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Samenvatting Bedrijfsstatistiek Brecht Cardoen Handelswetenschappen
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Bedrijfsstatistiek:Table of Contents
PART 1: DESCRIPTIVE STATISTICS: ....................................................................................................................1
1. CONCEPT OF VARIABLE ......................................................................................................................................... 1
2. ABOUT POPULATION AND SAMPLE .......................................................................................................................... 2
2.1 Sample strategieën: ................................................................................................................................ 2
2.2 Wat met errors? ...................................................................................................................................... 3
2.3 Steekproefgrootte bepaling: ................................................................................................................... 3
3. BESCHRIJVENDE STATISTIEK: SAMENVATTENDE METINGEN........................................................................................... 4
3.1 Metingen van centrale locatie: ............................................................................................................... 4
3.2 Spreidingsmaten ..................................................................................................................................... 4
3.3 Maatstaven van associaties .................................................................................................................... 5
4. BESCHRIJVENDE STATISTIEK: GRAFIEKEN .................................................................................................................. 5
5. ANALYSE DATA DELHAIZE ...................................................................................................................................... 6
6. SAMENVATTING .................................................................................................................................................. 6
PART 2: PROBABILITY & PROBABILITY DISTRIBUTIONS ....................................................................................7
1. INLEIDING VAN PROBABILITY (KANS) ........................................................................................................................ 7
1.1 Terminology ............................................................................................................................................ 7
1.2 Wat is probability? .................................................................................................................................. 7
1.3 Probability rules = kansregels .................................................................................................................. 8
2. REGELS VAN PROBABILITEIT ................................................................................................................................... 9
2.1 Complement rule ..................................................................................................................................... 9
2.2 Addition rule ............................................................................................................................................ 9
2.3 Multiplication rule ................................................................................................................................... 9
2.4 Total probability rule ............................................................................................................................. 11
2.5 Probability rules: Oefening .................................................................................................................... 12
3. COUNTING RULES = TELREGELS ............................................................................................................................ 13
3.1 Counting rule 1: hoeveel mogelijkheden ............................................................................................... 13
3.2 Counting rule 2: verschillende uitkomsten per keer .............................................................................. 13
3.3 Counting rule 3: manieren van ordenen ................................................................................................ 13
3.4 Counting rule 4: combinaties ................................................................................................................ 14
3.5 Counting rule 5: permutaties................................................................................................................. 14
3.6 Counting rules: Oefening ....................................................................................................................... 14
4. APPLICATION OF PROBABILITY CALCULATION DECISION TREE ...................................................................................... 16
4.1 What is an uncertain outcome? ............................................................................................................ 16
4.2 Decision tree: what? .............................................................................................................................. 16
5. PROBABILITY DISTRIBUTIONS = KANSVERDELINGEN ................................................................................................... 21
5.1 Discrete probability distributions .......................................................................................................... 23
5.2 Oefeningen op discrete kans ................................................................................................................. 28
5.3 Continuous probability distributions ..................................................................................................... 30
5.4 Oefeningen on continuous probability distributions ............................................................................. 36
PART 3: SAMPLING & SAMPLING DISTRIBUTION (DE STEEKPROEF VERDELING).............................................37
1. CENTRALE LIMIET STELLING VOOR MEAN “THE AVERAGE PERSPECTIVE”....................................................................... 37
1.1 CLT Mean “the average view” ............................................................................................................... 38
1.2 Voorbeeld: CLT Mean “The average view” ............................................................................................ 38
2. CENTRAL LIMIT THEOREM FOR MEAN “THE SUM OF VARIABLES PERSPECTIVE” .............................................................. 39
2.1 Voorbeeld: CLT Mean “The sum of variables view” ............................................................................... 39
3. CENTRAL LIMIT THEOREM FOR MEAN EXERCISE WHEEL OF FORTUNE.......................................................................... 40
3.1 Oefening Sampling Distribution Mean .................................................................................................. 40
4. CENTRAL LIMIT THEOREM FOR PROPORTION .......................................................................................................... 41
4.1 What is a proportion ............................................................................................................................. 41
, 4.2 Central Limit Theorem: proportion ........................................................................................................ 41
4.3 Oefening CLT Proportion ....................................................................................................................... 42
5. FINITE POPULATION CORRECTION FACTOR .............................................................................................................. 42
6. SAMPLE SIZE DETERMINATION = STEEKPROEFGROOTTE KEUZE .................................................................................... 43
