Statistical Methods for the
Social Sciences
\
,Chapter 1: Introduction
1.2 Descriptive Statistics and Inferential Statistics
• A statistical analysis is classified as descriptive or inferential
Populations and samples
• Subjects = the entities on which a study makes observations
• Population = the total set of subjects of interest in a study
• Sample = the subset of the population on which the study collects data
• Descriptive statistics = summarize the information in a collection of data (graphs,
tables)
• Inferential statistics = provide predictions about a population, based on data from a
sample of that population
Parameters and statistics
• Parameter = a numerical summary of the population
Defining populations: actual and conceptual
• Conceptual population = a population that does not actually exist
• Clinical trial = a medical study
• Treatments = the conditions compared in a clinical or other experiment
Chapter 2: Sampling and measurement
2.1 Variables and Their Measurement
• Variable = a characteristic that can vary in value among subjects in a sample or
population
• Measurement scale = the values the variable can take (for gender → (fe)male)
- Numerical-valued variable (income)
- Measurement scale consisting of categories (yes, no)
Quantitative variables and categorical variables
• Quantitative = when the measurement scale has numerical values that represent
different magnitudes of the variable (income, age)
• Categorical = when the measurement scale is a set of categories (marital status)
→ Categorical variables are often called qualitative
, Nominal, ordinal, and interval scales of measurement
• For a quantitative variable, the possible numerical values are said to form an interval
scale, because they have a numerical distance or interval between each pair of levels.
• Categorical variables have 2 types of scales:
1. Nominal scale = unordered categories (no ‘high’ or ‘low’ end).
2. Ordinal scale = categorical scales having a natural ordering of values (social
class). This is not nominal because the categories are ordered. They are not interval,
because there is no defined distance between levels.
Quantitative aspects of ordinal data
• Levels of nominal scales are qualitative, varying in quality, not in quantity.
• Levels of interval scales are quantitative, varying in magnitude. Each level has a
greater of smaller magnitude than another level.
Discrete and continuous variables
• Discrete variable = if its possible values form a set of separate numbers (0, 1, 2, 3)
→ number of siblings
• Continuous variable = if it can take an infinite continuum of possible real number
values
→ height
• Variables are either quantitative (numerical-valued) or categorical. Quantitative
variables are measured on an interval scale. Categorical variables with unordered
categories have a nominal scale, and categorical variables with ordered categories
have ordinal scale.
• Categorical variables (nominal or ordinal) are discrete. Quantitative variables can be
either discrete or continuous. Quantitative variables that can take lots of values are
treated as continuous.
2.2 Randomization
• Randomization = the mechanism for achieving good sample representation
• Sample size = letting n denote the number of subjects in the sample
Simple random sampling
• Simple random sample (of n subjects from a population) = each possible sample of
that size has the same probability (chance) of being selected
How to select a simple random sample?
• Sampling frame = a list of all subjects in the population (needed to select a random
sample)
Social Sciences
\
,Chapter 1: Introduction
1.2 Descriptive Statistics and Inferential Statistics
• A statistical analysis is classified as descriptive or inferential
Populations and samples
• Subjects = the entities on which a study makes observations
• Population = the total set of subjects of interest in a study
• Sample = the subset of the population on which the study collects data
• Descriptive statistics = summarize the information in a collection of data (graphs,
tables)
• Inferential statistics = provide predictions about a population, based on data from a
sample of that population
Parameters and statistics
• Parameter = a numerical summary of the population
Defining populations: actual and conceptual
• Conceptual population = a population that does not actually exist
• Clinical trial = a medical study
• Treatments = the conditions compared in a clinical or other experiment
Chapter 2: Sampling and measurement
2.1 Variables and Their Measurement
• Variable = a characteristic that can vary in value among subjects in a sample or
population
• Measurement scale = the values the variable can take (for gender → (fe)male)
- Numerical-valued variable (income)
- Measurement scale consisting of categories (yes, no)
Quantitative variables and categorical variables
• Quantitative = when the measurement scale has numerical values that represent
different magnitudes of the variable (income, age)
• Categorical = when the measurement scale is a set of categories (marital status)
→ Categorical variables are often called qualitative
, Nominal, ordinal, and interval scales of measurement
• For a quantitative variable, the possible numerical values are said to form an interval
scale, because they have a numerical distance or interval between each pair of levels.
• Categorical variables have 2 types of scales:
1. Nominal scale = unordered categories (no ‘high’ or ‘low’ end).
2. Ordinal scale = categorical scales having a natural ordering of values (social
class). This is not nominal because the categories are ordered. They are not interval,
because there is no defined distance between levels.
Quantitative aspects of ordinal data
• Levels of nominal scales are qualitative, varying in quality, not in quantity.
• Levels of interval scales are quantitative, varying in magnitude. Each level has a
greater of smaller magnitude than another level.
Discrete and continuous variables
• Discrete variable = if its possible values form a set of separate numbers (0, 1, 2, 3)
→ number of siblings
• Continuous variable = if it can take an infinite continuum of possible real number
values
→ height
• Variables are either quantitative (numerical-valued) or categorical. Quantitative
variables are measured on an interval scale. Categorical variables with unordered
categories have a nominal scale, and categorical variables with ordered categories
have ordinal scale.
• Categorical variables (nominal or ordinal) are discrete. Quantitative variables can be
either discrete or continuous. Quantitative variables that can take lots of values are
treated as continuous.
2.2 Randomization
• Randomization = the mechanism for achieving good sample representation
• Sample size = letting n denote the number of subjects in the sample
Simple random sampling
• Simple random sample (of n subjects from a population) = each possible sample of
that size has the same probability (chance) of being selected
How to select a simple random sample?
• Sampling frame = a list of all subjects in the population (needed to select a random
sample)
