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Statistiek 1: semester 2 - samenvatting
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Samenvatting Statistiek sem2.2022-2023
,SAMENVATTING STATISTIEK SEM2. 2022-2023......................................................................................................................... 1
LES 1 SEMESTER 2: HOOFDSTUK 8 (DEEL1): BASISBEGRIPPEN KANSBEREKENING......................................................................5
HET BELANG VAN KANSBEREKENING...................................................................................................................................................... 5
VAN BESCHRIJVENDE NAAR INFERENTIËLE STATISTIEK.................................................................................................................................5
OPZET CURSUS.................................................................................................................................................................................. 5
BEGRIPPEN KANSBEREKENING............................................................................................................................................................... 5
INTERMEZZO: SYMBOLEN UIT DE VERZAMELINGENLEER..............................................................................................................................5
BEGRIPPEN KANSBEREKENING............................................................................................................................................................... 6
KANSDEFINITIE................................................................................................................................................................................... 6
REKENREGELS KANSBEREKENING............................................................................................................................................................7
1. COMPLEMENTREGEL.......................................................................................................................................................................8
2. SOMREGEL.................................................................................................................................................................................... 8
3. PRODUCTREGEL..............................................................................................................................................................................8
4. VOORWAARDELIJKE KANS.................................................................................................................................................................9
OVERZICHT REGENREGELS.................................................................................................................................................................... 9
LES 2 SEMESTER 2: HOOFDSTUK 8 (DEEL2): BASISBEGRIPPEN KANSBEREKENING + HOOFDSTUK 9 (DEEL 1): STOCHASTEN,
VERWACHTINGSWAARDE EN VARIANTIE............................................................................................................................... 10
4. REGEL VOORWAARDELIJKE KANS......................................................................................................................................................10
5. REGEL TOTALE KANS......................................................................................................................................................................10
6. REGEL VAN BAYES........................................................................................................................................................................ 10
OVERZICHT NIEUWE REKENREGEL........................................................................................................................................................ 10
HOOFDSTUK 9: STOCHASTEN, VERWACHTINGSWAARDE EN VARIANTIE........................................................................................................11
HERHALING: DE FREQUENTIEVERDELING................................................................................................................................................11
STOCHAST....................................................................................................................................................................................... 11
VAN FREQUENTIEVERDELING NAAR KANSVERDELING................................................................................................................................11
KANSVERDELING...............................................................................................................................................................................11
VERWACHTE WAARDE VAN EEN STOCHAST............................................................................................................................................ 13
VARIANTIE VAN EEN STOCHAST........................................................................................................................................................... 13
LINEAIR GETRANSFORMEERDE STOCHASTEN...........................................................................................................................................13
GRAFISCHE VOORSTELLING VAN EEN DISCRETE STOCHAST.........................................................................................................................13
LES 3 SEMESTER 2: HOOFDSTUK 9 (DEEL 2): STOCHASTEN, VERWACHTINGSWAARDE EN VARIANTIE (AFWEZIG).....................14
SIMULTANE KANSVERDELINGEN...........................................................................................................................................................14
OVERZICHT REGELS........................................................................................................................................................................... 14
ANDERE REGELS (NIET KENNEN).......................................................................................................................................................... 14
DE CONDITIONELE/ VOORWAARDELIJKE VERDELING.................................................................................................................................14
LES 4 SEMESTER 2: HOOFDSTUK 10 (DEEL 1): BINOMIALE VERDELING (AFWEZIG)...................................................................15
DE VERJAARDAGENPARADOX.............................................................................................................................................................. 15
VORMEN VAN STEEKPROEFTREKKING (TV-SCHEMA)................................................................................................................................15
OPFRISSING: BINOMIALE COËFFICIËNTEN (LES 9)....................................................................................................................................15
DE BINOMIALE VERDELING................................................................................................................................................................. 15
TABEL BINOMIALE VERDELING............................................................................................................................................................. 16
3 SOORTEN TABELLEN:...................................................................................................................................................................... 16
WAT ALS DE KANS NIET IN DE TABEL STAAT?..........................................................................................................................................16
LES 5 SEMESTER 2: HOOFDSTUK 10 (DEEL 2): BINOMIALE VERDELING.....................................................................................17
VERWACHTINGSWAARDE................................................................................................................................................................... 17
VARIANTIE...................................................................................................................................................................................... 17
