QUANTITATIVE DATA
ANALYSIS
Chapter 11
LEVELS OF MEASUREMENT
• Variable attributes: the characteristics or
qualities that describe a variable
• Variable attributes can be defined at four
different levels of measurement
– Nominal
– Ordinal
– Interval
– Ratio
Nominal Measurement
• The lowest level of measurement
• Attributes or response categories of a
variable are
– mutually exclusive
Ordinal Measurement
• Second highest level of measurement
• Attributes or responses categories or a
variable are
– Mutually exclusive
– Rank ordered
Interval Measurement
• Third highest level of measurement
• Attributes or responses categories or a
variable are
– Mutually exclusive
– Rank ordered
– Equal distance from each other
Ratio Measurement
• Highest level of measurement
• Attributes or responses categories or a
variable are
– Mutually exclusive
– Rank ordered
– Equal distance from each other
– Based on a true 0 point
COMPUTER APPLICATIONS
• Variables must be coded (assigned a
distinct value) for data to be processed by
computer software
• The researcher must know the level of
measurement for each variable to
determine which statistical tests to use
DESCRIPTIVE STATISTICS
• Summarize a variable of interest and
portray how that particular variable is
distributed in the sample or population
– Frequency distributions
– Measures of Central Tendency
– Measures of Variability
Frequency Distributions
• A counting of the occurrences of each
response value of a variable, which can be
presented in
– Table form
– Graphic form (Frequency Polygon)
Measures of Central Tendency
• The value that represents the typical or
average score in a sample or population
• Three types:
– Mode, Median, and Mean
• Normal Curve: a bell-shaped frequency
polygon in which the mean, median, and
mode represent the average equally (See
Figure 17.4)
Mode
• The score or response value that occurs
most often (i.e., has the highest frequency)
in a sample or population
• Minimum level of measurement is nominal
Median
• The score or response value that divides
the a distribution into two equal halves
• Minimum level of measurement is ordinal
Mean
• Calculated by summing individual scores
and dividing by the total number of scores
• The most sophisticated measure of central
tendency
• Minimum level of measurement is interval
Measures of Variability
• A value or values that indicated how
widely scores are distributed in a sample
or population; a measure of dispersion
• Two common types
– Range
– Standard Deviation
Range
• The distance between the minimum and
maximum score in a distribution
• The larger the range, the greater the
amount of variation of scores in a
distribution
• Minimum level of measurement is ordinal
Standard Deviation
• A mathematically calculated value that
indicates the degree to which scores in a
distribution are scattered or dispersed
about the mean
• The mean and standard deviation define
the basic properties of the normal curve
• Minimum level of measurement is interval
INFERENTIAL STATISTICS
• Make it possible to study a sample and
“infer” the findings of that study to the
population from which the sample was
randomly drawn
• Based on chance or probability of error
– Commonly accepted levels of chance are
p < .01 (1 in 100) and p < .05 (5 in 100)
Statistics that Determine
Associations
• Statistics that determine whether or not a
relationship exists between two variables
• The values of one variable co-vary with
the values of another variable
– Chi-square (2)
– Correlation (r)
Chi-Square (2)
• Used with nominal or ordinal levels of
measurement
• Provides a measure of association based
on observed (actual scores) and expected
(statistically estimated) frequencies
• The direction or strength of the
relationship between the two variables is
not specified
Correlation (r)
• Typically used with interval and ratio levels
of measurement
• A measure of association between two
variables that also indicates direction and
strength of the relationship
– r=0 (no relationship), r=1.00 (perfect
relationship)
– A +r value (a direct relationship), -r value (an
inverse relationship)
Statistics that Determine
Differences
• Statistics used to determine whether group
differences exist on a specified variable
• Differences between
– Two related groups: Dependent t-test
– Two unrelated groups: Independent t-test
– More than two groups: ANOVA
Dependent t-test
• Used to compare two sets of scores
provided by one group of individuals
– Example: pretest and posttest scores
Independent t-test
• Used to compare two sets of scores, each
provided by a different group of individuals
– Example: Fathers and Mothers
One-Way Analysis of Variance
• Used to compare three or more sets of
scores, each provided by a different group
of individuals
– Example: Fathers, Mothers, and Children
SUMMARY
• Statistics are used to analyze quantitative
data
• The level of measurement must be
specified for each variable
• Descriptive and Inferential statistics are
used to build knowledge about a sample
or population