Inleiding statistiek
Uitzonderingen leerstof.................................................................................................... 3
Boek................................................................................................................................. 3
Appendix A: Basic Mathematics Review........................................................................3
1 | Introduction to Statistics.......................................................................................... 3
2 | Frequency Distributions............................................................................................ 5
3 | Central tendency...................................................................................................... 9
4 | Variability............................................................................................................... 11
5 | z-Scores: Location of Scores and Standardized Distributions.................................13
6 | Probability.............................................................................................................. 14
7 | Probability and Samples: The Distribution of Sample Means..................................15
8 | Introduction to Hypothesis Testing.........................................................................16
9 | Introduction to the t Statistic.................................................................................. 18
10 | The t Test for Two Independent Samples.............................................................19
11 | The t Test for Two Related Samples.....................................................................21
15 | Correlation............................................................................................................ 22
17 | The Chi-Square Statistic: Tests for Goodness of Fit and Independence................24
18 | The Binomial Test................................................................................................. 26
On-demand video’s........................................................................................................ 27
V3W1 | Het meten van variabelen en frequentieverdelingen......................................27
V1W2 | Centrale waardes van data............................................................................. 27
V2W2 | Spreiding van de data..................................................................................... 28
V1W3 | De z-score....................................................................................................... 28
V2W3 | Intro kansrekenen & de normale verdeling.....................................................29
V3W3 | De binomiale verdeling................................................................................... 29
V1W4 | Steekproeven en de verdeling van steekproefgemiddelden...........................29
V2W4 | Introductie hypothesetoetsing........................................................................30
V3W4 | Fouten bij inferenties...................................................................................... 31
V1W5 | Problemen met z-scores.................................................................................. 31
V2W5 | De t-statistiek.................................................................................................. 31
V3W5 | De one-sample hypothese-toets.....................................................................31
V1W6 | Onafhankelijke metingen................................................................................ 31
V2W6 | De t-waarde voor “independent measures designs”.......................................31
V3W6 | Hypothesetoetsing met de onafhankelijke t-toets...........................................32
V1W7 | Herhaalde metingen........................................................................................ 32
V2W7 | De t-waarde voor herhaalde metingen............................................................32
V3W7 | Hypothesetoetsing met de afhankelijke t-test................................................33
V1W9 | Effectgroottes.................................................................................................. 33
V2W9 | Betrouwbaarheidsintervallen..........................................................................33
V1W10 | Wat is statistische power?............................................................................. 33
V2W10 | Hoe kunnen we statistische power berekenen?............................................34
,Inleiding statistiek
V1W11 | Het idee van verbanden tussen variabelen...................................................34
V2W11 | Pearson correlatie......................................................................................... 34
V3W11 | Hypothese toetsing met de Pearson correlation...........................................35
V1W12 | Associaties tussen categorische variabelen..................................................35
V2W12 | De Chi-kwadraattoets voor verbanden tussen variabelen.............................35
V3W12 | Effectmaten voor de Chi-kwadraattoets........................................................36
V1W13 | De logica van de binomiaaltest.....................................................................36
V2W13 | Hypothesetoetsting met de binomiaaltest....................................................37
Overige aantekeningen van hoorcolleges.......................................................................38
08-03-22 (week 4)....................................................................................................... 38
19-04-22 (week 10)..................................................................................................... 38
Overige notities.............................................................................................................. 39
Paired sample t-test.................................................................................................... 39
,Inleiding statistiek
Uitzonderingen leerstof
- The effect size r2 for the t-test (page 281-284)
- Hartley’s F-max test (314-315)
- The “alternative to pooled variance” (Box 10.2 on page 315)
