Test 1: Inferential Statistics
Inhoud
Test 1: Inferential Statistics ..................................................................................................1
Lecture 1: Introducing the topic and the course of inferential statistics ..................................3
Chapter 501: Confidence interval for a proportion .................................................................5
Article: Analysing Data using Linear Models, Van den Berg, SM (2026) ................................5
Chapters of the book ........................................................................................................6
Videos chapter 501 ..........................................................................................................7
Chapter 502: confidence interval for a mean ....................................................................... 10
Article: Analysing Data using Linear Models, Van den Berg, SM (2026) .............................. 10
Videos 502 ..................................................................................................................... 13
503: Testing what the mean is ............................................................................................ 14
Article: Analysing Data using Linear Models, Van den Berg, SM (2026) .............................. 14
Videos 503 ..................................................................................................................... 22
Lecture 2: Associations of variables 28-04-2026 ................................................................. 23
Chapter 520: Describing and testing relationships between non-scale variables: chi-square 26
Statistic book: Chi Square .............................................................................................. 26
Article: Analysing Data using Linear Models, Van den Berg, SM (2026) .............................. 27
Videos 520 ..................................................................................................................... 30
Chapter 521: Testing relationships between scale variables: Pearson and Spearman
correlations ....................................................................................................................... 32
Statistic book: Pearsons correlation................................................................................ 32
Laerd statistics site: Spearmans correlation .................................................................... 32
Article: Analysing Data using Linear Models, Van den Berg (2026): chapter 4.8- 4.11 ......... 32
Videos Chapter 521 ........................................................................................................ 34
Chapter 522: Theorizing about relationships between variables using linear equations ........ 36
Article: Analysing Data using Linear Models, Van den Berg (2026): chapter 4.1 & 4.2 ......... 36
Videos 522 ..................................................................................................................... 36
Lecture 3: The basics of the linear model ............................................................................ 38
Chapter 530: Describing the linear relationship in a sample ................................................ 39
Article: Analysing Data using Linear Models, Van den Berg (2026) Chapter 4.3 to 4.6 ......... 39
Videos 530 ..................................................................................................................... 40
Chapter 531: Assessing a bivariate relationship using data .................................................. 41
, Article: Analysing Data using Linear Models, Van den Berg (2026) Chapter 4.7 to 4.6 ......... 41
Article: Chapter 1 (p. 1-16) of Lewis-Beck, C., & Lewis-Beck, M. (2016). Quantitative
Applications in the Social Sciences: applied regression. .................................................. 42
Videos 531 ..................................................................................................................... 45
Chapter 540: Describing and testing the effect of a dummy variable on a ratio variable ......... 46
Article: Analysing Data using Linear Models, Van den Berg (2026) Chapter 6.1 to 6.4 ......... 46
Videos 540 ..................................................................................................................... 48
Lecture 4: Linear models .................................................................................................... 50
Chapter 541: Differences between two groups .................................................................... 53
Article: Analysing Data using Linear Models, Van den Berg (2026) Chapter 6.7 and 6.8 ...... 53
Videos 541 ..................................................................................................................... 54
Chapter 551....................................................................................................................... 55
Article: Analysing Data using Linear Models, Van den Berg (2026) Chapter 4.11- 4.14........ 55
Article: Analysing Data using Linear Models, Van den Berg (2026) Chapter 6.9 -6.11 ......... 57
Article: Quantitative Applications in the Social Sciences: applied regression. Lewis-Beck,
C., & Lewis-Beck, M. (2016): Chapter 1 (p 16-22) ............................................................. 58
Videos 551 ..................................................................................................................... 59
,Lecture 1: Introducing the topic and the course of inferential
statistics
20-04-2026
Percentage: 0% -100%
Fraction: between 0 and 1
Matrix with data
Population <- number
Population_data <- rbinom(population, 1( or 0), percentage) %>% as.data.frame() %>% rename(
., trump + .)
All the population is called the population distrubtions
Scientific notation → switch it off on R
Notations
Population proportion: Π (pi)
Resarch question: “What is the proportion of … (Π)?”
