Introduction to quantitative analysis
Petr Ocelík
ESS401 Social Science Methodology
6th October 2015
Outline
• Data and data types
• Descriptive vs. inferential statistics
• Introduction to R
Data
• Concept of data usually taken for granted.
• Data is information that has been collected
and recorded.
• What we understand as data depends on our
philosophical position.
• Quantitative research is typically embedded in
positivist tradition.
Types of data
• Qualitative vs. quantitative data.
• Typically described as words vs. numbers.
• Blaikie: all primary data start as words.
Data
• What does data consist of?
• Case: is a unit of observation / analysis.
• Variable: is a concept that can have different
mutually exclusive values.
• Value / score: particular category or point on
a measurement scale.
(Kittel 2013)
Case-by-variable matrix (Kittel 2013)
Discrete and continuous variables
• Discrete variables: separate values without
intermediate values.
– Categories (single, married, divorced)
– Whole numbers (0, 1, 2, …)
• Continuous variables: any value over certain
interval.
– Real numbers (0, 1, 1/3, 0.333, 3.14, …)
Levels of measurement
• Categorical measurement:
– Assigns entity to a discrete category.
• Metric measurement:
– Assigns entity to a position at a given numerical
scale.
Levels of measurement
• Categorical measurement:
– Nominal
– Ordinal
• Metric measurement:
– Interval
– Ratio
Nominal measurement
• Construction of categories must be:
• Homogeneous
• Mutually exclusive
• Exhaustive
• We can arbitrarily assign numbers to
categories.
Ordinal measurement
• Defined by same conditions as nominal level
plus orders categories along some dimension.
• We can order categories, but distance
between them is not equal.
• Numbers indicate only order of categories.
Interval measurement
• Defined by same conditions as ordinal level
plus scores on a scale are at the same
distance apart.
• We can measure and compare intervals.
• No true zero: position of zero is arbitrary.
• Measures how many (counts),
not how much (ratios).
Ratio measurement
• Defined by same conditions as interval level
plus it has true zero.
• We can measure and compare ratios /
proportions.
• Degrees Celsius (interval) vs.
degrees Kelvin (ratio).
(Kittel 2013)
What do we mean by statistics
• Broad sense: collection and analysis of
numeric data.
• Narrow sense: “the mathematics of the
collection, organization, and interpretation of
numerical data, especially analysis of
population characteristics by inference from
sampling.” (American Heritage Dictionary).
Population and sample
• Population: a particular complete set of
objects / items with at least one shared
property of our interest.
– Parameter: numerical description of population
characteristic.
• Sample: a subset of population from which
data is collected.
– (Sample) statistic: numeric description of sample
characteristic.
Descriptive vs. inferential stats
• Descriptive: accounts for summarizing and
describing data.
• Inferential: uses sample statistics to estimate
population parameters.
Sampling
• Simple random sample:
– Define population
– Define sampling frame
– Specify sampling method
– Choose desired number of items to sample
Sampling variability: R example
• Population: sequence of whole numbers from
0 up to 100.
• Cases: integers from 0 up to 100.
• Mean of the population (parameter) = 50.
• Sample: 10 randomly drawn numbers from
the population.
• Mean of the sample (statistic).
Sampling error
• Sampling error: the difference between the
values of sample statistic and population
parameter.
• Sampling error is caused by random selection
of the sample.
• There is always sampling error since sample
does not include all members of population.
Sampling
• Simple random sample
• Stratified random sample
• Cluster random sample
Non-sampling errors
• Measurement error: the difference between
measured value of a quantity and its true
value.
– Systematic
– Random
Non-sampling errors
• Response bias
– Question wording
– Social acceptability
– Response set
• Non-response bias
– Refusal to participate in survey
– Refusal to respond a specific question
– Missing data
R: advantages
• Freeware
• Open source
• Worldwide active community
• Flexible and developed
R community / sources
• There is huge number of free resources
• R package / library manuals
• R site: http://cran.r-project.org
• Community forums:
– http://stackoverflow.com
– http://www.statmethods.net
– http://www.r-bloggers.com
• Youtube videos:
https://www.youtube.com/watch?v=qHfSTRNg6jE
• Googling (often fastest)
R libraries / packages
• Library / package:
– Can be though of as an extension that adds new
functionality.
– Libraries must be installed (just before the first
use) and loaded.
– Sometimes there can be conflicts among libraries
(e.g. different functions with same names) – we
can unload them.
– Often there are dependencies among libraries
(some libraries use functions from other libraries).
R: disadvantages
• Not as easily accessible as “clicking-programs”
• Data preparation could be demanding
• Could be slower for large datasets
R language
• object-oriented programming
– object: instance of certain data class that can be
manipulated according set of procedures (methods)
• functional-oriented programming
– function: relation that associates input(s) with
output(s)
• We can define certain objects and apply
functions on them and vice versa.
Data types
• Numeric: continuous numeric data (-1, 0.5, 10.49)
• Integer: discrete numeric data (-1, 0, 1, …)
• Character: string values = “anythingwithinquotes"
• Logical: output of logical operation
5 > 10 = FALSE
5 < 7 | 7 > 10 = TRUE
Data types: factor
• Factor: variable that take limited number of discrete
values - levels (categorical variable).
• Factor function converts vector of values into vector
of factor values (always have form of character).
• Factors can be unordered (nominal variable) or
ordered (ordinal variable).
http://www.r-tutor.com/
R: object and function
• Object:
vector <- c(1,2,3,4,5)
• Function:
fun <- function(x) { x^2 }
• Output:
fun(vector) = 1, 4, 9, 16, 25
• Nesting:
fun_2 <- function(x) { fun(x) + 1 }
R functions
• word() indicates function
• mean(vector)
• function(argument_1, argument_2, …)
• sample(0:100, 10, rep=FALSE)
• basic functions (part of the basic R package)
• package functions (part of the particular package)
• user functions (user-defined functions)
R objects
• Vector
– Sequence (1-dimensional) of elements of same data type
• Matrix
– 2-dimensional rectangular collection of elements of same
data type
– Array: n-dimensional matrix.
• List
– Vector that can contain elements of different data types
• Data frame
– List of vectors of equal length
– Table data
Vector
http://www.r-tutor.com/
Matrix
http://www.r-tutor.com/
List
http://www.r-tutor.com/
Data frame
http://www.r-tutor.com/