- Regression towards the mean (Box 15.3 on page 501)
- Partial correlations (page 502-505)
- The “special formula” for the Spearman correlation (page 514)
- Testing significance of the Spearman correlation (page 515-516)
- The point-biserial correlation (page 516-517)
- Special applications of the Chi-Square tests (page 587-591)
- “more about the binomial test. . . ” (page 612-617)
Boek
Appendix A: Basic Mathematics Review
Volgorde berekening: Haakjes
Kwadraten
Vermenigvuldiging/deling (van links naar rechts)
Plus/min (van links naar rechts)
Breuken delen vb.:
1| Introduction to
Statistics
1.1 | Statistics, Science, and Observations
Statistics/ statistical procedures: set of mathematical procedures for organizing,
summarizing and interpreting information
Population: set of all individuals of interest in a particular study
Parameter: (numerical) value that describes a population
Sample: set of individuals selected from a population, usually intended to represent
the population in a research study
Statistic: (numerical) value that describes a sample
Sampling error: natural discrepancy/error existing between a sample statistic and
the corresponding population parameter as the sample might not give a
perfectly accurate picture of the whole population
Variable: characteristic/condition that changes or has different values for different
individuals
Data: measurements or observations
Data set:collection of data
Datum/score/ raw score: single measurement or observation
Statistical methods
Descriptive statistics: statistics used to summarize, organize and simplify data
so they are more manageable
Inferential statistics: techniques that allow us to study samples and then
make generalizations about the populations from which they were
selected
,Inleiding statistiek
1.2 | Data Structures, Research Methods, and Statistics
Data structures
Correlational method: 2 different variables are observed to determine a
possible relationship (correlation)
Experimental method / experimental research strategy: 1 variable is
manipulated, another variable is
observed and measured. All other
variables are controlled
Experimental method
Characteristics:
1. Manipulation
2. Control
Variables that may influence the correlation:
1. Participant variables: characteristics that vary per individual (e.g. age,
gender)
2. Environmental variables: characteristics of the environment (e.g. weather,
time of day)
Control by:
- Using random assignment (equal chance of being assigned to each
condition)
- Matching (ensure equivalent groups/environments)
- Holding variables constant
Independent variable: variable manipulated by researcher
Dependent variable: variable observed to asses the treatment’s effect
Control condition: condition in which participants don’t receive experimental
treatment. Maybe receive a placebo
Experimental condition: condition in which participants receive experimental
treatment
Nonexperimental methods
: research designs that are not true experiments but still examine relationships
between variables by comparing groups of scores
Nonequivalent groups study: comparing 2 groups of scores but no control
over which participants go into which group
Pre-post study: obtaining 2 groups of scores by measuring the same variable
twice for each participant, but no control over the passage of time or
other variables changing with time
Quasi-independent variable: the ‘independent variable’ that is used to
create different groups in nonexperimental studies
1.3 | Variables and Measurement
Constructs: internal attributes/characteristics that cannot be directly observed but
can describe and explain behavior
Operational definition: measurement procedure for measuring an external behavior
and uses resulting measurements as a definition and measurement
of a hpothetical construct
Discrete variable: consists of separate, indivisible categories. No values between two
categories.
(e.g. one score 18 people and another score 17 people: no value in
between)
, Inleiding statistiek
Continuous variable: consists of divisible categories and has an infinite number of
possible values between categories
- Very rare to observe identical scores between individuals
- Mostly in intervals that are defined by boundaries (usually
rounded off numbers)
Real limits: boundaries of intervals for scores that are
represented on a continuous number line
Upper real limit: top of the interval
Lower real limit: bottom of the interval
(e.g. score of 31.1 indicates an upper real limit of 31.15
and a lower real limit of 31.05)
Score of 150.5 is neither assigned to 150 or 151.
Depends on own rule for rounding numbers.
Scales of measurement
- Nominal scale: set of categories that have different names but are not
systematically related and no quantitative distinctions (e.g. biology,
art)
- Ordinal scale: set of categories that have different names and are ordered in
rank. Yet the size of the difference between two categories is not
known
- Interval scale: set of categories that have different names, are ordered in
rank and form a series of intervals that are the same size. Has an
arbitrary zero point!: score of 0 is assigned to particular location on
the scale
- Ratio scale: set of categories that have different names, are ordered in rank
and form a series of intervals that are the same size. Doesn’t have an
arbitrary zero point!: score of 0 means there is a complete absence of
the dependent variable. This way the size of the difference between
scores can be measured in terms of a ratio
1.4 | Statistical Notation
N = number of scores in a population
n = number of scores in a sample
∑ (sigma) = summation
(e.g. ∑(X-1)2 = all individual scores for (X-1)2 added up)
- Always followed by a symbol or mathematical expression
- Use correct order of operations for mathematical operations
2 | Frequency Distributions
2.1 | Frequency Distributions and Frequency Distribution Tables
Frequency distribution: organized tabulation of the number of individuals located
in each category on the scale of measurement, procedure of
descriptive statistics
Organizes set of scores in order from highest to lowest & grouping
the same scores.
Frequency distribution tables
X as column heading for scores, f as column heading for frequencies.
