We zeggen dat het gemiddelde van de steekproef een zuivere schatter is van het gemiddelde van de populatie. Verklaar \'zuivere\' en \'schatter\'.
Answer: Zuiver = er zullen geen systematische afwijkingen zijn wanneer men kijkt naar het gemiddelde van alle mogelijke steekproeven om de populatiegrootheid te schatten.
Schatter = we schatten met behulp van het steekproevengemiddelde het populatiegemiddelde.
2.
Hoe weten we wanneer de vorm normaal verdeeld is? Verklaar het Centrale Limiet Theorama:
Answer: Hoe groter we de steekproeven trekken, hoe meer de steekproevenverdeling van het gemiddelde de normale verdeling benadert.
3.
Wanneer is een steekproef normaal verdeeld?
Answer: Als de populatie waaruit de steekproef normaal verdeeld is of N > 30.
4.
Mu en Sigma bepalen de normaalverdeling. Verklaar deze begrippen:
Answer: Mu = gemiddelde van de normale verdeling. Bepaalt de plaats van het midden van de verdeling.
Sigma = standaardafwijking (spreiding) van de verdeling. Bepaalt de breedte van de verdeling.
5.
Waarvoor gebruiken we Z-scores?
Answer: Gebruiken we om de waarden uit onze originele normale verdeling te transformeren/standaardiseren zodat ze bruikbaar is in de standaardnormale verdeling.
6.
Wat is een puntschatting?
Answer: Schatten van de populatieparameter via 1 getal. (bv gemiddelden uit verschillende steekproeven).
7.
Wat is een intervalschatting?
Answer: Rond het steekproevengemiddelde (X) een interval afbakenen met de kans dat het populatiegemiddelde (mu) daartussen ligt.
8.
Wat is een betrouwbaarheidsinterval?
Answer: Dit is een intervalschatting waar een interval in ligt. We zijn van dit interval redelijk zeker dat het populatiegemiddelde erin ligt.
* Grootte van interval bepalen we zelf.
* Steekproef moet aselect getrokken zijn.
* Afweging tussen zekerheid en informativiteit.
9.
Wat is de type 1 fout (alfa fout)?
Answer: De nulhypothese ten onrecht verwerpen.
10.
Wat is de type 2 fout ( beta fout)?
Answer: De nulhypothese ten onrecht niet verwerpen.
Content preview
Statistiek 2
Samenvatting
1
,Inhoud
Hoofdstuk 1 ..........................................................................................................................................................................6
De empirische cyclus ...................................................................................................................................................6
Waarom statistiek? .......................................................................................................................................................6
Problemen in de inductieve statistiek ..................................................................................................................6
Statistische significantie .............................................................................................................................................7
Kansberekening .............................................................................................................................................................7
Toetsen ..............................................................................................................................................................................7
Misbruik van statistiek................................................................................................................................................8
Validiteit ............................................................................................................................................................................8
Interne validiteit .......................................................................................................................................................8
Externe validiteit ......................................................................................................................................................9
Kwalitatief onderzoek ......................................................................................................................................................9
1. Van beleidsvraag naar heldere onderzoeksvraag .......................................................................................9
1.1 Beleidsvraag en probleemdefinitie............................................................................................................9
1.2 Onderzoeksdoel .............................................................................................................................................. 10
2. Wat is dan kwalitatief onderzoek? ................................................................................................................. 11
2.1 Doel ...................................................................................................................................................................... 11
2.2 Basisprincipes ................................................................................................................................................. 11
2.3 Gevolg - verandering in probleemstelling kan................................................................................... 11
In het kort … ............................................................................................................................................................ 12
3. Data-analyse? Eerst data verzamelen. .......................................................................................................... 12
4. Met welke kwalitatieve onderzoeksmethode? .......................................................................................... 12
4.1 Observeren ....................................................................................................................................................... 12
4.2 Kwalitatieve survey....................................................................................................................................... 13
Data analyse met manuele inhoudsanalyse ............................................................................................... 14
4.3 Laboratoriumtests ......................................................................................................................................... 17
5. Hoe de betrouwbaarheid van kwalitatief onderzoek en de data-analyse ervan verhogen? . 17
H2 - Kansverdeling en kansberekening ................................................................................................................. 17
Kansenverdeling ......................................................................................................................................................... 17
1) interval estimatie ............................................................................................................................................. 18
2) Hypothesetoetsing .......................................................................................................................................... 18
Behulpzame begrippen ....................................................................................................................................... 18
Gemiddelde/variantie/standaarddeviatie v/d kansverdeling................................................................ 19
2
, Kansverdeling v/h steekproefgemiddelde ...................................................................................................... 19
Standaardfout v/h gemiddelde berekenen................................................................................................. 21
Vorm v/d steekproevenverdeling v/h gemiddelde ................................................................................ 21
De populatie en steekproeven hangen samen… ....................................................................................... 21
Kansen berekenen in de steekproevenverdeling.......................................................................................... 22
Intermezzo – de (standaard)normale verdeling ........................................................................................... 22
Z-scores ..................................................................................................................................................................... 23
Hoofdstuk 3 - Betrouwbaarheidsintervallen en hypothesetoetsing ......................................................... 24
Betrouwbaarheidsintervallen ............................................................................................................................... 24
Wat is een betrouwbaarheidsinterval? ........................................................................................................ 24
De 68, 95 en 99,7 regel ........................................................................................................................................ 25
Hypothesetoetsing ..................................................................................................................................................... 26
Grote of kleine kans ? ........................................................................................................................................... 27
Samenvattend ......................................................................................................................................................... 27
Eenzijdig en tweezijdig toetsen ....................................................................................................................... 27
