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

STUDY OBJECTIVES 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 X X

Mode X X XMedian X XMean X

UNIVARIATE STATISTICS: Measures of Dispersion

LEVEL/MEASURE

Nominal Ordinal Interval or Ratio

Range XVariance XStandardDeviation

X

BIVARIATE STATISTICS: Nonparametric Tests of Association

SAMPLE/LEVEL

IndependentSamples

RelatedSamples

Nominal Fisher’s exact test(2X2 table)Chi-square contingency table analysis

McNemar test for significance of changes (2X2 table)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

MEASURE/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

MEASURE/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 analysisLog linear analysisWeighted least squaresMantel-Haenszel chi-square

Cochran Q-test

Ordinal (association of ranks between three or more rank variables)

Chi-square multi-dimensional contingency table analysis

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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

Multiple regression(where Y = change or difference score)

Mixed (differences in means between groups, controlling for Z)

ANOVA, when Z=nominalANCOVA, when Z=interval

ANOVA w/repeated measuresANCOVA 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

MEASURE/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)

Multiple correlation coefficient

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).