Introduction to statistics

Variables
•A variable is a characteristic or condition
that can change or take on different values.
•Most research begins with a general
question about the relationship between
two variables for a specific group of
individuals.
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Population
•The entire group of individuals is called the
population.
•For example, a researcher may be interested in
the relation between class size (variable 1) and
academic performance (variable 2) for the
population of third-grade children.
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Sample
•Usually populations are so large that a
researcher cannot examine the entire group.
Therefore, a sample is selected to represent the
population in a research study. The goal is to
use the results obtained from the sample to help
answer questions about the population.
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Types of Variables
•Variables can be classified as discrete or
continuous.
•Discrete variables (such as class size) consist of
indivisible categories, and continuous variables
(such as time or weight) are infinitely divisible
into whatever units a researcher may choose.
For example, time can be measured to the
nearest minute, second, half-second, etc.
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Measuring Variables
•To establish relationships between
variables, researchers must observe the
variables and record their observations.
This requires that the variables be
measured.
•The process of measuring a variable
requires a set of categories called a scale
of measurement and a process that
classifies each individual into one
category.
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4 Types of Measurement
Scales
1. A nominal scale is an unordered set of categories
identified only by name. Nominal measurements
only permit you to determine whether two
individuals are the same or different.
2. An ordinal scale is an ordered set of categories.
Ordinal measurements tell you the direction of
difference between two individuals.
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4 Types of Measurement Scales
3. An interval scale is an ordered series of equal-sized
categories. Interval measurements identify the
direction and magnitude of a difference. The zero
point is located arbitrarily on an interval scale.
4. A ratio scale is an interval scale where a value of
zero indicates none of the variable. Ratio
measurements identify the direction and
magnitude of differences and allow ratio
comparisons of measurements.
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Correlational Studies
• The goal of a correlational study is to determine whether there is a
relationship between two variables and to describe the relationship.
• A correlational study simply observes the two variables as they exist
naturally.
14

Experiments
•The goal of an experiment is to
demonstrate a cause-and-effect
relationship between two variables;
that is, to show that changing the
value of one variable causes changes
to occur in a second variable.
16

Experiments (cont.)
• In an experiment, one variable is manipulated to create
treatment conditions. A second variable is observed and
measured to obtain scores for a group of individuals in each
of the treatment conditions. The measurements are then
compared to see if there are differences between treatment
conditions. All other variables are controlled to prevent
them from influencing the results.
• In an experiment, the manipulated variable is called the
independent variable and the observed variable is the
dependent variable.
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Other Types of Studies
• Other types of research studies, know as non-
experimental or quasi-experimental, are
similar to experiments because they also
compare groups of scores.
• These studies do not use a manipulated
variable to differentiate the groups. Instead,
the variable that differentiates the groups is
usually a pre-existing participant variable (such
as male/female) or a time variable (such as
before/after).
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Other Types of Studies (cont.)
•Because these studies do not use the manipulation
and control of true experiments, they cannot
demonstrate cause and effect relationships. As a
result, they are similar to correlational research
because they simply demonstrate and describe
relationships.
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Data
•The measurements obtained in a research study
are called the data.
•The goal of statistics is to help researchers
organize and interpret the data.
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Descriptive Statistics
•Descriptive statistics are methods for organizing and
summarizing data.
•For example, tables or graphs are used to organize
data, and descriptive values such as the average score
are used to summarize data.
•A descriptive value for a population is called a
parameter and a descriptive value for a sample is
called a statistic.
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Inferential Statistics
•Inferential statistics are methods for using sample
data to make general conclusions (inferences) about
populations.
•Because a sample is typically only a part of the whole
population, sample data provide only limited
information about the population. As a result, sample
statistics are generally imperfect representatives of
the corresponding population parameters.
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Introduction to statistics

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