1. ANALYSIS PLAN: STATISTICAL PROCEDURES
Lu Ann Aday, Ph.D.
The University of Texas
School of Public Health

2. TYPE OF ANALYSIS PROCEDURES: Alternative Assumptions
DESCRIPTIVE STATISTICS
Estimate for a sample
EXISTENCE OF ASSOCIATION
Statistically test the presence of a relationship
INDEPENDENT SAMPLES
Distinct or unrelated groups
INFERENTIAL STATISTICS
Infer to a population
STRENGTH OF ASSOCIATION
Statistically measure the strength of a relationship
RELATED
SAMPLES
Matched or correlated groups

3. TYPE OF ANALYSIS PROCEDURES: Alternative Assumptions
PARAMETRIC PROCEDURES
Random sampling
Normal distribution
> 30 cases
Interval or ratio data
NON-PARAMETRIC PROCEDURES
Random or nonrandom sampling
Normal or non-normal distribution
< 30 or > 30 cases
Nominal or ordinal data

4. RELATE STUDY OBJECTIVES & TYPE OF ANALYSIS
1. TO DESCRIBE
X, Y, or Z
2. TO COMPARE Y by X, or Z by X
3. TO TEST THE IMPACT/ANALYZE THE RELATIVE IMPORTANCE of X on Y [controlling for Z] (assumes Ho)
TYPE OF ANALYSIS
Univariate
Bivariate
Multivariate

5. UNIVARIATE STATISTICS: Measures of Central Tendency
LEVEL/
MEASURE
Nominal
Ordinal
Interval or Ratio
Frequencies X
Mode
Median
Mean

6. UNIVARIATE STATISTICS: Measures of Dispersion
LEVEL/
MEASURE
Nominal
Ordinal
Interval or Ratio
Range X
Variance
Standard
Deviation

7. BIVARIATE STATISTICS: Nonparametric Tests of Association
SAMPLE/
LEVEL
Independent
Samples
Related
Nominal
Fisher’s exact test
(2X2 table)
Chi-square contingency table analysis
McNemar test for significance of changes
Cochran Q-test
Ordinal
Chi-square contingency table analysis --
Mixed (differences in ranks between groups)
Median test Mann-Whitney U test Kolmogorov-Smirnov Wald-Wolfowitz runs test Kruskal-Wallis (3+ groups)
Sign test Wilcoxon matched-pairs signed ranks test Friedman two-way analysis of variance (3+ groups)

8. BIVARIATE STATISTICS: Nonparametric Measures of Strength of Association
LEVEL
MEASURES OF STRENGTH OF ASSOCIATION
Nominal
Phi coefficient, Yule’s Q (2XK table), Coefficient of contingency, Cramer’s V, Lambda, Odds ratio
Ordinal
Goodman and Kruskal’s gamma, Kendall’s tau-a, tau-b, tau-c, Somer’s d, Spearman rank order coefficient
Mixed
(differences in ranks between groups)
Lambda, uncertainty coefficient, Goodman and Kruskal’s gamma, Somer’s d, Eta coefficient

9. BIVARIATE STATISTICS: Parametric Tests of Association
SAMPLE/ LEVEL
Independent Samples
Related Samples
Interval or Ratio (extent to which Y has linear relationship
with X)
Bivariate regression
Bivariate regression (where Y = change or difference score)
Mixed (differences in means between groups)
t-test of difference between means (2 groups)
One-way ANOVA (3+groups)
Paired t-test of difference between means (2 groups) One-way ANOVA w/ repeated measures
(3+related measures)

10. BIVARIATE STATISTICS: Parametric Measures of Strength of Association
LEVEL
MEASURES OF STRENGTH OF ASSOCIATION
Interval or Ratio (extent to which Y has linear relationship with X)
Pearson correlation coefficient
Mixed (differences in means between groups)
Biserial correlation (2 groups) Eta coefficient (3+ groups)

11. MULTIVARIATE STATISTICS: Nonparametric Tests of Association
SAMPLE/
LEVEL
Independent Samples
Related Samples
Nominal
(cross-tabulation of dependent variable by independent by control variables)
Chi-square multi-dimensional contingency table analysis
Log linear analysis
Weighted least squares
Mantel-Haenszel chi-square
Cochran
Q-test
Ordinal (association of ranks between three or more rank variables) --

12. MULTIVARIATE STATISTICS: Nonparametric Measures of Strength of Association
MEASURE/ LEVEL
MEASURES OF STRENGTH OF ASSOCIATION
Nominal
(cross-tabulation of dependent variable by independent by control variable)
Coefficient of contingency, Cramer’s V, Lambda, Symmetric Lambda, Odds ratio
Ordinal (association of ranks between three or more rank variables)
Kendall coefficient of concordance

13. MULTIVARIATE STATISTICS: Parametric Tests of Association
SAMPLE/
LEVEL
Independent Samples
Related Samples
Interval or Ratio (extent to which Y has linear relationship with X, Z, etc.)
Multiple regression
(where Y = change or difference score)
Mixed (differences in means between groups, controlling for Z)
ANOVA, when Z=nominal
ANCOVA, when Z=interval
ANOVA w/repeated measures
ANCOVA w/repeated measures
Mixed (differences in proportions between groups, controlling for Z)
Logistic regression
Logistic regression of change in status

14. MULTIVARIATE STATISTICS: Parametric Measures of Strength of Association
LEVEL
MEASURES OF STRENGTH OF ASSOCIATION
Interval or Ratio (extent to which Y has linear relationship with X, Z, etc.)
Multiple correlation coefficient
Mixed (differences in means between groups, controlling for Z)
Mixed (differences in proportions between groups, controlling for Z)
Odds ratio

15. DATA ANALYSIS MATRIX STUDY OBJECTIVES TYPES OF VARIABLES
ANALYTIC PROCEDURES
TO DESCRIBE
One variable (neither independent or dependent)
Univariate
TO COMPARE
One independent and one dependent variable
Bivariate
TO ANALYZE THE RELATIVE IMPORTANCE
Two or more independent/controlvariables and one dependent variable
Multivariate

17. STATISTICAL PROCEDURE SELECTION: SOFTWARE
SELECTING STATISTICS
You could access and use the “Selecting Statistics” website in deciding which statistical procedures are most appropriate, given your study objectives and associated level of measurement of study variables:

18. SAMPLE MOCK & ANALYSIS TABLES
See Word file with Sample Mock Tables and Analysis Tables.

19. SURVEY ERRORS: Planning and Implementing the Analysis of the Data
Systematic Errors: poor statistical conclusion validity
Variable Errors: low statistical power or precision
Solutions to errors
Match the selection of statistical analysis procedures to the study design and objectives, level of measurement of study variables, and/or the underlying population distribution.
Map out the analysis plan to address each of the study objectives in advance of conducting the study, and estimate the number of cases required to achieve a desired level of power or precision for each objective (also see Chapter Seven).