Statistics I, Summary
Summary written by Saskia Kriege
Cognitive Science and Artificial Intelligence
Including all lectures from the whole semester, Lecture 1 – 12
,Lecture 1 – Introduction
Generating and Testing Theories
Theory =
Hypothesized general principle or set of principles that explains known findings about
a topic and from which new hypotheses can be generated
Hypothesis =
Prediction typically derived from theory/obersvation
Falsification =
Act of disproving a theory or hypothesis
Scales of measurement
Categorical =
Divided into distinct categories
- Binary → two categories
- Nominal → more than two categories
- Ordinal → same as nominal, but categories have logical order
Continuous =
- Interval → equal intervals on the variable represent equal differences in
property being measured
- Ratio → same as interval, but ratios of scores on the scale must also make
sense and have a true 0 value.
,Reliability of our measures
Reliability =
Ability of the measure to produce same results under same conditions
Test-retest reliability =
Ability of a measure to produce consistent results when the same entities are tested
at two different points in time
Inter-rater reliability =
Consistency across people, do they produce same answer?
Parallel Forms Reliability =
Do different measures that are supposed to measure the same thing actually
measure it the same?
Internal consistency reliability =
Do things that are supposed to measure the same thing actually measure it?
Common Types of Research
Correlational research =
Observing what naturally goes on in the world without directly interfering with it
Cross-sectional research =
Data come from people at different age points, with different people representing
each age point.
Could be quasi-experimental, case study, naturalistic observation
Experimental research =
One or more variable is systematically manipulated to see their effect on an outcome
variable.
Randomization
Statements can often be made about cause and effect
Be careful for:
- Confounds → unmeasured variable that could be related to the variables of
interest
- Artefacts → something that might threaten the external validity or construct
validity of your results
, Types of Validity
Internal validity =
Extent to which you are able to draw the correct conclusion about the causal
relationships between variables
External validity =
Generalizability of your findings. To what extent do you see the same pattern of
results in ‘real life’ as you saw in your study
Construct validity =
Whether you are actually measuring what you want to be measuring
Face validity =
Whether or not a measure ‘looks like’ it is doing what it is supposed to do
Ecological validity =
Entire set up of the study should closely approximate the real world scenario that is
being investigated
Lecture 2 – Introduction to R
& = and
| = or
! = not
If you don’t give an argument to R, it uses the default values (i.e. values that are
given automatically, for example rounded to 0 decimals)
Remove NA’s → na.rm = TRUE
Create function → name_function <- function(…)
fahrenheit_to_celsius <- function(temp_F) { temp_C <- (temp_F - 32) *
return(temp_C) }
Variables =
Used to store information, use <- to create
- Numeric variables → store numbers
- Character variables → store text (“bob”)
- Logical variables → TRUE/FALSE
Vectors =
Store multiple pieces of information
Create using c(), extract specific elements using [ ]
Data frames =
Way R stores a typical data set
Collection of variables ‘bundled’ together
Each row is a case
Each column is a variable
Summary written by Saskia Kriege
Cognitive Science and Artificial Intelligence
Including all lectures from the whole semester, Lecture 1 – 12
,Lecture 1 – Introduction
Generating and Testing Theories
Theory =
Hypothesized general principle or set of principles that explains known findings about
a topic and from which new hypotheses can be generated
Hypothesis =
Prediction typically derived from theory/obersvation
Falsification =
Act of disproving a theory or hypothesis
Scales of measurement
Categorical =
Divided into distinct categories
- Binary → two categories
- Nominal → more than two categories
- Ordinal → same as nominal, but categories have logical order
Continuous =
- Interval → equal intervals on the variable represent equal differences in
property being measured
- Ratio → same as interval, but ratios of scores on the scale must also make
sense and have a true 0 value.
,Reliability of our measures
Reliability =
Ability of the measure to produce same results under same conditions
Test-retest reliability =
Ability of a measure to produce consistent results when the same entities are tested
at two different points in time
Inter-rater reliability =
Consistency across people, do they produce same answer?
Parallel Forms Reliability =
Do different measures that are supposed to measure the same thing actually
measure it the same?
Internal consistency reliability =
Do things that are supposed to measure the same thing actually measure it?
Common Types of Research
Correlational research =
Observing what naturally goes on in the world without directly interfering with it
Cross-sectional research =
Data come from people at different age points, with different people representing
each age point.
Could be quasi-experimental, case study, naturalistic observation
Experimental research =
One or more variable is systematically manipulated to see their effect on an outcome
variable.
Randomization
Statements can often be made about cause and effect
Be careful for:
- Confounds → unmeasured variable that could be related to the variables of
interest
- Artefacts → something that might threaten the external validity or construct
validity of your results
, Types of Validity
Internal validity =
Extent to which you are able to draw the correct conclusion about the causal
relationships between variables
External validity =
Generalizability of your findings. To what extent do you see the same pattern of
results in ‘real life’ as you saw in your study
Construct validity =
Whether you are actually measuring what you want to be measuring
Face validity =
Whether or not a measure ‘looks like’ it is doing what it is supposed to do
Ecological validity =
Entire set up of the study should closely approximate the real world scenario that is
being investigated
Lecture 2 – Introduction to R
& = and
| = or
! = not
If you don’t give an argument to R, it uses the default values (i.e. values that are
given automatically, for example rounded to 0 decimals)
Remove NA’s → na.rm = TRUE
Create function → name_function <- function(…)
fahrenheit_to_celsius <- function(temp_F) { temp_C <- (temp_F - 32) *
return(temp_C) }
Variables =
Used to store information, use <- to create
- Numeric variables → store numbers
- Character variables → store text (“bob”)
- Logical variables → TRUE/FALSE
Vectors =
Store multiple pieces of information
Create using c(), extract specific elements using [ ]
Data frames =
Way R stores a typical data set
Collection of variables ‘bundled’ together
Each row is a case
Each column is a variable