INTERMEZZO: TV-SCHEMA................................................................................................................................................................. 17
HYPERGEOMETRISCHE VERDELING........................................................................................................................................................17
VERWACHTINGSWAARDE EN VARIANTIE................................................................................................................................................17
ANDERE DISCRETE VERDELINGEN (NIET TE KENNEN).................................................................................................................................18
LES 6 SEMESTER 2: HOOFDSTUK 11 (DEEL 1): DE NORMALE VERDELING..................................................................................19
WAT IS EEN ‘VERDELING’?................................................................................................................................................................. 19
DE NORMALE VERDELING: INTRODUCTIE............................................................................................................................................... 19
EIGENSCHAPPEN V/D NORMALE VERDELING...........................................................................................................................................19
DE NORMALE DICHTHEIDSFUNCTIE.......................................................................................................................................................20
KANSEN BEREKENEN......................................................................................................................................................................... 20
STANDAARDISEREN EN Z-SCORES......................................................................................................................................................... 20
, GEMIDDELDE EN STANDAARDAFWIJKING VAN GESTANDAARDISEERDE WAARDEN..........................................................................................20
STAPPENPLAN VOOR BEREKENINGEN:................................................................................................................................................... 21
TWEE SOORTEN VRAGEN OVER NORMALE VERDELING..............................................................................................................................21
LES 7 SEMESTER 2: HOOFDSTUK 11 (DEEL 2): DE NORMALE VERDELING..................................................................................22
GOED OM TE ONTHOUDEN….............................................................................................................................................................. 22
STELLING VAN CHEBYCHEV................................................................................................................................................................. 22
DE NORMALE VERDELING................................................................................................................................................................... 22
NORMALITEITSTOETSING....................................................................................................................................................................22
CHI²-TEST....................................................................................................................................................................................... 24
QQ-PLOT....................................................................................................................................................................................... 24
CONTINUÏTEITSCORRECTIE.................................................................................................................................................................. 25
LES 8 SEMESTER 2: HOOFDSTUK 12: NORMALE BENADERING V/D BINOMIALE VERDELING + HOOFDSTUK 13 (DEEL1):
SCHATTEN............................................................................................................................................................................. 26
CENTRALE LIMIETSTELLING (CLS).........................................................................................................................................................26
ILLUSTRATIE CLQ: GALTON BORD....................................................................................................................................................... 26
VEREISTE N..................................................................................................................................................................................... 26
EFFECT VAN N EN P...........................................................................................................................................................................26
NORMALE BENADERING V/D BINOMIALE VERDELING................................................................................................................................26
HOOFDSTUK 13: HET SCHATTEN VAN STEEKPROEFPROPORTIES..................................................................................................................27
STEEKPROEFPROPORATIES.................................................................................................................................................................. 27
SAMENGEVAT.................................................................................................................................................................................. 31
STEEKPROEFVERDELING VAN...............................................................................................................................................................31
LES 9 SEMESTER 2: HOOFDSTUK 13 (DEEL2): SCHATTEN.......................................................................................................... 32
OMKERING VAN DE VRAAGSTELLING.....................................................................................................................................................32
2 SOORTEN SCHATTINGEN.................................................................................................................................................................. 32
PUNTSCHATTING VOOR P................................................................................................................................................................... 32
EEN ZUIVERE PUNTSCHATTING?...........................................................................................................................................................32
EEN EFFICIËNTE PUNTSCHATTING?....................................................................................................................................................... 32
UITWEIDING OVER DE STANDAARDFOUT............................................................................................................................................... 33
PUNTSCHATTING VOOR P................................................................................................................................................................... 33
INTERVALSCHATTING VOOR P..............................................................................................................................................................33
95% B.I. – ALGEMEEN… (B.I. = BETROUWBAARDHEIDSINTERVAL)............................................................................................................33
INTERVALSCHATTING VOOR P..............................................................................................................................................................34
95% B.I. VOOR P.............................................................................................................................................................................34
ANDERE BETROUWBAARHEIDSINTERVALLEN...........................................................................................................................................35
“C. 100% B.I.” VOOR P................................................................................................................................................................... 35
