2021/2022 Statistical Methods
in Research
An extensive summary of Research
Training I
G. Rozenblad
ERASMUS UNIVERSITY ROTTERDAM – PREMASTER
INTERNATIONAL BUSINESS ADMINISTRATION
,Table of Contents
Module 1: Elements of statistical research......................................................................... 3
Examples of statistical research....................................................................................... 3
Presentation of statistical research .............................................................................. 3
School example ............................................................................................................. 3
Choosing the appropriate statistical methods and techniques ................................. 3
Variables ......................................................................................................................... 3
Measurement levels of variables ................................................................................. 4
Qualitative measurement levels: ................................................................................. 4
Quantitative measurement levels: .............................................................................. 4
Degeneration ................................................................................................................ 4
Enhancement ................................................................................................................ 4
Summary measures (or descriptive measures) .......................................................... 4
Bar chart vs. Pie chart ................................................................................................... 4
Histogram ....................................................................................................................... 4
Frequency table ............................................................................................................ 4
Complexity of analyses ................................................................................................. 5
Business and empirical research ..................................................................................... 5
Business and management: empirical science ......................................................... 5
Assumptions of empirical research.............................................................................. 5
Models ................................................................................................................................ 6
Causal relationship schemes ....................................................................................... 6
Causality and association ............................................................................................ 6
Causal patterns ............................................................................................................. 7
Role of models in research ........................................................................................... 8
Module 2: Population and sample, descriptive analysis and statistical estimation ... 10
Sample and population ................................................................................................. 10
Concepts...................................................................................................................... 10
Sampling errors ............................................................................................................ 11
Descriptive analysis ......................................................................................................... 11
Quantitative data ....................................................................................................... 11
Qualitative data .......................................................................................................... 12
Reporting: Figures and tables .................................................................................... 13
Inferential analysis: basic concepts .............................................................................. 14
Properties of sample statistics .................................................................................... 14
1
, Summary of sampling distributions ............................................................................ 16
Inferential analysis: estimation ....................................................................................... 16
Concept and estimation problem ............................................................................ 16
Background interval estimation and summary ........................................................ 18
Applications: mean, variance and proportion ........................................................ 20
Particularities of statistical estimation ........................................................................... 22
Interpretation of interval estimators .......................................................................... 22
Accuracy of interval estimators ................................................................................. 23
Determine minimum required sample size ............................................................... 24
Module 3: Hypothesis Testing ............................................................................................ 26
Univariate testing: idea .................................................................................................. 26
Testing: 7-steps scheme (Neyman-Pearson procedure) ............................................ 29
Overview test statistics and example test variance ................................................... 32
Overview test statistics ................................................................................................ 32
Example test variance ................................................................................................ 33
Peculiarities hypothesis testing ...................................................................................... 35
Reporting ...................................................................................................................... 35
Choice significance level α ........................................................................................ 35
One-sided and two-sided testing .............................................................................. 36
Fisher's p-approach to testing .................................................................................... 36
Type II errors and power of a test .............................................................................. 39
Minimum required sample size................................................................................... 42
Significance and relevance....................................................................................... 43
Module 4: Analysis of pairwise associations.................................................................... 45
Analysis of dependencies .............................................................................................. 45
Overview methods and techniques ......................................................................... 45
Parametric and non-parametric techniques ........................................................... 47
Techniques for independent and dependent samples ......................................... 47
Analysis method and points of attention.................................................................. 48
Core concept: statistical independence .................................................................... 49
Causality and statistical dependence ..................................................................... 49
Definition of statistical independence ...................................................................... 49
2
, Statistical Methods in Research I
Module 1: Elements of statistical research
Examples of statistical research
Presentation of statistical research
o The title, graph as a whole, matching header?, x- and y-axis, does the axis start
at 0?, comparison of data
School example
o Research question, which methods and techniques are appropriate to analyse
these data?
o Research design
- time series [one single unit that is observed at multiple moments or periods in
time] (e.g. daily cases corona)
- cross section [variables that are measured at a moment in time and deal with
different versions of the same unit of analyses](e.g. elections)
- panel [combinations of time series and cross section) (e.g. state voting
behaviour for all US elections instead of just one/daily covid cases for a year
in different regions of a country)
o Sampling design
- random (but in practice too costly)
- stratified
- cluster
o Information content variables (measurement level)
- nominal, ordinal, interval or ratio
o Complexity analysis
- Univariate (limited to one variable at a time)
- Bivariate (relations between two or more variables)
- Multivariate (relations between two or more variables)
o Other
- Communication, politics, resources, etc.
