Statistics for Premaster CIS midterm
Midterm 35% 26th of March
Endterm 65% 4th of June
Index
Chapter 1 Why do we learn statistics......................................................................................... 3
1.1 On the psychology of statistics......................................................................................... 3
1.2 The cautionary tale of Simpson’s paradox........................................................................3
1.3 Statistics in psychology..................................................................................................... 3
Chapter 2 A brief introduction to research design......................................................................3
2.1 Introduction to psychological measurement.....................................................................3
2.2 Scales of measurement..................................................................................................... 4
2.3 Assessing the reliability of a measurement.......................................................................4
2.4 The ‘role’ of variables: predictors and outcomes..............................................................5
2.5 Experimental and non-experimental research..................................................................5
2.6 Assessing the validity of a study....................................................................................... 5
2.7 Confounders, artefacts and other threats to validity.........................................................6
Chapter 3 Getting started with jamovi....................................................................................... 7
Chapter 4 Descriptive statistics.................................................................................................. 7
4.1 Measures of central tendency........................................................................................... 7
4.2 Measures of variability...................................................................................................... 7
4.3 Skew and kurtosis............................................................................................................. 9
4.4 Descriptive statistics separately for each group...............................................................9
4.5 Standard scores.............................................................................................................. 10
Chapter 5 Drawing graphs........................................................................................................ 10
5.1 Histograms...................................................................................................................... 10
5.2 Boxplots.......................................................................................................................... 10
5.3 Bar graphs....................................................................................................................... 11
Chapter 6 Pragmatic matters (6.2 & 6.4 optional)....................................................................11
6.1 Tabulating and cross-tabulating data..............................................................................11
6.3 Transforming and recoding a variable.............................................................................11
6.5 Extracting a subset of the data....................................................................................... 12
Chapter 7 (optional)................................................................................................................. 12
Chapter 8 Estimating unknown quantities from a sample........................................................12
8.1 Samples, populations and sampling................................................................................12
8.2 The law of large numbers................................................................................................ 13
8.3 Sampling distributions and the central limit theorem.....................................................13
8.4 Estimating population parameters..................................................................................14
8.5 Estimating a confidence interval..................................................................................... 15
,Chapter 9 Hypothesis testing................................................................................................... 15
9.1 A menagerie of hypotheses............................................................................................. 15
9.2 Two types of errors......................................................................................................... 16
9.3 Test statistics and sampling distributions.......................................................................16
9.4 Making decisions............................................................................................................. 17
9.5 The p-value of a test....................................................................................................... 17
9.6 Reporting the results of a hypothesis test.......................................................................18
9.7 Running the hypothesis test in practice..........................................................................18
9.8 Effect size, sample size and power..................................................................................18
9.9 Some issues to consider.................................................................................................. 20
Chapter 11 Comparing two means........................................................................................... 20
11.1 The one-sample z-test................................................................................................... 20
11.2 The one-sample t-test................................................................................................... 21
11.3 The independent samples t-test (Student test).............................................................21
11.4 Completing the test....................................................................................................... 22
11.5 The independent samples t-test (Welch test)................................................................22
11.6 The paired-samples t-test............................................................................................. 23
11.7 One-sided tests............................................................................................................. 24
11.8 Effect size...................................................................................................................... 24
11.9 Checking the normality of a sample.............................................................................. 25
11.10 Testing non-normal data............................................................................................. 25
Chapter 13 Comparing several means (one-way ANOVA)........................................................26
13.2 How ANOVA works........................................................................................................ 26
13.3 Running an ANOVA in jamovi........................................................................................ 27
13.4 Effect size...................................................................................................................... 27
13.5 Multiple comparisons and post hoc tests......................................................................27
13.6 The assumptions of one-way ANOVA............................................................................ 28
13.7 Repeated measures one-way ANOVA............................................................................29
13.8 The Friedman non-parametric repeated measures ANOVA test....................................29
13.9 On the relationship between ANOVA and the Student t-test.........................................30
Chapter 15 (only section 15.5)................................................................................................. 30
15.5 Internal consistency reliability analysis.........................................................................30
Practice Units........................................................................................................................... 30
Practice Unit 1....................................................................................................................... 30
Practice Unit 2....................................................................................................................... 31
Practice Unit 3....................................................................................................................... 31
Practice Unit 4....................................................................................................................... 32
Practice Unit 5....................................................................................................................... 33
Practice Unit 6....................................................................................................................... 36
2
,Chapter 1 Why do we learn statistics
1.1 On the psychology of statistics
Statistics are used because humans are susceptible to biases. Humans find it hard to be neutral, to evaluate evidence
impartially and without being swayed by pre-existing biases.