6.1 Sample size determenation for mean ................................................................................................... 44
6.2 Sample size determenation for proportion ........................................................................................... 44
7. OEFENING OP STEEKPROEF VERDELINGEN ............................................................................................................... 45
7.1 Oefening 1 ............................................................................................................................................. 45
7.2 Oefening 2 ............................................................................................................................................. 46
PART 4: HYPOTHESE TESTING ........................................................................................................................47
1. HYPOTHESIS TESTING OF THE MEAN ABOUT THE MECHANISM..................................................................................... 47
Wat is hypothese testing ............................................................................................................................. 47
1.1 CONFIDENCE: ........................................................................................................................................ 49
1.2 Drie methodes voor hypothese testen................................................................................................... 50
1.3 Sampling error ....................................................................................................................................... 53
1.4 Oefening op hypothese testing PERFECT VOORBEELD EXAMENVRAAG .............................................. 55
2. HYPOTHESIS TESTING OF THE MEAN FROM ‘Z’ TO ‘T’ ................................................................................................. 56
2.1 Normal distribution vs t-distribution ..................................................................................................... 56
2.2 Wat is hypothese testing ....................................................................................................................... 57
2.3 Oefening op hypothese testing ............................................................................................................. 58
3. HYPOTHESIS TESTING OF THE PROPORTION ............................................................................................................. 60
3.1 Wat is een proportie? ............................................................................................................................ 60
3.2 Getrouwheidsinterval van de populatie proportie ................................................................................ 60
3.3 Hypothesis test of population proportion: Z-stat .................................................................................. 60
4. OEFENINGEN .................................................................................................................................................... 61
5. SAMENVATTING ONE SAMPLE: FROM KEY QUESTIONS TO KEY INSIGHTS ........................................................................ 63
6. HYPOTHESIS TESTING OF THE MEAN: TWO SAMPLE VIEW – DEPENDENT SAMPLES........................................................... 64
6.1 Population variance (𝜎2) known ........................................................................................................... 65
6.2 Population variance (𝜎2) unknown ....................................................................................................... 65
6.3 Illustration of paired testing: Population variance unknown ................................................................ 66
7. HYPOTHESIS TESTING OF THE MEAN: TWO SAMPLE VIEW – INDEPENDENT SAMPLES........................................................ 67
7.1 Population variances known → z-stat................................................................................................... 67
7.2 Population variances unknown – equal variances → t-stat .................................................................. 68
7.3 Population variances unknown – unequal variances → t-stat .............................................................. 69
7.4 Important questions! ............................................................................................................................. 70
7.5 Illustration: Population variances unknown – unequal variances ......................................................... 70
7.6 Third important question ...................................................................................................................... 71
8. HYPOTHESIS TESTING OF THE VARIANCE: ONE- AND TWO-SAMPLE VIEW ....................................................................... 72
8.1 One-sample view → Chi-square distribution ......................................................................................... 72
8.2 Two-sample view: ratio of variances → F-distribution ......................................................................... 74
9. SAMENVATTING EN VOLGENDE STAPPEN ................................................................................................................ 76
9.1 Structuring hypothesis testing ............................................................................................................... 76
Two sample view voor properties zelf studeren in het boek! ................................................................... 76
9.2 Assumptions underlying population ...................................................................................................... 76
10. ANALYSIS OF VARIANCE: ONE-WAY ANOVA ........................................................................................................ 77
10.1 Introduction to ANOVA........................................................................................................................ 77
10.2 Between-treatments → De teller van de breuk................................................................................... 79
10.3 Within-treatments ............................................................................................................................... 80
10.4 ANOVA tabel ....................................................................................................................................... 81
10.5 Laten we beslissen over de test ........................................................................................................... 81
10.6 ANOVA met MS EXCEL......................................................................................................................... 82
11. DOES MY VARIABLE FOLLOW A NORMAL DISTRIBUTION? JARQUE-BERA TEST ............................................................... 83
11.1 Introduction to Jarques-Bera test ........................................................................................................ 83
11.2 Over de test ......................................................................................................................................... 83
11.3 Voorbeeld ............................................................................................................................................ 84
12. DOES MY VARIABLE FOLLOW A NORMAL DISTRIBUTION? GOODNESS-OF-FIT TEST ......................................................... 85
, 12.1 Introduction goodness-of-fit test ........................................................................................................ 85
12.2 Over de goodness-of-fit test ................................................................................................................ 86
12.3 Voorbeeld ............................................................................................................................................ 86
13. DOES MY VARIABLE FOLLOW ANY PARTICULAR DISTRIBUTION? GOODNESS-OF-FIT TEST ................................................. 87