STEEKPROEFGROOTTE BEPALEN IN FUNCTIE VAN FOUTMARGE...................................................................................................................35
LES 10 SEMESTER 2: HOOFDSTUK 13 (DEEL3): SCHATTEN + HOOFDSTUK 14 (DEEL1): HYPOTHESETOETSING............................37
EINDIGHEIDSCORRECTIE..................................................................................................................................................................... 37
STEEKPROEFVERDELING VAN ?............................................................................................................................................................ 37
HERHALING: STEEKPROEFVERDELING VAN............................................................................................................................................. 37
SCENARIO (A).................................................................................................................................................................................. 38
UITLEG BIJ SCENARIO (A)................................................................................................................................................................... 38
SCENARIO (B).................................................................................................................................................................................. 39
CENTRALE LIMIETSTELLING (CLS) (LYAPUNOV).......................................................................................................................................40
STEEKPROEFVERDELING VAN STEEKPROEFGEMIDDELDEN...........................................................................................................................41
CENTRALE LIMIETSTELLING: WAAROM NUTTIG?......................................................................................................................................41
SCENARIO (A) EN (B) SAMENGEVAT..................................................................................................................................................... 41
PUNTSCHATTING VOOR Μ.................................................................................................................................................................. 41
C.100% B.I. VOOR Μ...................................................................................................................................................................... 41
INTERVALSCHATTING VOOR Μ.............................................................................................................................................................42
SAMENVATTING: SCHATTEN VAN Μ ALS Σ BEKEND IS...............................................................................................................................42
STEEKPROEFVERDELING VAN ?............................................................................................................................................................ 42
PROBLEEM: WE KENNEN Σ VAAK NIET!..................................................................................................................................................42
SCENARIO (C)................................................................................................................................................................................. 42
T-VERDELING................................................................................................................................................................................... 43
BETROUWBAARHEIDSINTERVAL........................................................................................................................................................... 43
SCENARIO (D).................................................................................................................................................................................. 43
SCENARIO (C) EN (D) SAMENGEVAT..................................................................................................................................................... 43
, STAPPENPLAN BETROUWBAARHEIDSINTERVAL GEMIDDELDE......................................................................................................................44
INLEIDING H14: HYPOTHESETOETSING.................................................................................................................................................44
VOORBEELD.................................................................................................................................................................................... 44
HYPOTHESETOETSING........................................................................................................................................................................ 45
STAP 1: H0 EN HA BEPALEN................................................................................................................................................................ 45
STAP 2: TOETSINGSGROOTHEID EN VERDELING.......................................................................................................................................45
STAP 3: VERWERPINGSGEBIED............................................................................................................................................................ 45
STAP 4: SITUEREN TOETSINGSGROOTHEID – KRITIEKE WAARDE..................................................................................................................45
STAP 5: CONCLUSIE.......................................................................................................................................................................... 47
LES 11 SEMESTER 2: HOOFDSTUK 14 (DEEL1): HYPOTHESETOETSING......................................................................................48
TOETSEN........................................................................................................................................................................................ 48
HYPOTHESETOETSEN PROPORTIES........................................................................................................................................................ 48
EEN HYPOTHESE/SIGNIFICANTIETOETS...................................................................................................................................................49
WAT ALS … DE CUMULATIEVE STERREN................................................................................................................................................49
VOORBEELD.................................................................................................................................................................................... 49
HYPOTHESETOETSEN VOOR GEMIDDELDEN............................................................................................................................................ 50
EEN HYPOTHESE/ SIGNIFICANTIETOETS..................................................................................................................................................51
LES 12 SEMESTER 2: HOOFDSTUK 14 (DEEL2): HYPOTHESETOETSING......................................................................................52
HYPOTHESETOETSEN GEMIDDELDE.......................................................................................................................................................52
WAT ALS Σ ONBEKEND IS?..................................................................................................................................................................52
TYPE I-FOUT EN TYPE II-FOUT.............................................................................................................................................................52
TYPE I-FOUT.................................................................................................................................................................................... 52
TYPE II-FOUT................................................................................................................................................................................... 52
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