Statistiek voor bedrijfswetenschappen
QQ-plot komt altijd voor op het examen
Inhoudsopgave
1 hoofdstuk 1: getting started ........................................................................................................... 5
1.1 R Framework for Statistical Computing .................................................................................. 5
2 hoofdstuk 2: introduction to probability ........................................................................................ 6
2.1 Defenition of probability ........................................................................................................ 6
2.2 Jeffreys’ axiom system............................................................................................................ 7
2.2.1 Axiom 1: comparability – vergelijkbaarheid ................................................................... 7
2.2.2 axiom 2: transitivity - transitiviteit .................................................................................. 7
2.2.3 axiom 3: deducibility – deduceerbaarheid...................................................................... 7
2.3 Stelling van Bayes ................................................................................................................... 8
2.3.1 theorie ............................................................................................................................ 8
2.3.2 Voorbeeld ..................................................................................................................... 10
2.3.3 specificiteit en de sesitiviteit ........................................................................................ 11
2.4 Multinomial Naive Bayes Classifier ....................................................................................... 12
2.4.1 voorbeeld ..................................................................................................................... 12
2.4.2 interactie effect ............................................................................................................ 14
2.4.3 Zero Probabilities .......................................................................................................... 15
2.4.4 Types of Naive Bayes Classifiers ................................................................................... 15
2.4.5 Wet van de grote getallen ............................................................................................ 16
2.4.6 Voorbeeld om het uit te leggen .................................................................................... 16
3 hoofdstuk 3: waarschijnlijkheidsverdelingen ............................................................................... 19
3.1 beschrijvende statistieken .................................................................................................... 19
3.2 discrete waarschijnlijkheidsverdeling ................................................................................... 20
3.2.1 bernoulli verdeling ........................................................................................................ 20
3.2.2 binomiaal verdeling ...................................................................................................... 21
3.2.3 multinominiaal verdeling .............................................................................................. 24
3.3 continue verdelingen ............................................................................................................ 25
3.3.1 uniforme verdeling ....................................................................................................... 25
3.3.2 de normale verdeling = gausse verdeling ..................................................................... 27
3.3.3 willekeurige verdeling ................................................................................................... 32
RStudio ................................................................................................................................................. 35
3.3.4 Gaussian naive bayes classifier ..................................................................................... 40
3.3.5 Chi verdeling ................................................................................................................. 44
1
, 3.3.6 Chi kwadraat verdeling (1 parameter) .......................................................................... 44
3.3.7 Chi kwadraat verdeling (2 parameters) ........................................................................ 47
3.3.8 student t-verdeling ....................................................................................................... 47
3.3.9 fisher f-verdeling........................................................................................................... 49
3.4 conclusies ............................................................................................................................. 49
4 hoofdstuk 4: Beschrijvende statistiek en exploratieve gegevensanalyse ..................................... 51
4.1 types of data ......................................................................................................................... 51
4.1.1 kwalitatieve data .......................................................................................................... 51
4.1.2 kwantitatieve data ........................................................................................................ 51
4.2 kwalitatieve data .................................................................................................................. 51
4.2.1 frequency plot (bar plot)............................................................................................... 51
4.2.2 frequentietabel ............................................................................................................. 52
4.2.3 contingentie tabel......................................................................................................... 53
4.2.4 Binonomial classification metrics ................................................................................. 53
4.3 kwantitatieve data ................................................................................................................ 55
4.3.1 stem-and-leaf plot ........................................................................................................ 55
4.3.2 histogram...................................................................................................................... 56
4.3.3 Quantiles/ kwantielen .................................................................................................. 60
4.3.4 central tendency ........................................................................................................... 64
4.3.5 Variabiliteit ................................................................................................................... 70
4.3.6 Skewness en kurtosis .................................................................................................... 74
4.3.7 concentratiemaatstaven ............................................................................................... 78
4.3.8 notched boxplot ........................................................................................................... 78
4.3.9 Scatterplot .................................................................................................................... 80
4.3.10 pearson correlatie ........................................................................................................ 81