Proportion measures the fraction of the total group that is associated with each
score. Also called relative frequencies.
f
proportion= p=
N
Uitzonderingen leerstof.................................................................................................... 3
Boek................................................................................................................................. 3
Appendix A: Basic Mathematics Review........................................................................3
1 | Introduction to Statistics.......................................................................................... 3
2 | Frequency Distributions............................................................................................ 5
3 | Central tendency...................................................................................................... 9
4 | Variability............................................................................................................... 11
5 | z-Scores: Location of Scores and Standardized Distributions.................................13
6 | Probability.............................................................................................................. 14
7 | Probability and Samples: The Distribution of Sample Means..................................15
8 | Introduction to Hypothesis Testing.........................................................................16
9 | Introduction to the t Statistic.................................................................................. 18
10 | The t Test for Two Independent Samples.............................................................19
11 | The t Test for Two Related Samples.....................................................................21
15 | Correlation............................................................................................................ 22
17 | The Chi-Square Statistic: Tests for Goodness of Fit and Independence................24
18 | The Binomial Test................................................................................................. 26
On-demand video’s........................................................................................................ 27
V3W1 | Het meten van variabelen en frequentieverdelingen......................................27
V1W2 | Centrale waardes van data............................................................................. 27
V2W2 | Spreiding van de data..................................................................................... 28
V1W3 | De z-score....................................................................................................... 28
V2W3 | Intro kansrekenen & de normale verdeling.....................................................29
V3W3 | De binomiale verdeling................................................................................... 29
V1W4 | Steekproeven en de verdeling van steekproefgemiddelden...........................29
V2W4 | Introductie hypothesetoetsing........................................................................30
V3W4 | Fouten bij inferenties...................................................................................... 31
V1W5 | Problemen met z-scores.................................................................................. 31
V2W5 | De t-statistiek.................................................................................................. 31
V3W5 | De one-sample hypothese-toets.....................................................................31
V1W6 | Onafhankelijke metingen................................................................................ 31
V2W6 | De t-waarde voor “independent measures designs”.......................................31
V3W6 | Hypothesetoetsing met de onafhankelijke t-toets...........................................32
V1W7 | Herhaalde metingen........................................................................................ 32
V2W7 | De t-waarde voor herhaalde metingen............................................................32
V3W7 | Hypothesetoetsing met de afhankelijke t-test................................................33
V1W9 | Effectgroottes.................................................................................................. 33
V2W9 | Betrouwbaarheidsintervallen..........................................................................33
V1W10 | Wat is statistische power?............................................................................. 33
V2W10 | Hoe kunnen we statistische power berekenen?............................................34
,Inleiding statistiek
V1W11 | Het idee van verbanden tussen variabelen...................................................34
V2W11 | Pearson correlatie......................................................................................... 34
V3W11 | Hypothese toetsing met de Pearson correlation...........................................35
V1W12 | Associaties tussen categorische variabelen..................................................35
V2W12 | De Chi-kwadraattoets voor verbanden tussen variabelen.............................35
V3W12 | Effectmaten voor de Chi-kwadraattoets........................................................36
V1W13 | De logica van de binomiaaltest.....................................................................36
V2W13 | Hypothesetoetsting met de binomiaaltest....................................................37
Overige aantekeningen van hoorcolleges.......................................................................38
08-03-22 (week 4)....................................................................................................... 38
19-04-22 (week 10)..................................................................................................... 38
Overige notities.............................................................................................................. 39
Paired sample t-test.................................................................................................... 39
,Inleiding statistiek
Uitzonderingen leerstof
- The effect size r2 for the t-test (page 281-284)
- Hartley’s F-max test (314-315)
- The “alternative to pooled variance” (Box 10.2 on page 315)