Hypotheses and RQ’s are about “The population”
Sampling
Simple random sampling vs Non-random sampling
- Inferential statistics is focused on random samples and not representative samples
- Non-representativeness may be an indication that the sample was not random, but it
may be that we have a non-representative RANDOM sample
- A random sample is not something “formal. It is also based on substantive assumptions.
Sampling in R
Sample <- datafile %>% slice_sample(n=50)
- 50 is the sample size
- 50 is the sample distribution
Two observations
- A simple ranbdom sample is not always a perfect reflection of what is going on
- Simple random samples differ from eachother
Many samples
- If you do a lot of samples, all those samples do say something about 1 sample
Observation
Inferential statistics is answering the question: “What we can conclude, assuming we have one
random sample from a population”
- Sample proportions of 10.000 samples looks like a binominal distribution, which looks
very much like a the normal distribution.
- Sampling distribution is saying something about multiple samples
- With a bigger sample size, the spread of the sample proportion becomes smaller.
Distrubutions
1. Population distrubtions (the population)
2. Sample distribution (one sample)
3. The sampling distribution (many samples)
, Standard error
“The (estimate of the) standard deviation of the sampling distribution”
- The standard error generally depends on the sample size (n)and on the population
standard deviation (s)
- We do not know the population standard deviation, we use the sample standard
deviation. → This introduces some extra error, especially when sample sizes are small.
- The distance between 95% of the possible samples and the true population parameter is
not more thean 1,96 standard errors.
- If we have one smaple, we can argue that the population proportion is very likely in the
range of +/- 1.96 standard errors away from the observerd proportion.
Statistics:
Descriptive part:
- Proportion: mean, effect, correlation
Inferential part:
- Confidence interval (where do we think the parameter most likely is?)
- Test ( are we sure the parameter is not zero ( or some other number we start with)
Why is there so much statistics?
- One variable (dich/nominal/ordinal/scale)
- Two variables (different types of associations)
- Many variables (different types of associations interactions between relationships)
Inhoud
Test 1: Inferential Statistics ..................................................................................................1
Lecture 1: Introducing the topic and the course of inferential statistics ..................................3
Chapter 501: Confidence interval for a proportion .................................................................5
Article: Analysing Data using Linear Models, Van den Berg, SM (2026) ................................5
Chapters of the book ........................................................................................................6
Videos chapter 501 ..........................................................................................................7
Chapter 502: confidence interval for a mean ....................................................................... 10
Article: Analysing Data using Linear Models, Van den Berg, SM (2026) .............................. 10
Videos 502 ..................................................................................................................... 13
503: Testing what the mean is ............................................................................................ 14
Article: Analysing Data using Linear Models, Van den Berg, SM (2026) .............................. 14
Videos 503 ..................................................................................................................... 22
Lecture 2: Associations of variables 28-04-2026 ................................................................. 23
Chapter 520: Describing and testing relationships between non-scale variables: chi-square 26
Statistic book: Chi Square .............................................................................................. 26
Article: Analysing Data using Linear Models, Van den Berg, SM (2026) .............................. 27
Videos 520 ..................................................................................................................... 30
Chapter 521: Testing relationships between scale variables: Pearson and Spearman
correlations ....................................................................................................................... 32
Statistic book: Pearsons correlation................................................................................ 32
Laerd statistics site: Spearmans correlation .................................................................... 32
Article: Analysing Data using Linear Models, Van den Berg (2026): chapter 4.8- 4.11 ......... 32
Videos Chapter 521 ........................................................................................................ 34
Chapter 522: Theorizing about relationships between variables using linear equations ........ 36
Article: Analysing Data using Linear Models, Van den Berg (2026): chapter 4.1 & 4.2 ......... 36
Videos 522 ..................................................................................................................... 36
