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