Advanced Statistical Topics

This section is intended to be a quick reference for a selection of basic statistical tools for hypothesis testing. You can also calculate confidence intervals for most of these examples based on the descriptive measures. Before using this reference, review the definitions in the Statistical Terms Dictionary to help you determine which statistic is best for your project.

Caution Sign Consider consulting with a statistician. You can contact a statistician on the NEDARC staff. All statistical tests rely on mathematical assumptions which should be evaluated prior to using and interpreting the statistics.

How to use the tables (below):

Determine what type of outcome you are evaluating. Options include continuous, categorical, and survival.
Determine whether you are describing a single sample, comparing two or more independent samples, or evaluating matched pairs or repeated measures.
Review the purpose of the statistic you want to calculate and the conditions or assumptions that apply. You may need to discuss the appropriate tool with NEDARC statisticians.
Calculate your test statistic and p-value (hypothesis testing) or confidence interval in your statistical software of choice. Remember to consider how your project was designed when interpreting your results!

The following tables are available:

Continuous Outcomes

Categorical Outcomes

Survival (Time-to-Event) Outcomes

Continuous Outcomes
Groups	Purpose	Conditions or Assumptions	Test	Descriptive Measures (also used to calculate CIs)
Single sample	Compare mean to historical or hypothetical (known) mean	Standard deviation known or N large and approximate normality	One-sample z-test	Mean, std deviation, difference from historical mean
	Compare mean to historical or hypothetical (known) mean	Standard deviation unknown; approximate normality	One-sample t-test	Mean, std deviation, difference from historical mean
Two independent samples	Compare means	Approximate normality	Two-sample t-test	Means, std deviations, pooled std deviation, difference in means
	Compare medians (Pr (X < Y))	Use for highly non-normal outcomes	Wilcoxon rank-sum test Mann-Whitney U test	Medians, quartiles, difference between medians
Two+ independent samples	Compare means (any or overall difference)	Approximate normality	Analysis of variance (ANOVA)	Means, std deviations, pairwise differences in means
	Compare medians (outcome distributions)	Use for highly non-normal outcomes	Kruskal-Wallis test	Medians, quartiles, pairwise differences in medians
Matched Pairs (2)	Evaluate whether mean of differences nonzero	Approximate normality	Paired t-test	Mean of differences, std deviation of differences
	Evaluate whether median of differences nonzero	Use for highly non-normal outcomes	Wilcoxon sign-rank test	Median of differences, quartiles of differences
Matched Sets (> 2)	Evaluate whether mean of differences nonzero	Approximate normality	Repeated measures ANOVA	Mean of differences, std deviation of differences
	Evaluate whether median of differences nonzero	Use for highly non-normal outcomes	Friedman test	Median of differences, quartiles of differences

Categorical Outcomes
Groups	Purpose	Conditions or Assumptions	Test	Descriptive Measures (also used to calculate CIs)
Single sample	Compare proportion to historical or hypothetical (known) proportion	N > 30	One-sample z-test (exact binomial N < 30)	Proportion, difference from historical proportion
	Compare proportion to historical or hypothetical (known) proportion		Exact binomial test (one-sample)	Proportion, difference from historical proportion
	Compare proportion(s) to hypothetical (known) proportion(s)	Allows overall comparison of > 2 categories	Pearson's goodness-of-fit Chi-square	Proportion(s) relative to historical proportion(s)
Two independent samples	Compare proportions (absolute difference)	N large (> 30)	Normal approximation to binomial	Difference between two proportions
	Compare proportions (absolute difference)		Exact binomial test (two samples)	Difference between two proportions
Two+ independent samples	Compare proportions or test for association	Expected cell count > 1; most > 5	Chi-square test	Odds ratio, row and column percentages,
	Compare proportions and test for association	Use for empty cells or small cell counts	Fisher's exact test	Odds ratio, row and column percentages,
	Compare rates and test for association	Population denominators available (able to calculate valid rates)	Chi-square or Fisher's exact test	Relative risk, row and column percentages
Matched Pairs (2)	Compare proportions or test for association		McNemar's test	Difference between two proportions (different std dev than unmatched)
Matched Sets (> 2)	Compare proportions or test for association		Cochrane Q test	Difference between pairs of proportions

Survival (Time-to-Event) Outcomes
Groups	Purpose	Conditions or Assumptions	Test	Descriptive Measures (also used to calculate CIs)
Single sample	Describe survival and hazard	Non-informative censoring; reasonable number of events	One-sample log-rank test	Kaplan-Meier survival curve, median survival, hazard
Two+ independent samples	Compare survival	Non-informative censoring; reasonable number of events	Log-rank test	Kaplan-Meier survival curves, median survival, hazard ratio
Matched Pairs or Sets (2+)	Compare survival	Non-informative censoring; reasonable number of events	Sign test or conditional proportional hazards	Kaplan-Meier survival curves, median survival, hazard

rev. 23-Oct-2008

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Analyzing Data:

Analyzing Data for Performance Measures

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