4.3.11 rank correlatie .............................................................................................................. 85
4.3.12 partiële pearson correlatie ........................................................................................... 86
4.3.13 simple linear regression ................................................................................................ 90
4.3.14 momenten .................................................................................................................... 90
4.3.15 Kwantiel-kwantielplot (QQ-plot)................................................................................... 91
4.3.15 Kwantiel-kwantielplot (QQ-plot)................................................................................... 92
4.3.16 Probability Plot Correlation Coefficient Plot (PPCC- plot) ............................................. 98
4.3.17 kernel density estimation ............................................................................................. 99
4.3.18 bivariate Kernel Density Plot ........................................................................................ 99
4.3.19 Bootstrap Plot (central tendency)............................................................................... 100
4.3.20 survey scores rank order comparison ......................................................................... 102
2
, 4.3.21 cronbach alpha ........................................................................................................... 105
4.4 kwantitatieve gegevens met tijdsdimensie/ tijdreeksen .................................................... 106
4.4.1 Equi-distante tijdreeksen ............................................................................................ 106
4.4.2 time series plot (run sequence plot ............................................................................ 107
4.4.3 mean plot ................................................................................................................... 107
4.4.4 blocked bootstrap plot (central tendency) ................................................................. 110
4.4.5 standaard deviation-mean plot .................................................................................. 111
4.4.6 Variatie reduction matrix ............................................................................................ 112
4.4.7 (partiële) autocorrelatie functie ................................................................................. 113
4.4.8 Periodogram en cumulatief periodogram .................................................................. 114
5 hoofdstuk 5: Hypothese testen .................................................................................................. 120
5.1 the central limit theorem ................................................................................................... 121
5.2 Statistische toets van het populatiegemiddelde met bekende variantie (veronderstelling)
121
5.2.1 voorbeeld: Statistische hypothese: Testen van het gemiddelde met bekende variantie -
Voorbeeld 1: Kritische waarde (Regio) ....................................................................................... 124
5.2.2 Voorbeeld: Statistische hypothese: Testen van het gemiddelde met bekende variantie -
Voorbeeld 2: P-waarde (waarschijnlijkheid ................................................................................ 124
5.3 Hypothesetests voor onderzoeksdoeleinden ..................................................................... 125
5.3.1 één steekproef t-Test/ one sample t-test ................................................................... 125
5.3.2 Skewness & kurtosis test ............................................................................................ 129
5.3.3 Gepaarde twee-steekproef t-Test............................................................................... 131
5.3.4 WILCOXON SIGNED-rank test ..................................................................................... 133
5.3.5 unpaird two sample t-test .......................................................................................... 134
5.3.6 unpaired two sample welch test ................................................................................. 137
5.3.7 mann-whitney u test (wilcoxon rank-sum test) .......................................................... 138
5.3.8 bayesian two sample test ........................................................................................... 139
5.3.9 Chi-squared tests for count data ................................................................................ 139
5.3.10 one way analysis of variance (1-way anova) ............................................................... 142
5.3.11 two way analysis of variance (2-way anova) .............................................................. 144
6 hoofdstuk 6: regressie modellen ................................................................................................ 148
6.1 Eenvoudig lineair regressiemodel (SLRM) .......................................................................... 148
6.2 Meervoudig lineair regressiemodel (MLRM) ...................................................................... 150
6.3 Hypothesetests met lineaire regressiemodellen (vanuit praktisch perspectief) ................. 151
7 Inleiding tot de analyse van tijdreeksen ..................................................................................... 156
7.1 Case: markt van gezondheids- en persoonlijke verzorgingsproducten (HPC) ..................... 156
7.2 decompositie van een tijdreeks .......................................................................................... 156
3
, 7.2.1 Klassieke decompositie van tijdreeksen door geleidende gemiddelden..................... 156
7.2.2 Seizoensgebonden decompositie van tijdreeksen door loess..................................... 158
7.2.3 Decompositie door structurele tijdreeksmodellen ..................................................... 158
7.3 Ad hoc voorspelling van tijdreeksen ................................................................................... 159
7.3.1 Regressieanalyse van tijdreeksen ............................................................................... 160
7.3.2 Afvlakmodellen/ Smoothing Models .......................................................................... 163
8 hoofdstuk 8: Univariate box-jenkins analyse .............................................................................. 166
8.1 data .................................................................................................................................... 167
8.2 theoretische concepten ...................................................................................................... 168
8.2.1 stationair proces ......................................................................................................... 168
8.2.2 white noice ................................................................................................................. 168
8.3 stationariteit ....................................................................................................................... 168
8.3.1 stationariteit in het gemiddelde ................................................................................. 168
8.3.2 Stationariteit in de variantie ....................................................................................... 169
4
