This document provides an overview of key concepts in data analysis, including: 1) Data is organized in a matrix with observations as rows and variables as columns. 2) There are two types of variables - numerical/quantitative and categorical/qualitative. Numerical variables can be continuous or discrete. 3) Variables can be associated (dependent) if connected or independent if no evident connection. Hypothesis testing involves starting with a null hypothesis, conducting a test assuming it is true, and either rejecting or not rejecting the null in favor of the alternative hypothesis based on test results.

1. +
Data Basics
Slides edited by Valerio Di Fonzo for www.globalpolis.org
Based on the work of Mine Çetinkaya-Rundel of OpenIntro
The slides may be copied, edited, and/or shared via the CC BY-SA license

2. Data matrix
Data are organized in what we call a data matrix, where each row
represents an observation or a case, and each column represents a
variable:

3. Types of variables
There are two types of variables,
numerical and categorical. Numerical, in
other words quantitative, variables take on
numerical values. It is sensible to add,
subtract, take averages, et cetera, with
these values. Categorical, or qualitative,
variables. Take on a limited number
of distinct categories. These categories
can be identified with numbers. For
example, it is customary to see the gender
variable coded as zero for male and one
for females, but it wouldn't be sensible to
do arithmetic operations with these
values.
Numerical variables can further be
categorized as continuous or discrete.
Continuous numerical variables are
usually measured, such as height.
These variables can take on any
number of infinite values given,
within a given range. Discrete
numerical variables are those
that take on one of a specific set of
numeric values where we're able to
count or enumerate all of the
possibilities. One example of a
discrete variable is the number of cars
a household owns. In general, count
data are an example of discrete
variables.
Categorical variables that have
ordered levels are called ordinal.
Think about a survey question
where you're asked how satisfied
you are with the customer service
you received. And the options are
very unsatisfied, unsatisfied, neutral,
satisfied, and very satisfied. These
levels have an inherent ordering.
Hence the variable would be called
ordinal. If the levels of categorical
variable do not have an inherent
ordering to them, then the variable is
simply called categorical.

4. Types of variables (cont.)
gender - categorical
sleep - numerical, continuous
bedtime - categorical, ordinal
countries - numerical, discrete
dread - categorical, ordinal (could also be used as numerical)

5. Associated vs. independent
● When two variables show some connection with one
another, they are called associated variables.
○ Associated variables can also be called
dependent variables and vice-versa.
● If two variables are not associated, i.e. there is no
evident connection between the two, then they are
said to be independent.

6. Hypothesis Testing Framework
● We start with a null hypothesis (H0) that represents the status
quo.
● We also have an alternative hypothesis (HA) that represents
our research question, i.e. what we're testing for.
● We conduct a hypothesis test under the assumption that the
null hypothesis is true, either via simulation or theoretical
methods.
● If the test results suggest that the data do not provide
convincing evidence for the alternative hypothesis, we stick
with the null hypothesis. If they do, then we reject the null
hypothesis in favor of the alternative.
N.B. The slides of the case study on gender discrimination provide specific
information regarding hypothesis testing.