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