QQ-plot komt altijd voor op het examen
Inhoudsopgave
1 hoofdstuk 1: getting started ........................................................................................................... 5
1.1 R Framework for Statistical Computing .................................................................................. 5
2 hoofdstuk 2: introduction to probability ........................................................................................ 6
2.1 Defenition of probability ........................................................................................................ 6
2.2 Jeffreys’ axiom system............................................................................................................ 7
2.2.1 Axiom 1: comparability – vergelijkbaarheid ................................................................... 7
2.2.2 axiom 2: transitivity - transitiviteit .................................................................................. 7
2.2.3 axiom 3: deducibility – deduceerbaarheid...................................................................... 7
2.3 Stelling van Bayes ................................................................................................................... 8
2.3.1 theorie ............................................................................................................................ 8
2.3.2 Voorbeeld ..................................................................................................................... 10
2.3.3 specificiteit en de sesitiviteit ........................................................................................ 11
2.4 Multinomial Naive Bayes Classifier ....................................................................................... 12
2.4.1 voorbeeld ..................................................................................................................... 12
2.4.2 interactie effect ............................................................................................................ 14
2.4.3 Zero Probabilities .......................................................................................................... 15
2.4.4 Types of Naive Bayes Classifiers ................................................................................... 15
2.4.5 Wet van de grote getallen ............................................................................................ 16
2.4.6 Voorbeeld om het uit te leggen .................................................................................... 16
3 hoofdstuk 3: waarschijnlijkheidsverdelingen ............................................................................... 19
3.1 beschrijvende statistieken .................................................................................................... 19
3.2 discrete waarschijnlijkheidsverdeling ................................................................................... 20
3.2.1 bernoulli verdeling ........................................................................................................ 20
3.2.2 binomiaal verdeling ...................................................................................................... 21
3.2.3 multinominiaal verdeling .............................................................................................. 24
3.3 continue verdelingen ............................................................................................................ 25
3.3.1 uniforme verdeling ....................................................................................................... 25
3.3.2 de normale verdeling = gausse verdeling ..................................................................... 27
3.3.3 willekeurige verdeling ................................................................................................... 32
RStudio ................................................................................................................................................. 35
3.3.4 Gaussian naive bayes classifier ..................................................................................... 40
3.3.5 Chi verdeling ................................................................................................................. 44
1
, 3.3.6 Chi kwadraat verdeling (1 parameter) .......................................................................... 44
3.3.7 Chi kwadraat verdeling (2 parameters) ........................................................................ 47
3.3.8 student t-verdeling ....................................................................................................... 47
3.3.9 fisher f-verdeling........................................................................................................... 49
3.4 conclusies ............................................................................................................................. 49
4 hoofdstuk 4: Beschrijvende statistiek en exploratieve gegevensanalyse ..................................... 51
4.1 types of data ......................................................................................................................... 51
4.1.1 kwalitatieve data .......................................................................................................... 51
4.1.2 kwantitatieve data ........................................................................................................ 51
4.2 kwalitatieve data .................................................................................................................. 51
4.2.1 frequency plot (bar plot)............................................................................................... 51
4.2.2 frequentietabel ............................................................................................................. 52
4.2.3 contingentie tabel......................................................................................................... 53
4.2.4 Binonomial classification metrics ................................................................................. 53
4.3 kwantitatieve data ................................................................................................................ 55
4.3.1 stem-and-leaf plot ........................................................................................................ 55
4.3.2 histogram...................................................................................................................... 56
4.3.3 Quantiles/ kwantielen .................................................................................................. 60
4.3.4 central tendency ........................................................................................................... 64
4.3.5 Variabiliteit ................................................................................................................... 70
4.3.6 Skewness en kurtosis .................................................................................................... 74
4.3.7 concentratiemaatstaven ............................................................................................... 78
4.3.8 notched boxplot ........................................................................................................... 78
4.3.9 Scatterplot .................................................................................................................... 80
4.3.10 pearson correlatie ........................................................................................................ 81
