Samenvatting
Statistics 1
Periode 1, Vakcode: MAT 15303, Lecture Notes 2020
,Inhoudsopgave
Tutorial 1) Population, sample, variables, frequency table...........................................................................3
Research question, population and sample.............................................................................................. 3
Units and variables.................................................................................................................................... 3
Verschillende variables............................................................................................................................. 3
Drawing a sample from a population........................................................................................................ 3
Problemen met samples........................................................................................................................... 3
Observational vs experimental research................................................................................................... 4
Tutorial 2) Numerical summery of data........................................................................................................ 5
Central tendencies.................................................................................................................................... 5
Measures of variability.............................................................................................................................. 5
Five-number summary.............................................................................................................................. 5
Frequency and probability........................................................................................................................ 5
Law of large numbers................................................................................................................................ 5
Random phenomena................................................................................................................................ 6
Probability distribution voor een discrete variable...................................................................................6
Definitie van probability door LaPlace....................................................................................................... 6
Statistical events....................................................................................................................................... 6
Tutorial 3) laws of probability theory, expectation and variance of a variable..............................................7
Multiplication law..................................................................................................................................... 7
Addition law.............................................................................................................................................. 7
Expectation of a variable........................................................................................................................... 7
Tutorial 4) Binomial distribution, research question and hypothesis............................................................8
Binomial distribution................................................................................................................................. 8
Binomial formula...................................................................................................................................... 8
Expected value and variance binomial distribution...................................................................................8
Statistical test: hypothesis........................................................................................................................ 8
Tutorial 5) Exact binomial test for a population proportion/probability π....................................................9
The seven steps of a test........................................................................................................................... 9
Two-sided P-value..................................................................................................................................... 9
Tutorial 6) Normal distribution................................................................................................................... 10
Continuous random variable................................................................................................................... 10
Histogram............................................................................................................................................... 10
Probability and continuous random variables......................................................................................... 10
Normal distribution................................................................................................................................. 10
1
, Standard normal distribution.................................................................................................................. 10
Tutorial 7) Laws for calculating expectations and variances, probability distribution of a sum and a mean11
Laws for expectation and variance.......................................................................................................... 11
Laws for calculating expected values...................................................................................................... 11
Laws for calculating variances................................................................................................................. 11
Laws 1 en 2 combined............................................................................................................................. 11
Independent drawings from a single distribution....................................................................................11
of a sample mean.................................................................................................................................... 12
Overview................................................................................................................................................. 12
Tutorial 8) Central limit theorem, test for a population mean µ.................................................................13
Central limit theorem.............................................................................................................................. 13
Two-sided test........................................................................................................................................ 13
Tutorial 9) Type 1 and type 2 error, relation sample size and P-value, summary and intergration of the
course content............................................................................................................................................ 14
Type 1 and type 2 error........................................................................................................................... 14
Issues with big samples........................................................................................................................... 14
2
, Tutorial 1) Population, sample, variables,
frequency table
Research question, population and sample
Als je een onderzoek start heb je het volgende nodig:
Research question (vraag die je wilt beantwoorden)
Population (elk lid van een groep waarvan je informatie wilt)
Sample (steekproef uit de populatie)
Units and variables
Betekenis
Een unit is het element (eenheid) van de steekproef (bijvoorbeeld “zwangere vrouw”)
Een variable is hetgeen dat je meet (bijvoorbeeld “gewicht”)
Verschillende variables
Er zijn verschillende typen variables, namelijk:
Quantitative variables
Quantitative variables (gaat over getallen). Deze variables kunnen continuous of discrete zijn.
Continuous variables beschrijven elk mogelijk getal (bijvoorbeeld “aantal gram”). Discrete variables
zijn enkel hele getallen (bijvoorbeeld “aantal kinderen”).
Qualitative variables
Qualitative variables (gaat over eigenschappen). Deze variables kunnen nominal of ordinal zijn.
Nominal variables beschrijven iets wat niet op rang in te delen is (bijvoorbeeld “haarkleur”). Ordinal
variables kunnen wel op rang ingedeeld worden (bijvoorbeeld “opleidingsniveau”).
Note: met quantitative variables kan je rekenen, met qualitative variables niet.
Drawing a sample from a population
Een sample moet:
Representatief zijn voor de population
Alle delen van de populatie dekken. Voorkom dat bepaalde delen van de population
overdekt of onderdekt zijn (sampling bias)
Simple random sampling (SRS)
Bij simple random sampling worden units random uit de populatie getrokken. Dit vormt de sample.
Elke sample heeft hierdoor units die gelijke kansen hebben. Hierdoor wordt zogenaamde sampling
bias voorkomen.
Note: Denk aan sinterklaaslootjes trekken. Iedereen heeft evenveel kans om een bepaald persoon te
trekken.