- Regression towards the mean (Box 15.3 on page 501)
- Partial correlations (page 502-505)
- The “special formula” for the Spearman correlation (page 514)
- Testing significance of the Spearman correlation (page 515-516)
- The point-biserial correlation (page 516-517)
- Special applications of the Chi-Square tests (page 587-591)
- “more about the binomial test. . . ” (page 612-617)
Boek
Appendix A: Basic Mathematics Review
Volgorde berekening: Haakjes
Kwadraten
Vermenigvuldiging/deling (van links naar rechts)
Plus/min (van links naar rechts)
Breuken delen vb.:
1| Introduction to
Statistics
1.1 | Statistics, Science, and Observations
Statistics/ statistical procedures: set of mathematical procedures for organizing,
summarizing and interpreting information
Population: set of all individuals of interest in a particular study
Parameter: (numerical) value that describes a population
Sample: set of individuals selected from a population, usually intended to represent
the population in a research study
Statistic: (numerical) value that describes a sample
Sampling error: natural discrepancy/error existing between a sample statistic and
the corresponding population parameter as the sample might not give a
perfectly accurate picture of the whole population
Variable: characteristic/condition that changes or has different values for different
individuals
Data: measurements or observations
Data set:collection of data
Datum/score/ raw score: single measurement or observation
Statistical methods
Descriptive statistics: statistics used to summarize, organize and simplify data
so they are more manageable
Inferential statistics: techniques that allow us to study samples and then
make generalizations about the populations from which they were
selected
,Inleiding statistiek
1.2 | Data Structures, Research Methods, and Statistics
Data structures
Correlational method: 2 different variables are observed to determine a
possible relationship (correlation)
Experimental method / experimental research strategy: 1 variable is
manipulated, another variable is
observed and measured. All other
variables are controlled
Experimental method
Characteristics:
1. Manipulation
2. Control
Variables that may influence the correlation:
1. Participant variables: characteristics that vary per individual (e.g. age,
gender)
2. Environmental variables: characteristics of the environment (e.g. weather,
time of day)
Control by:
- Using random assignment (equal chance of being assigned to each
condition)
- Matching (ensure equivalent groups/environments)
- Holding variables constant
Independent variable: variable manipulated by researcher
Dependent variable: variable observed to asses the treatment’s effect
Control condition: condition in which participants don’t receive experimental
treatment. Maybe receive a placebo
Experimental condition: condition in which participants receive experimental
treatment
Nonexperimental methods
: research designs that are not true experiments but still examine relationships
between variables by comparing groups of scores
Nonequivalent groups study: comparing 2 groups of scores but no control
over which participants go into which group
Pre-post study: obtaining 2 groups of scores by measuring the same variable
twice for each participant, but no control over the passage of time or
other variables changing with time
Quasi-independent variable: the ‘independent variable’ that is used to
create different groups in nonexperimental studies
1.3 | Variables and Measurement
Constructs: internal attributes/characteristics that cannot be directly observed but
can describe and explain behavior
Operational definition: measurement procedure for measuring an external behavior
and uses resulting measurements as a definition and measurement
of a hpothetical construct
Discrete variable: consists of separate, indivisible categories. No values between two
categories.
(e.g. one score 18 people and another score 17 people: no value in
between)
, Inleiding statistiek
Continuous variable: consists of divisible categories and has an infinite number of
possible values between categories
- Very rare to observe identical scores between individuals
- Mostly in intervals that are defined by boundaries (usually
rounded off numbers)
Real limits: boundaries of intervals for scores that are
represented on a continuous number line
Upper real limit: top of the interval
Lower real limit: bottom of the interval
(e.g. score of 31.1 indicates an upper real limit of 31.15
and a lower real limit of 31.05)
Score of 150.5 is neither assigned to 150 or 151.
Depends on own rule for rounding numbers.
Scales of measurement
- Nominal scale: set of categories that have different names but are not
systematically related and no quantitative distinctions (e.g. biology,
art)
- Ordinal scale: set of categories that have different names and are ordered in
rank. Yet the size of the difference between two categories is not
known
- Interval scale: set of categories that have different names, are ordered in
rank and form a series of intervals that are the same size. Has an
arbitrary zero point!: score of 0 is assigned to particular location on
the scale
- Ratio scale: set of categories that have different names, are ordered in rank
and form a series of intervals that are the same size. Doesn’t have an
arbitrary zero point!: score of 0 means there is a complete absence of
the dependent variable. This way the size of the difference between
scores can be measured in terms of a ratio
1.4 | Statistical Notation
N = number of scores in a population
n = number of scores in a sample
∑ (sigma) = summation
(e.g. ∑(X-1)2 = all individual scores for (X-1)2 added up)
- Always followed by a symbol or mathematical expression
- Use correct order of operations for mathematical operations
2 | Frequency Distributions
2.1 | Frequency Distributions and Frequency Distribution Tables
Frequency distribution: organized tabulation of the number of individuals located
in each category on the scale of measurement, procedure of
descriptive statistics
Organizes set of scores in order from highest to lowest & grouping
the same scores.
Frequency distribution tables
X as column heading for scores, f as column heading for frequencies.
Proportion measures the fraction of the total group that is associated with each
score. Also called relative frequencies.
f
proportion= p=
N