4.3.11 rank correlatie .............................................................................................................. 85
4.3.12 partiële pearson correlatie ........................................................................................... 86
4.3.13 simple linear regression ................................................................................................ 90
4.3.14 momenten .................................................................................................................... 90
4.3.15 Kwantiel-kwantielplot (QQ-plot)................................................................................... 91
4.3.15 Kwantiel-kwantielplot (QQ-plot)................................................................................... 92
4.3.16 Probability Plot Correlation Coefficient Plot (PPCC- plot) ............................................. 98
4.3.17 kernel density estimation ............................................................................................. 99
4.3.18 bivariate Kernel Density Plot ........................................................................................ 99
4.3.19 Bootstrap Plot (central tendency)............................................................................... 100
4.3.20 survey scores rank order comparison ......................................................................... 102
2
, 4.3.21 cronbach alpha ........................................................................................................... 105
4.4 kwantitatieve gegevens met tijdsdimensie/ tijdreeksen .................................................... 106
4.4.1 Equi-distante tijdreeksen ............................................................................................ 106
4.4.2 time series plot (run sequence plot ............................................................................ 107
4.4.3 mean plot ................................................................................................................... 107
4.4.4 blocked bootstrap plot (central tendency) ................................................................. 110
4.4.5 standaard deviation-mean plot .................................................................................. 111
4.4.6 Variatie reduction matrix ............................................................................................ 112
4.4.7 (partiële) autocorrelatie functie ................................................................................. 113
4.4.8 Periodogram en cumulatief periodogram .................................................................. 114
5 hoofdstuk 5: Hypothese testen .................................................................................................. 120
5.1 the central limit theorem ................................................................................................... 121
5.2 Statistische toets van het populatiegemiddelde met bekende variantie (veronderstelling)
121
5.2.1 voorbeeld: Statistische hypothese: Testen van het gemiddelde met bekende variantie -
Voorbeeld 1: Kritische waarde (Regio) ....................................................................................... 124
5.2.2 Voorbeeld: Statistische hypothese: Testen van het gemiddelde met bekende variantie -
Voorbeeld 2: P-waarde (waarschijnlijkheid ................................................................................ 124
5.3 Hypothesetests voor onderzoeksdoeleinden ..................................................................... 125
5.3.1 één steekproef t-Test/ one sample t-test ................................................................... 125
5.3.2 Skewness & kurtosis test ............................................................................................ 129
5.3.3 Gepaarde twee-steekproef t-Test............................................................................... 131
5.3.4 WILCOXON SIGNED-rank test ..................................................................................... 133
5.3.5 unpaird two sample t-test .......................................................................................... 134
5.3.6 unpaired two sample welch test ................................................................................. 137
5.3.7 mann-whitney u test (wilcoxon rank-sum test) .......................................................... 138
5.3.8 bayesian two sample test ........................................................................................... 139
5.3.9 Chi-squared tests for count data ................................................................................ 139
5.3.10 one way analysis of variance (1-way anova) ............................................................... 142
5.3.11 two way analysis of variance (2-way anova) .............................................................. 144
6 hoofdstuk 6: regressie modellen ................................................................................................ 148
6.1 Eenvoudig lineair regressiemodel (SLRM) .......................................................................... 148
6.2 Meervoudig lineair regressiemodel (MLRM) ...................................................................... 150
6.3 Hypothesetests met lineaire regressiemodellen (vanuit praktisch perspectief) ................. 151
7 Inleiding tot de analyse van tijdreeksen ..................................................................................... 156
7.1 Case: markt van gezondheids- en persoonlijke verzorgingsproducten (HPC) ..................... 156
7.2 decompositie van een tijdreeks .......................................................................................... 156
3
, 7.2.1 Klassieke decompositie van tijdreeksen door geleidende gemiddelden..................... 156
7.2.2 Seizoensgebonden decompositie van tijdreeksen door loess..................................... 158
7.2.3 Decompositie door structurele tijdreeksmodellen ..................................................... 158
7.3 Ad hoc voorspelling van tijdreeksen ................................................................................... 159
7.3.1 Regressieanalyse van tijdreeksen ............................................................................... 160
7.3.2 Afvlakmodellen/ Smoothing Models .......................................................................... 163
8 hoofdstuk 8: Univariate box-jenkins analyse .............................................................................. 166
8.1 data .................................................................................................................................... 167
8.2 theoretische concepten ...................................................................................................... 168
8.2.1 stationair proces ......................................................................................................... 168
8.2.2 white noice ................................................................................................................. 168
8.3 stationariteit ....................................................................................................................... 168
8.3.1 stationariteit in het gemiddelde ................................................................................. 168
8.3.2 Stationariteit in de variantie ....................................................................................... 169
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