This document provides an overview of descriptive and inferential statistics. Descriptive statistics summarize and describe data through measures like central tendency, variability, and relationships between variables. Inferential statistics help draw conclusions from samples to populations through hypothesis testing. Variables can be independent or dependent, discrete or continuous, and measured at the nominal, ordinal, or interval-ratio level. Different statistical analyses require different variable types and levels of measurement. The document concludes with examples of classifying variable levels and a homework assignment.

1. Chapter 1
The Functions of Statistics

2. Two Classes of Statistics:
1. Descriptive
2. Inferential

3. Descriptive Statistics:
Functions of Descriptive Statistics:
a) Data reduction:
 allow a few numbers to summarize many
b) Measures of association
 quantify strength and direction of a relationship.
Types of Descriptive Statistics:
 Univariate Descriptive Statistics:
 Describes the distribution of a single variable
 Bivariate Descriptive Statistics
 Summarize relationship between two variables
 Multivariate Descriptive Statistics
 Summarize relationship between 3 or more
variables

4. Inferential Statistics:

Functions of Inferential Statistics:
a) Aids researchers in drawing inferences from
samples to populations
 Population
 all cases in which the researcher is interested.
 Samples
 carefully chosen subsets of the population.
b) Used to test significance of hypotheses

5. Types Of Variables
 Variables may be:
 Independent or dependent
 Discrete or continuous
 Nominal, ordinal, or interval-ratio

6. Types Of Variables:
Independent or Dependent
 In causal relationships:
CAUSE

EFFECT
independent variable  dependent variable

7. Types Of Variables:
Discrete or Continuous
 Discrete variables are measured in units that cannot
be subdivided.
 Anything regarding people
 Wrong when you hear the average number of children per
household being 2 ½…
 Continuous variables are measured in a unit that
can be subdivided infinitely.

8. Types of Variables:
Level Of Measurement

Levels of Measurement represent different
levels of numerical information contained
within the variable:
1. Nominal
2. Ordinal
3. Interval-ratio

9. Nominal Level Variables
 Used to classify or categorize
 Simplest (or crudest) level of measurement
 Numbers are for classification purposes only
 Examples:
Religion: 1 = Protestant, 2 = Catholic, 3=Jew,
4=None, 5=Other
Gender (dichotomy): 1 = Female, 0 = Male

10. Ordinal Level Variables
 Used to rank or order in a logical way
 Scores can be ranked from high to low or from more
to less
 Offers the property of “more than” or “less than” to
classifications

11. Example of an Ordinal Level Variable:
“Do you agree or disagree that University Health
Services should offer free contraceptives?”
5=strongly agree
4=agree
3=neutral
2=disagree
1=strongly disagree
 Because you can distinguish between the
scores of the variable using terms such as
“more, less, higher, or lower” the variable is
ordinal.

12. Interval-ratio Variables
 Scores are “actual” numbers
 Ratio variables meet the criteria for interval but also
have meaningful and true zero points
 Have equal intervals between scores indicating exact
distance, thus:
 Can indicate “how much more” (or less)
 Permits the use of mathematical operations
 Examples:
Age (in years)
Income (in dollars)
Number of children
 A true zero point (0 = no children)
 Equal intervals: each child adds one unit

13.  Different statistics require different
mathematical operations (ranking, addition,
square root, etc.)
 The level of measurement of a variable tells us
which statistics are permissible and
appropriate.

14. Determining the Level of Measurement of a Variable

15. Classify the level of measurement of the
following variables and tell level of
measurement:
 The numbers on an athlete’s jersey
 The dorm you live in
 Number of children in a family
 Fear of crime ( a lot, some, none)
 Number of hours per day respondent watches tv
 Tuition in dollars

16. Homework Assignment for Chapter 1:
 Problems 1.5 and 1.7