Chapter 19
Learning Objective 1
Distinguish between univariate and multivariate
analyses.
Univariate analyses are conducted on individual variables; multivariate analyses
involve multiple variables.
Learning Objective 2
Describe frequency analysis.
A frequency analysis, or one-way tabulation, is a univariate technique that involves
counting the number of responses that fall into various response categories.
Learning Objective 3
Explain the various ways in which frequency analysis can be used.
Frequency analysis can be used (1) to communicate the results of a study, (2) to
determine the degree of item nonresponse, (3) to locate blunders, (4) to locate outliers,
and (5) to determine the empirical distribution of the variable in question.
Learning Objective 4
Discuss confidence intervals for proportions.
The confidence interval is the range within which a population parameter will lie, with
a given level of confidence based on a statistic obtained from a probabilistic sample
(usually 95% confidence).
Learning Objective 5
Describe commonly used descriptive statistics.
The most commonly used descriptive statistics for continuous measures (interval- or
ratio-level measures) are the mean, or arithmetic average, and the standard deviation.
The mean is a measure of central tendency; the standard deviation provides a
convenient measure of the dispersion of responses.
Learning Objective 6
Discuss confidence intervals for means.
The confidence interval is the range within which the true mean value for the
population will fall, with a given level of confidence (usually 95%). The confidence
interval is equal to the sample mean plus or minus estimated sampling error.
Learning Objective 7
List the steps involved in hypothesis testing.
The steps in hypothesis testing include
1. Specify null and alternative hypotheses
2. Choose the appropriate test statistic
3. Specify significance level for the test
4. Compute value of test statistic based on sample data
5. Determine probability of test statistic given true null hypothesis
6. Compare obtained probability with specified significance level
Learning Objective 8
Describe the chi-square goodness-of-fit test and compare it to the KolmogorovSmirnov test.
The chi-square goodness-of-fit test is a univariate analysis in which the frequency
distribution obtained on a categorical variable is compared against a standard to
determine if the obtained frequency is statistically different from the standard. The
Kolmogorov-Smirnov test is a similar, but more powerful, univariate analysis that can
be applied if the categories are ordinal in nature.
Learning Objective 9
Discuss the process for comparing a proportion against a standard.
A sample proportion is compared against a standard by calculating a z statistic, finding
the probability of obtaining this level of z given a true null hypothesis, and comparing
the obtained probability with the significance level of the test.
Learning Objective 10
Describe the appropriate tests for comparing a mean against a standard for (a)
small samples and (b) large samples.
For small samples, a sample mean is compared against a standard by calculating a t
statistic, finding the probability of the obtained t statistic given a true null hypothesis,
and comparing the obtained probability with the significance level of the test. For
large samples, the process is similar, except that a z statistic is calculated instead of the
t statistic.