14. SAMENVATTING .............................................................................................................................................. 88
14.1 Test for independent samples ............................................................................................................. 88
14.2 Assumptions underlying population .................................................................................................... 89
PART 5: REGRESSION ANALYSIS .....................................................................................................................90
1. INTRODUCTION TO REGRESSION ANALYSIS: WHAT’S THE NEED? .................................................................................. 90
1.1 What’s the need? .................................................................................................................................. 90
1.2 Scatterplot ............................................................................................................................................. 90
1.3 Covariance ............................................................................................................................................. 91
1.4 Correlation............................................................................................................................................. 91
1.5 What’s the need? .................................................................................................................................. 92
1.6 We need regression analysis ................................................................................................................. 92
2. INTRO TO SIMPLE LINEAR REGRESSION: ONE EXPLANATORY VARIABLE ......................................................................... 93
2.1 Introduction to simple linear regression................................................................................................ 93
2.2 Concept of residuals .............................................................................................................................. 93
2.3 Least squares estimation ....................................................................................................................... 94
2.4 Using excel to get the regression equation ........................................................................................... 94
3. INTRO TO MULTIPLE LINEAR REGRESSION: MORE THAN ONE EXPLANATORY VARIABLE .................................................... 96
3.1 Introduction to multiple linear regression ............................................................................................. 96
3.2 Voorbeeld: Price of house ...................................................................................................................... 96
4. GOODNESS-OF-FIT MEASURES ............................................................................................................................. 97
4.1 Standard error of estimate: 𝑆𝑒 .............................................................................................................. 97
4.2 Coefficient of determination: 𝑅2 ........................................................................................................... 99
5. SIGNIFICANTIE TESTEN IN REGRESSIE: INDIVIDUAL AND JOINT SIGNIFICANCE ................................................................. 101
5.1 Key questions to solve: individual significance ................................................................................... 101
5.2 Key questions to solve: joint significance ............................................................................................ 103
6. OEFENINGEN .................................................................................................................................................. 104
6.1 Oefening Delhaize ............................................................................................................................... 104
7. SAMENVATTING .............................................................................................................................................. 105
8. WHAT ABOUT THE UNDERLYING ASSUMPTIONS? RESIDUAL ANALYSIS......................................................................... 106
8.1 Assumption 1: Expected value of error terms ..................................................................................... 106
8.2 Assumption 2: Variance of error terms (variantie van de residuen is gelijk (constant) ....................... 107
8.3 Assumption 3: Distribution of the error terms .................................................................................... 108
8.4 Assumption 4: independency of error terms ....................................................................................... 110
8.5 Assumption 5: Linear combinations of variables ................................................................................. 111
9. DEALING WITH NON-LINEAR PATTERNS ................................................................................................................ 112
9.1 Quadratic regression (1ste voorbeeld niet lineaire patroon) .............................................................. 112
9.2 Regression with logarithms ................................................................................................................. 113
10. INCORPORATING CATEGORIES: DUMMY VARIABLES .............................................................................................. 115
10.1 Veronderstel variabele heeft 2 verschillende uitkomsten ................................................................. 115
10.2 Veronderstel variabele heeft meer dan 2 verschillende uitkomsten ................................................. 116
11. FORECASTING WITH REGRESSION ANALYSIS: INTRODUCTION ................................................................................... 117
11.1 Components of time-driven data ...................................................................................................... 117
11.2 Classification of forecasting .............................................................................................................. 117
11.3 Time series methods .......................................................................................................................... 117
11.4 Causal models ................................................................................................................................... 118
11.5 Oefeningen ........................................................................................................................................ 119
SAMENVATTING LEERSTOF .......................................................................................................................... 120
, Part 1: Descriptive statistics:
1. Concept of variable
Twee Types variabelen:
• Categorische variabelen
o Vbn.:
▪ Kleur, Auto merken
• Numerische:
o Discrete:
→ Alle mogelijke uitkomsten kan ik oplijsten
→ Eindig aantal uitkomsten
→ !Kunnen ook komma getallen zijn!
▪ Vbn.:
• Getallen op de lotto trekking
• Aantal kinderen dat een persoon heeft
• Punten op 20 dat je geeft op een examen (kan dus ook
komma)
o Continue:
→ Kunnen niet alle mogelijke uitkomsten gaan oplijsten
▪ Vbn.:
• Priemgetallen
• Het loon dat ja zal verdienen
• Inkomsten van een bedrijf
• Hoogte van een persoon uitgedrukt in cm
Schalen van metingen:
• NOMINAL
o Distinct categories without ‘magnitude’
o Geen volgorde
o Vbn.: Haarkleur
• ORDINAL
Telkens interessanter
o Ordered categories
o Wel volgorde maar geen betekenisvolle verschillen
o Vbn.: Hoe men zich voelt
• INTERVAL
o Meaningful distances without absolute zero point
o Vaak gebruiken bij numerische waarden
o Nulpunt is niet absoluut
o Vbn.:
▪ Hoe goed voel je u (score van 0 tot 10).
▪ Temperatuur (graden celcius, calvin, fahrenheit)
• RATIO
o Meaningful distances with absolute zero point
o Duidelijke nulwaarde
o Vbn.: Resultaat van een bedrijf
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