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 (2)
Correlation (r)

19. 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

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