Belief bias effect = if you ask people to decide whether a particular argument is logically valid (ie. the
conclusion would be true if the premises were true), we tend to be influenced by the believability of the
conclusion, even when we should not.
1.2 The cautionary tale of Simpson’s paradox
Simpson’s paradox = a statistical phenomenon in which a trend appears in several groups of
data, but disappears of or even reverses when the groups are combined. [see image]
However, there are also a lot of (qualitative) questions that statistics cannot answer.
1.3 Statistics in psychology
It’s important to be able to do basic statistics for 3 reasons:
1. Statistics is deeply intertwined with research design. If you want to be good at designing studies, you need to
at the very least understand the basics of stats.
2. You have to be able to understand the literature, including the results of the statistical analyses.
3. You need it in everyday life, for example to understand journalistic articles.
Chapter 2 A brief introduction to research design
2.1 Introduction to psychological measurement
Data collection is a kind of measurement, since we are measuring something about human behavior or the human
mind.
Some thoughts about psychological measurement
Measurement mostly tries to put a number or label to rather abstract ‘stuff’. Some things are easier to measure (eg.
age), however, even this is tricky. Do you measure age in years, or months, or days? Also, what methodology will you
use for this question: self-report (only works for people old enough to understand their age), ask an authoritative
figure, eg. a parent, or rather official records (which is time-consuming).
Operationalization: defining your measurement
Operationalization = the process by which we take a meaningful but somewhat vague concept and turn it into a
precise measurement. This can involve several different things:
1. Being precise about what you are trying to measure.
Eg. age: time since conception, or time since birth.
2. Determining what method you will use to measure it.
Eg. self-report, ask parent, official record.
3. Defining the set of allowable values that the measurement can take.
Eg. years, months, days, hours, etc. or female/male/x/?
This means that operationalization needs to be thought through on a case-by-case basis terminology:
A theoretical construct = the thing you’re trying to take a measurement of (eg. age, gender, etc.). These can’t
be directly observed.
A measure = refers to the method/tool you use to make your observations (eg. question in survey, brain scan,
etc.).
An operationalization = refers to the logical connection between the measure and the theoretical construct,
or the process by which we try to derive a measure from a theoretical construct.
3
, A variable = the actual ‘data’ from the data sets.
2.2 Scales of measurement
Scales of measurement can be used to distinguish between the different types of variables:
Nominal scale
Ordinal scale
Interval scale
Ratio scale
Nominal scale There is no particular relationship between the different possibilities (eg. eye color, or gender).
Not one possibility is ‘better’ or ‘bigger’ than the other one. The only thing that makes these
possibilities different is the fact that they are different.
Ordinal scale Ordinal scale variables have a bit more structure than nominal scale variables, but not by a lot.
Eg. ‘finishing position in a race’, where first might be better than last. However, it doesn’t say
anything about the difference in time between 1 st and 2nd position, and 2nd to 3rd, etc.
Interval scale The numerical value is meaningful. With interval scale variables, the differences between the
numbers are interpretable, but the variable doesn’t have a ‘natural’ zero value, eg. degrees
Celsius. Zero degrees does not mean ‘no temperature’.
Ratio scale In ratio scale, zero means zero and it’s okay to multiply and divide. Response time (RT) is a good
example, because it’s an indicator of how hard a task is. Here, 0 RT actually means ‘no time at all’.
Continuous versus discrete variables
Discrete variables Continuous variables
= a variable in which it might be the case that there = one in which, for any two values that you can think of, it’s
is nothing in the middle, it isn’t ‘continuous’. always logically possible to have another value in between.
Eg. transportation type (bike, car, train, etc.) Eg. response time
Some complexities
Likert scale is an example of a limited tool. What kind of variable are they? They are discrete, but are they ordinal
scale or interval scale? Is there a difference between ‘strongly agree’ and ‘agree’, and is this the same difference as
‘agree’ and ‘neither agree or disagree’?
Likert scale is to be thought of as quasi-interval scale.
2.3 Assessing the reliability of a measurement
Assessing whether the measurement is a good measurement is done through reliability and validity.
Reliability Validity
= the extent to which the outcomes are consistent = the extent to which the instruments that are used in
when the experiment is repeated more than once. the experiment measure exactly what you want them to
measure.
Reliability is measured in different ways:
Test-retest reliability = consistency over time.
o Eg. same answer at a different time.
Inter-rater reliability = consistency across people.
o Eg. same answer with different people measuring.
Parallel forms reliability = consistency across theoretically-equivalent measurements.