Problemen met samples
Je samples zijn niet goed gemaakt als er sprake is van:
Undersampling (bepaalde groepen zijn onderdekt)
3
Statistics 1
Periode 1, Vakcode: MAT 15303, Lecture Notes 2020
,Inhoudsopgave
Tutorial 1) Population, sample, variables, frequency table...........................................................................3
Research question, population and sample.............................................................................................. 3
Units and variables.................................................................................................................................... 3
Verschillende variables............................................................................................................................. 3
Drawing a sample from a population........................................................................................................ 3
Problemen met samples........................................................................................................................... 3
Observational vs experimental research................................................................................................... 4
Tutorial 2) Numerical summery of data........................................................................................................ 5
Central tendencies.................................................................................................................................... 5
Measures of variability.............................................................................................................................. 5
Five-number summary.............................................................................................................................. 5
Frequency and probability........................................................................................................................ 5
Law of large numbers................................................................................................................................ 5
Random phenomena................................................................................................................................ 6
Probability distribution voor een discrete variable...................................................................................6
Definitie van probability door LaPlace....................................................................................................... 6
Statistical events....................................................................................................................................... 6
Tutorial 3) laws of probability theory, expectation and variance of a variable..............................................7
Multiplication law..................................................................................................................................... 7
Addition law.............................................................................................................................................. 7
Expectation of a variable........................................................................................................................... 7
Tutorial 4) Binomial distribution, research question and hypothesis............................................................8
Binomial distribution................................................................................................................................. 8
Binomial formula...................................................................................................................................... 8
Expected value and variance binomial distribution...................................................................................8
Statistical test: hypothesis........................................................................................................................ 8
Tutorial 5) Exact binomial test for a population proportion/probability π....................................................9
The seven steps of a test........................................................................................................................... 9
Two-sided P-value..................................................................................................................................... 9
Tutorial 6) Normal distribution................................................................................................................... 10
Continuous random variable................................................................................................................... 10
Histogram............................................................................................................................................... 10
Probability and continuous random variables......................................................................................... 10
Normal distribution................................................................................................................................. 10
1
, Standard normal distribution.................................................................................................................. 10
Tutorial 7) Laws for calculating expectations and variances, probability distribution of a sum and a mean11
Laws for expectation and variance.......................................................................................................... 11
Laws for calculating expected values...................................................................................................... 11
Laws for calculating variances................................................................................................................. 11
Laws 1 en 2 combined............................................................................................................................. 11
Independent drawings from a single distribution....................................................................................11
of a sample mean.................................................................................................................................... 12
Overview................................................................................................................................................. 12
Tutorial 8) Central limit theorem, test for a population mean µ.................................................................13
Central limit theorem.............................................................................................................................. 13
Two-sided test........................................................................................................................................ 13
Tutorial 9) Type 1 and type 2 error, relation sample size and P-value, summary and intergration of the
course content............................................................................................................................................ 14
Type 1 and type 2 error........................................................................................................................... 14
Issues with big samples........................................................................................................................... 14
2
, Tutorial 1) Population, sample, variables,
frequency table
Research question, population and sample
Als je een onderzoek start heb je het volgende nodig:
Research question (vraag die je wilt beantwoorden)
Population (elk lid van een groep waarvan je informatie wilt)
Sample (steekproef uit de populatie)
Units and variables
Betekenis
Een unit is het element (eenheid) van de steekproef (bijvoorbeeld “zwangere vrouw”)
Een variable is hetgeen dat je meet (bijvoorbeeld “gewicht”)
Verschillende variables
Er zijn verschillende typen variables, namelijk:
Quantitative variables
Quantitative variables (gaat over getallen). Deze variables kunnen continuous of discrete zijn.
Continuous variables beschrijven elk mogelijk getal (bijvoorbeeld “aantal gram”). Discrete variables
zijn enkel hele getallen (bijvoorbeeld “aantal kinderen”).
Qualitative variables
Qualitative variables (gaat over eigenschappen). Deze variables kunnen nominal of ordinal zijn.
Nominal variables beschrijven iets wat niet op rang in te delen is (bijvoorbeeld “haarkleur”). Ordinal
variables kunnen wel op rang ingedeeld worden (bijvoorbeeld “opleidingsniveau”).
Note: met quantitative variables kan je rekenen, met qualitative variables niet.
Drawing a sample from a population
Een sample moet:
Representatief zijn voor de population
Alle delen van de populatie dekken. Voorkom dat bepaalde delen van de population
overdekt of onderdekt zijn (sampling bias)
Simple random sampling (SRS)
Bij simple random sampling worden units random uit de populatie getrokken. Dit vormt de sample.
Elke sample heeft hierdoor units die gelijke kansen hebben. Hierdoor wordt zogenaamde sampling
bias voorkomen.
Note: Denk aan sinterklaaslootjes trekken. Iedereen heeft evenveel kans om een bepaald persoon te
trekken.
Problemen met samples
Je samples zijn niet goed gemaakt als er sprake is van:
Undersampling (bepaalde groepen zijn onderdekt)
3