Kritieke waarden ................................................................................................................................................... 28
Onzekerheden bij hypothesetoetsing ........................................................................................................... 29
Effectgroottes .......................................................................................................................................................... 29
Parametrisch of non-parametrisch toetsen................................................................................................ 30
Hoofdstuk 4: toetsen voor één populatie .............................................................................................................. 31
T-toets voor het gemiddelde ................................................................................................................................. 31
Z-toets / T-toets ..................................................................................................................................................... 32
De t-verdeling… ...................................................................................................................................................... 32
Vrijheidsgraden (df)............................................................................................................................................. 32
Beslissingsregels .................................................................................................................................................... 33
Kritieke waarden ................................................................................................................................................... 33
Effectgroottes .......................................................................................................................................................... 34
Rapporteren............................................................................................................................................................. 34
Chikwadraattoets voor frequenties .................................................................................................................... 34
De situatie ................................................................................................................................................................. 34
De voorwaarden..................................................................................................................................................... 35
Hypothesen formuleren...................................................................................................................................... 35
Het principe ............................................................................................................................................................. 35
Beslissingsregels .................................................................................................................................................... 35
Effectgroottes (phi) .............................................................................................................................................. 36
Rapporteren............................................................................................................................................................. 36
Hoofdstuk 5: toetsen voor twee populaties ......................................................................................................... 37
3
, T-toets voor twee onafhankelijke steekproeven........................................................................................... 37
Twee populaties vergelijken, verschillende mogelijkheden… ............................................................ 37
De situatie ................................................................................................................................................................. 38
Voorwaarden........................................................................................................................................................... 38
Hypothesen formuleren...................................................................................................................................... 38
Principe bij de T-toets ......................................................................................................................................... 39
Standaardfout van de steekproevenverdeling berekenen ................................................................... 39
(on)gelijke varianties nagaan .......................................................................................................................... 39
Principe bij de F-toets.......................................................................................................................................... 40
Beslissingsregels F-toets .................................................................................................................................... 40
Beslissingsregels t-toets ..................................................................................................................................... 40
Effectgroottes .......................................................................................................................................................... 41
Rapporteren............................................................................................................................................................. 41
Wilcoxon rank-sum toets ........................................................................................................................................ 41
Situatie en voorwaarden .................................................................................................................................... 41
Hypothesen formuleren...................................................................................................................................... 41
Principe...................................................................................................................................................................... 42
Beslissingsregels .................................................................................................................................................... 42
Effectgroottes .......................................................................................................................................................... 43
Hoofdstuk 6: toetsen voor twee populaties – afhankelijke steekproeven .............................................. 44
Opfrissing ...................................................................................................................................................................... 44
T-toets voor twee afhankelijke steekproeven ................................................................................................ 45
De situatie ................................................................................................................................................................. 45
Voorwaarden........................................................................................................................................................... 45
Hypothesen formuleren...................................................................................................................................... 46
Het principe bij de t-toets .................................................................................................................................. 46
Beslissingsregels t-toets….................................................................................................................................. 46
Effectgroottes .......................................................................................................................................................... 47
Rapportage ............................................................................................................................................................... 47
Oefening dia 18 + 19 ........................................................................................................................................... 47
Hoofdstuk 7: toetsen voor meer dan twee populaties – variantieanalyse .............................................. 48
Eenwegsvariantieanalyse (= one-way-anova).............................................................................................. 48
Situatie ....................................................................................................................................................................... 48
Significantie ............................................................................................................................................................. 48
Voorwaarden........................................................................................................................................................... 48
Hypothesen formuleren...................................................................................................................................... 49
Het principe bij de eenwegsvariantieanalyse ............................................................................................ 49
4
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