## The Basics of Quantitative Data Analysis

```  I.  What is statistics?
A.  A branch of applied mathematics concerned with decision-making.
B.  Types of statistics.
1.  Descriptive statistics.
a.  Numerically describing and summarizing the characteristics and
features of a set of objects.
b.  Frequency, central tendency, and dispersion.
c.  Tables, charts, and graphs.
2.  Inferential statistics.
a.  Drawing conclusions about the characteristics and features of
a large collection of objects by observing a small randomly
selected sample of the objects.
b.  Populations and samples.
c.  Statistics, parameters, and inference.
d.  Sampling and sampling distributions.
e.  Sampling error and probability.
f.  Estimation and hypothesis testing.

II.  The Role of Statistics in Research.
A.  The traditional model of science.
1.  Theories, models and hypotheses.
2.  Deductive logic and hypothesis testing.
B.  Empirical model building.
1.  Finding patterns in the data.
2.  Using inductive logic to build empirical models.

III.  The language of concepts and variables.
A.  Theories, models, and hypotheses.
1.  Concepts, variables, and statements of relationships.
2.  Description and explanation.
3.  Good models/hypotheses.
a.  Concepts are clear and precisely defined.
b.  Relationships between concepts are clear and stated precisely.
c.  Concepts can be measured and relationships evaluated.
B.  Operationalization and measurement of concepts.
1.  Defining concepts.
a.  Concepts as constructs.
b.  Conceptual definitions.
2.  Identifying and measuring indicators.
a.  Identifying indicators.
i.  Indicators should be valid.
ii.  Indicators should be reliable.
b.  Measuring indicators.
i.  Experiments.
ii.  Surveys.
iii.  Analysis of existing quantitative data.
iv.  Content analysis.
3.  Types of variables.
a.  Numerical variables.
i.  Continuous numerical variables.
ii.  Discrete numerical variables.
b.  Categorical variables.
i.  Categories should be exclusive.
ii.  Categories should be exhaustive.
4.  Levels of measurement.
a.  Nominal categorical variables.
b.  Ordinal categorical variables.
c.  Interval variables.
C.  Relationships between variables.
1.  Associations and correlation.
a.  Positive.
b.  Negative.
c.  Curvilinear.
2.  Causality.
a.  Causal statements.
i.  Independent, dependent, and intervening variables.
ii.  Direct causal relationships.
iii.  Indirect causal relationshps.
iv.  Interactions.
v.  Causal models.
b.  Criteria of causality.
i.  The variables must be associated.
ii.  The independent variable must precede the dependent
variable in time.
iii.  Other possible causes of change in the dependent variable
must be controlled.
3.  Spuriousness.```