Samenvatting Inleiding Statistiek boek EN on-demand video's (Zelf een 8 gehaald)
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Cours
Inleiding Statistiek (424504B5)
Établissement
Tilburg University (UVT)
Deze samenvatting bevat alle informatie zoals die gegeven werd in de on-demand video's van de docent en het boek "Statistics for the Behavioral Sciences" van Gravetter, Frederick J. Wallnau, en Larry B.. Het is een overzichtelijke samenvatting die niet is geschreven in volledige zinnen, maar enkel ...
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
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