3.1 Wel of geen samenhang? ................................................................................................................ 44
7.3.2 Samenhangsmaten .......................................................................................................................... 45
7.3.2.1 Verwachte frequen2es berekenen ......................................................................................... 45
7.3.2.2 Chi-kwadraat (𝑋2) .................................................................................................................. 46
7.3.2.3 Cramer’s V .............................................................................................................................. 47
7.3.2.4 Phi (𝜑)..................................................................................................................................... 47
8 Hoorcollege 8 – Kansen en kansverdeling ............................................................................................. 48
8.1 Basisbegrippen .................................................................................................................................... 48
8.2 Kenmerken van kansen ........................................................................................................................ 49
8.2.1 Interpreta2e kansen ........................................................................................................................ 50
8.2.2 OnaYankelijk en aYankelijkheid .................................................................................................... 50
8.2.3 Uitsluitende gebeurtenissen ........................................................................................................... 50
8.2.4 Trekkingen met of zonder terugleggen ........................................................................................... 50
8.3 Rekenen met kansen ............................................................................................................................ 50
8.3.1 Somregel ......................................................................................................................................... 50
8.3.1.1 Voorwaardelijke kans = B gegeven A ...................................................................................... 51
8.3.2 Productregel .................................................................................................................................... 51
8.3.3 Sta2s2sche (on)aYankelijkheid ...................................................................................................... 52
8.4 Kansverdelingen .................................................................................................................................. 52
8.4.1 Begrippen ........................................................................................................................................ 52
8.4.2 Con2nue variabele .......................................................................................................................... 53
8.4.3 Discrete variabele ............................................................................................................................ 53
9 Hoorcollege 9 – Kansen in een normale verdeling................................................................................. 54
9.1 Normaalverdeling ................................................................................................................................ 54
9.1.1 Normale verdeling als kansverdeling .............................................................................................. 55
9.2 Standaardnormale verdeling ............................................................................................................... 55
9.2.1 Standaardnormale verdeling als kansverdeling............................................................................... 56
9.2.2 Empirische regel .............................................................................................................................. 56
, 2022-2023
9.3 Gebruik z-tabel (Field Appendix A.1) ................................................................................................... 56
9.3.1 Kans bepalen m.b.v. z-scores ........................................................................................................... 57
9.4 Bepalen van kansen ............................................................................................................................. 58
9.4.1 Z-score/ruwe score bepalen m.b.v. kans ......................................................................................... 58
10 Hoorcollege 10 – Steekproevenverdeling voor het gemiddelde ........................................................ 58
10.1 Van steekproef naar popula2e ............................................................................................................ 58
10.1.1 Select en aselect .......................................................................................................................... 58
10.2 Scha^en en toetsen ............................................................................................................................. 59
10.2.1 Steekproefvarian2e/ Steekproefvariabiliteit (sampling error) (Field 2.7) ................................... 59
10.2.2 Steekproevenverdeling ............................................................................................................... 59
10.3 Standaardfout...................................................................................................................................... 60
10.3.1 Centrale limietstelling ................................................................................................................. 60
10.3.2 Centrum van de steekproevenverdeling ..................................................................................... 60
10.4 Steekproevenverdeling voor een gemiddelde ...................................................................................... 61
10.4.1 Voorspellingsinterval voor een gemiddelde................................................................................ 62
10.5 Kri2eke Z-waarden ............................................................................................................................... 62
10.5.1 Veel voorkomende kri2eke waarden van z en foutenkans 𝛼 ...................................................... 62
10.5.2 Kri2eke waarden 𝑋 ..................................................................................................................... 63
10.6 Voorspellingsintervallen voor steekproefgemiddelden ........................................................................ 63
11 Hoorcollege 11 – Betrouwbaarheidsinterval en Z-toets voor 1 gemiddelde....................................... 64
11.1 Scha^en ............................................................................................................................................... 64
11.2 Betrouwbaarheidsinterval voor popula2egemiddelde µ. .................................................................... 64
11.2.1 Pas op voor onjuist formuleren! ................................................................................................. 65
11.2.2 Betrouwbaarheidsinterval – voorspellingsinterval ..................................................................... 65
11.2.3 Opmerkingen .............................................................................................................................. 65
11.3 Het principe van toetsen en de hypothesen ......................................................................................... 65
11.4 Z-toets voor één gemiddelde, sta2s2sche toetsing.............................................................................. 66
11.4.1 Alpha 𝛼 à foutenkans ................................................................................................................ 66
11.4.2 Beslissingen met de kri2eke Z-waarde à toetsingsgrootheid .................................................... 66
11.4.3 Beslissingen met overschrijdingskans p-waarde ......................................................................... 66
11.4.4 Mogelijke fouten ......................................................................................................................... 67
11.4.5 Assump2es .................................................................................................................................. 67
11.4.6 Stappenplan ................................................................................................................................ 67
11.4.7 Kansverdeling: de standaardnormale verdeling.......................................................................... 68
11.4.8 Beslissingen over H0 à Verwerpen of niet? ............................................................................... 68
11.4.9 Conclusie ..................................................................................................................................... 68
11.4.9.1 Wat noteer je: .................................................................................................................... 69
11.5 Effectgroo^e à Cohen’s D ................................................................................................................... 69
11.5.1 Interpreta2e effectgroo^e/ Normen voor effectgroo^e Cohen’s d: ........................................... 69
12 Hoorcollege 12 – Eenzijdig toetsen, twee soorten fouten en onderscheidingsvermogen ................... 70
12.1 Eenzijdig toetsen .................................................................................................................................. 70
12.1.1 Stappenplan ................................................................................................................................ 71
12.1.1.1 Voorbeeld ........................................................................................................................... 71
12.1.2 Keuze van het significan2eniveau ............................................................................................... 72
12.2 Twee soorten fouten ............................................................................................................................ 72
12.2.1 Onderscheidingsvermogen ......................................................................................................... 73
12.2.2 I-fout/II-fout ................................................................................................................................ 73
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