4
Midterm 35% 26th of March
Endterm 65% 4th of June
Index
Chapter 1 Why do we learn statistics......................................................................................... 3
1.1 On the psychology of statistics......................................................................................... 3
1.2 The cautionary tale of Simpson’s paradox........................................................................3
1.3 Statistics in psychology..................................................................................................... 3
Chapter 2 A brief introduction to research design......................................................................3
2.1 Introduction to psychological measurement.....................................................................3
2.2 Scales of measurement..................................................................................................... 4
2.3 Assessing the reliability of a measurement.......................................................................4
2.4 The ‘role’ of variables: predictors and outcomes..............................................................5
2.5 Experimental and non-experimental research..................................................................5
2.6 Assessing the validity of a study....................................................................................... 5
2.7 Confounders, artefacts and other threats to validity.........................................................6
Chapter 3 Getting started with jamovi....................................................................................... 7
Chapter 4 Descriptive statistics.................................................................................................. 7
4.1 Measures of central tendency........................................................................................... 7
4.2 Measures of variability...................................................................................................... 7
4.3 Skew and kurtosis............................................................................................................. 9
4.4 Descriptive statistics separately for each group...............................................................9
4.5 Standard scores.............................................................................................................. 10
Chapter 5 Drawing graphs........................................................................................................ 10
5.1 Histograms...................................................................................................................... 10
5.2 Boxplots.......................................................................................................................... 10
5.3 Bar graphs....................................................................................................................... 11
Chapter 6 Pragmatic matters (6.2 & 6.4 optional)....................................................................11
6.1 Tabulating and cross-tabulating data..............................................................................11
6.3 Transforming and recoding a variable.............................................................................11
6.5 Extracting a subset of the data....................................................................................... 12
Chapter 7 (optional)................................................................................................................. 12
Chapter 8 Estimating unknown quantities from a sample........................................................12
8.1 Samples, populations and sampling................................................................................12
8.2 The law of large numbers................................................................................................ 13
8.3 Sampling distributions and the central limit theorem.....................................................13
8.4 Estimating population parameters..................................................................................14
8.5 Estimating a confidence interval..................................................................................... 15
,Chapter 9 Hypothesis testing................................................................................................... 15
9.1 A menagerie of hypotheses............................................................................................. 15
9.2 Two types of errors......................................................................................................... 16
9.3 Test statistics and sampling distributions.......................................................................16
9.4 Making decisions............................................................................................................. 17
9.5 The p-value of a test....................................................................................................... 17
9.6 Reporting the results of a hypothesis test.......................................................................18
9.7 Running the hypothesis test in practice..........................................................................18
9.8 Effect size, sample size and power..................................................................................18
9.9 Some issues to consider.................................................................................................. 20
Chapter 11 Comparing two means........................................................................................... 20
11.1 The one-sample z-test................................................................................................... 20
11.2 The one-sample t-test................................................................................................... 21
11.3 The independent samples t-test (Student test).............................................................21
11.4 Completing the test....................................................................................................... 22
11.5 The independent samples t-test (Welch test)................................................................22
11.6 The paired-samples t-test............................................................................................. 23
11.7 One-sided tests............................................................................................................. 24
11.8 Effect size...................................................................................................................... 24
11.9 Checking the normality of a sample.............................................................................. 25
11.10 Testing non-normal data............................................................................................. 25
Chapter 13 Comparing several means (one-way ANOVA)........................................................26
13.2 How ANOVA works........................................................................................................ 26
13.3 Running an ANOVA in jamovi........................................................................................ 27
13.4 Effect size...................................................................................................................... 27
13.5 Multiple comparisons and post hoc tests......................................................................27
13.6 The assumptions of one-way ANOVA............................................................................ 28
13.7 Repeated measures one-way ANOVA............................................................................29
13.8 The Friedman non-parametric repeated measures ANOVA test....................................29
13.9 On the relationship between ANOVA and the Student t-test.........................................30
Chapter 15 (only section 15.5)................................................................................................. 30
15.5 Internal consistency reliability analysis.........................................................................30
Practice Units........................................................................................................................... 30
Practice Unit 1....................................................................................................................... 30
Practice Unit 2....................................................................................................................... 31
Practice Unit 3....................................................................................................................... 31
Practice Unit 4....................................................................................................................... 32
Practice Unit 5....................................................................................................................... 33
Practice Unit 6....................................................................................................................... 36
2
,Chapter 1 Why do we learn statistics
1.1 On the psychology of statistics
Statistics are used because humans are susceptible to biases. Humans find it hard to be neutral, to evaluate evidence
impartially and without being swayed by pre-existing biases.
