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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

 

 

 

rev. 04-Aug-2022

 

 

 

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This website is supported by the Health Resources and Services Administration (HRSA) of the U.S. Department of Health and Human Services (HHS) as part of the Emergency Medical Services for Children Data Center award totaling $3,200,000 with 0% financed with non-governmental sources. The contents are those of the author(s) and do not necessarily represent the official views of, nor an endorsement, by HRSA, HHS, or the U.S. Government. For more information, please visit HRSA.gov.

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