This document discusses quantitative data analysis and different levels of measurement and statistical techniques. It describes four levels of measurement - nominal, ordinal, interval, and ratio - and explains their characteristics. Descriptive statistics like frequency distributions, measures of central tendency (mode, median, mean), and measures of variability (range, standard deviation) are used to summarize variables. Inferential statistics allow researchers to generalize from a sample to a population and include techniques like chi-square, correlation, t-tests, and ANOVA to determine relationships, differences between groups, and whether differences could occur by chance.

1. QUANTITATIVE DATA
ANALYSIS
Chapter 11

2. 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

3. Nominal Measurement
• The lowest level of measurement
• Attributes or response categories of a
variable are
– mutually exclusive

4. Ordinal Measurement
• Second highest level of measurement
• Attributes or responses categories or a
variable are
– Mutually exclusive
– Rank ordered

5. Interval Measurement
• Third highest level of measurement
• Attributes or responses categories or a
variable are
– Mutually exclusive
– Rank ordered
– Equal distance from each other

6. 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

7. 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

8. 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

9. 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)

10. 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)

11. 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

12. Median
• The score or response value that divides
the a distribution into two equal halves
• Minimum level of measurement is ordinal

13. 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

14. 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

15. 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

16. 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

17. 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)

18. 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 (χ2
)
– Correlation (r)

19. Chi-Square (χ2
)
• 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

20. 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)

21. 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

22. Dependent t-test
• Used to compare two sets of scores
provided by one group of individuals
– Example: pretest and posttest scores

23. Independent t-test
• Used to compare two sets of scores, each
provided by a different group of individuals
– Example: Fathers and Mothers

24. 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

25. 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