Belief bias effect = if you ask people to decide whether a particular argument is logically valid (ie. the
conclusion would be true if the premises were true), we tend to be influenced by the believability of the
conclusion, even when we should not.
1.2 The cautionary tale of Simpson’s paradox
Simpson’s paradox = a statistical phenomenon in which a trend appears in several groups of
data, but disappears of or even reverses when the groups are combined. [see image]
However, there are also a lot of (qualitative) questions that statistics cannot answer.
1.3 Statistics in psychology
It’s important to be able to do basic statistics for 3 reasons:
1. Statistics is deeply intertwined with research design. If you want to be good at designing studies, you need to
at the very least understand the basics of stats.
2. You have to be able to understand the literature, including the results of the statistical analyses.
3. You need it in everyday life, for example to understand journalistic articles.
Chapter 2 A brief introduction to research design
2.1 Introduction to psychological measurement
Data collection is a kind of measurement, since we are measuring something about human behavior or the human
mind.
Some thoughts about psychological measurement
Measurement mostly tries to put a number or label to rather abstract ‘stuff’. Some things are easier to measure (eg.
age), however, even this is tricky. Do you measure age in years, or months, or days? Also, what methodology will you
use for this question: self-report (only works for people old enough to understand their age), ask an authoritative
figure, eg. a parent, or rather official records (which is time-consuming).
Operationalization: defining your measurement
Operationalization = the process by which we take a meaningful but somewhat vague concept and turn it into a
precise measurement. This can involve several different things:
1. Being precise about what you are trying to measure.
Eg. age: time since conception, or time since birth.
2. Determining what method you will use to measure it.
Eg. self-report, ask parent, official record.
3. Defining the set of allowable values that the measurement can take.
Eg. years, months, days, hours, etc. or female/male/x/?
This means that operationalization needs to be thought through on a case-by-case basis terminology:
A theoretical construct = the thing you’re trying to take a measurement of (eg. age, gender, etc.). These can’t
be directly observed.
A measure = refers to the method/tool you use to make your observations (eg. question in survey, brain scan,
etc.).
An operationalization = refers to the logical connection between the measure and the theoretical construct,
or the process by which we try to derive a measure from a theoretical construct.
3
, A variable = the actual ‘data’ from the data sets.
2.2 Scales of measurement
Scales of measurement can be used to distinguish between the different types of variables:
Nominal scale
Ordinal scale
Interval scale
Ratio scale
Nominal scale There is no particular relationship between the different possibilities (eg. eye color, or gender).
Not one possibility is ‘better’ or ‘bigger’ than the other one. The only thing that makes these
possibilities different is the fact that they are different.
Ordinal scale Ordinal scale variables have a bit more structure than nominal scale variables, but not by a lot.
Eg. ‘finishing position in a race’, where first might be better than last. However, it doesn’t say
anything about the difference in time between 1 st and 2nd position, and 2nd to 3rd, etc.
Interval scale The numerical value is meaningful. With interval scale variables, the differences between the
numbers are interpretable, but the variable doesn’t have a ‘natural’ zero value, eg. degrees
Celsius. Zero degrees does not mean ‘no temperature’.
Ratio scale In ratio scale, zero means zero and it’s okay to multiply and divide. Response time (RT) is a good
example, because it’s an indicator of how hard a task is. Here, 0 RT actually means ‘no time at all’.
Continuous versus discrete variables
Discrete variables Continuous variables
= a variable in which it might be the case that there = one in which, for any two values that you can think of, it’s
is nothing in the middle, it isn’t ‘continuous’. always logically possible to have another value in between.
Eg. transportation type (bike, car, train, etc.) Eg. response time
Some complexities
Likert scale is an example of a limited tool. What kind of variable are they? They are discrete, but are they ordinal
scale or interval scale? Is there a difference between ‘strongly agree’ and ‘agree’, and is this the same difference as
‘agree’ and ‘neither agree or disagree’?
Likert scale is to be thought of as quasi-interval scale.
2.3 Assessing the reliability of a measurement
Assessing whether the measurement is a good measurement is done through reliability and validity.
Reliability Validity
= the extent to which the outcomes are consistent = the extent to which the instruments that are used in
when the experiment is repeated more than once. the experiment measure exactly what you want them to
measure.
Reliability is measured in different ways:
Test-retest reliability = consistency over time.
o Eg. same answer at a different time.
Inter-rater reliability = consistency across people.
o Eg. same answer with different people measuring.
Parallel forms reliability = consistency across theoretically-equivalent measurements.
4