Choosing the appropriate statistical methods and techniques
Variables
Quantities (aspects of subjects, processes or phenomena) that can have varying
outcomes for different subjects or for the same subjects on different moments in time
o Measured on their own or together with other quantities:
- Univariate analysis: a single variable (height)
- Bivariate analysis: two variables (height, weight)
- Multivariate analysis: more variables (height, weight, gender)
o The scale on which variables are measured defines their measurement level;
Measurement levels determine the interpretation and application possibilities of
observation outcomes
3
in Research
An extensive summary of Research
Training I
G. Rozenblad
ERASMUS UNIVERSITY ROTTERDAM – PREMASTER
INTERNATIONAL BUSINESS ADMINISTRATION
,Table of Contents
Module 1: Elements of statistical research......................................................................... 3
Examples of statistical research....................................................................................... 3
Presentation of statistical research .............................................................................. 3
School example ............................................................................................................. 3
Choosing the appropriate statistical methods and techniques ................................. 3
Variables ......................................................................................................................... 3
Measurement levels of variables ................................................................................. 4
Qualitative measurement levels: ................................................................................. 4
Quantitative measurement levels: .............................................................................. 4
Degeneration ................................................................................................................ 4
Enhancement ................................................................................................................ 4
Summary measures (or descriptive measures) .......................................................... 4
Bar chart vs. Pie chart ................................................................................................... 4
Histogram ....................................................................................................................... 4
Frequency table ............................................................................................................ 4
Complexity of analyses ................................................................................................. 5
Business and empirical research ..................................................................................... 5
Business and management: empirical science ......................................................... 5
Assumptions of empirical research.............................................................................. 5
Models ................................................................................................................................ 6
Causal relationship schemes ....................................................................................... 6
Causality and association ............................................................................................ 6
Causal patterns ............................................................................................................. 7
Role of models in research ........................................................................................... 8
Module 2: Population and sample, descriptive analysis and statistical estimation ... 10
Sample and population ................................................................................................. 10
Concepts...................................................................................................................... 10
Sampling errors ............................................................................................................ 11
Descriptive analysis ......................................................................................................... 11
Quantitative data ....................................................................................................... 11
Qualitative data .......................................................................................................... 12
Reporting: Figures and tables .................................................................................... 13
Inferential analysis: basic concepts .............................................................................. 14
Properties of sample statistics .................................................................................... 14
1
, Summary of sampling distributions ............................................................................ 16
Inferential analysis: estimation ....................................................................................... 16
Concept and estimation problem ............................................................................ 16
Background interval estimation and summary ........................................................ 18
Applications: mean, variance and proportion ........................................................ 20
Particularities of statistical estimation ........................................................................... 22
Interpretation of interval estimators .......................................................................... 22
Accuracy of interval estimators ................................................................................. 23
Determine minimum required sample size ............................................................... 24
Module 3: Hypothesis Testing ............................................................................................ 26
Univariate testing: idea .................................................................................................. 26
Testing: 7-steps scheme (Neyman-Pearson procedure) ............................................ 29
Overview test statistics and example test variance ................................................... 32
Overview test statistics ................................................................................................ 32
Example test variance ................................................................................................ 33
Peculiarities hypothesis testing ...................................................................................... 35
Reporting ...................................................................................................................... 35
Choice significance level α ........................................................................................ 35
One-sided and two-sided testing .............................................................................. 36
Fisher's p-approach to testing .................................................................................... 36
Type II errors and power of a test .............................................................................. 39
Minimum required sample size................................................................................... 42
Significance and relevance....................................................................................... 43
Module 4: Analysis of pairwise associations.................................................................... 45
Analysis of dependencies .............................................................................................. 45
Overview methods and techniques ......................................................................... 45
Parametric and non-parametric techniques ........................................................... 47
Techniques for independent and dependent samples ......................................... 47
Analysis method and points of attention.................................................................. 48
Core concept: statistical independence .................................................................... 49
Causality and statistical dependence ..................................................................... 49
Definition of statistical independence ...................................................................... 49
2
, Statistical Methods in Research I
Module 1: Elements of statistical research
Examples of statistical research
Presentation of statistical research
o The title, graph as a whole, matching header?, x- and y-axis, does the axis start
at 0?, comparison of data
School example
o Research question, which methods and techniques are appropriate to analyse
these data?
o Research design
- time series [one single unit that is observed at multiple moments or periods in
time] (e.g. daily cases corona)
- cross section [variables that are measured at a moment in time and deal with
different versions of the same unit of analyses](e.g. elections)
- panel [combinations of time series and cross section) (e.g. state voting
behaviour for all US elections instead of just one/daily covid cases for a year
in different regions of a country)
o Sampling design
- random (but in practice too costly)
- stratified
- cluster
o Information content variables (measurement level)
- nominal, ordinal, interval or ratio
o Complexity analysis
- Univariate (limited to one variable at a time)
- Bivariate (relations between two or more variables)
- Multivariate (relations between two or more variables)
o Other
- Communication, politics, resources, etc.
Choosing the appropriate statistical methods and techniques
Variables
Quantities (aspects of subjects, processes or phenomena) that can have varying
outcomes for different subjects or for the same subjects on different moments in time
o Measured on their own or together with other quantities:
- Univariate analysis: a single variable (height)
- Bivariate analysis: two variables (height, weight)
- Multivariate analysis: more variables (height, weight, gender)
o The scale on which variables are measured defines their measurement level;
Measurement levels determine the interpretation and application possibilities of
observation outcomes
3
