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

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

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

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

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

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

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)

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

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)

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)

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) --

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

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

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

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

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: http://www.socialresearchmethods.net/selstat/ssstart.htm

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

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).