Lecture 3: The basics of the linear model ............................................................................ 38
Chapter 530: Describing the linear relationship in a sample ................................................ 39
Article: Analysing Data using Linear Models, Van den Berg (2026) Chapter 4.3 to 4.6 ......... 39
Videos 530 ..................................................................................................................... 40
Chapter 531: Assessing a bivariate relationship using data .................................................. 41
, Article: Analysing Data using Linear Models, Van den Berg (2026) Chapter 4.7 to 4.6 ......... 41
Article: Chapter 1 (p. 1-16) of Lewis-Beck, C., & Lewis-Beck, M. (2016). Quantitative
Applications in the Social Sciences: applied regression. .................................................. 42
Videos 531 ..................................................................................................................... 45
Chapter 540: Describing and testing the effect of a dummy variable on a ratio variable ......... 46
Article: Analysing Data using Linear Models, Van den Berg (2026) Chapter 6.1 to 6.4 ......... 46
Videos 540 ..................................................................................................................... 48
Lecture 4: Linear models .................................................................................................... 50
Chapter 541: Differences between two groups .................................................................... 53
Article: Analysing Data using Linear Models, Van den Berg (2026) Chapter 6.7 and 6.8 ...... 53
Videos 541 ..................................................................................................................... 54
Chapter 551....................................................................................................................... 55
Article: Analysing Data using Linear Models, Van den Berg (2026) Chapter 4.11- 4.14........ 55
Article: Analysing Data using Linear Models, Van den Berg (2026) Chapter 6.9 -6.11 ......... 57
Article: Quantitative Applications in the Social Sciences: applied regression. Lewis-Beck,
C., & Lewis-Beck, M. (2016): Chapter 1 (p 16-22) ............................................................. 58
Videos 551 ..................................................................................................................... 59
,Lecture 1: Introducing the topic and the course of inferential
statistics
20-04-2026
Percentage: 0% -100%
Fraction: between 0 and 1
Matrix with data
Population <- number
Population_data <- rbinom(population, 1( or 0), percentage) %>% as.data.frame() %>% rename(
., trump + .)
All the population is called the population distrubtions
Scientific notation → switch it off on R
Notations
Population proportion: Π (pi)
Resarch question: “What is the proportion of … (Π)?”
Hypotheses and RQ’s are about “The population”
Sampling
Simple random sampling vs Non-random sampling
- Inferential statistics is focused on random samples and not representative samples
- Non-representativeness may be an indication that the sample was not random, but it
may be that we have a non-representative RANDOM sample
- A random sample is not something “formal. It is also based on substantive assumptions.
Sampling in R
Sample <- datafile %>% slice_sample(n=50)
- 50 is the sample size
- 50 is the sample distribution
Two observations
- A simple ranbdom sample is not always a perfect reflection of what is going on
- Simple random samples differ from eachother
Many samples
- If you do a lot of samples, all those samples do say something about 1 sample
Observation
Inferential statistics is answering the question: “What we can conclude, assuming we have one
random sample from a population”
- Sample proportions of 10.000 samples looks like a binominal distribution, which looks
very much like a the normal distribution.
- Sampling distribution is saying something about multiple samples
- With a bigger sample size, the spread of the sample proportion becomes smaller.
Distrubutions
1. Population distrubtions (the population)
2. Sample distribution (one sample)
3. The sampling distribution (many samples)
, Standard error
“The (estimate of the) standard deviation of the sampling distribution”
- The standard error generally depends on the sample size (n)and on the population
standard deviation (s)
- We do not know the population standard deviation, we use the sample standard
deviation. → This introduces some extra error, especially when sample sizes are small.
- The distance between 95% of the possible samples and the true population parameter is
not more thean 1,96 standard errors.
- If we have one smaple, we can argue that the population proportion is very likely in the
range of +/- 1.96 standard errors away from the observerd proportion.
Statistics:
Descriptive part:
- Proportion: mean, effect, correlation
Inferential part:
- Confidence interval (where do we think the parameter most likely is?)
- Test ( are we sure the parameter is not zero ( or some other number we start with)
Why is there so much statistics?
- One variable (dich/nominal/ordinal/scale)
- Two variables (different types of associations)
- Many variables (different types of associations interactions between relationships)
