Types of statistical tests

Background

There are many statistical tests used for biomedical research. The type of test depends on the type of data, population type, distribution, and number of groups. Below are listings of the statistical tests by data type and sample requirements.

Descriptive Statistics

Descriptive Statistics with one variable/outcome
Scale/Type of Measurement	Measure	Statistic
Ratio or Interval / (continuous/numerical) Normally Distributed	Proportion of normal distribution below Z score	Z
Ratio or Interval / (continuous/numerical) Normally Distributed	Z score at upper end of proportion of standard normal curve	Z
Ratio or Interval (continuous/numerical) Normally Distributed	Central Tendency	Mean
	Dispersion	SD
Ratio or Interval/(continuous/numerical) Not Normally Distributed	Central Tendency	Median, mode
	Dispersion	Range, IQR
Ordinal (ranks)	Central Tendency	Median, mode
	Dispersion	Range, IQR
Nominal (categories)	Central Tendency	Mode
	Dispersion	#of categories

One Sample

Comparison of One Sample to a Population
Scale/Type of Measurement	Requirement	Test
Ratio or Interval (continuous/numerical)	Normal distribution or n>30	One sample t
Nominal (categories)		One sample binomial
		Confidence interval for proportion
	np and n(1-p) >5	Z approximation

Two or more Groups

Comparison of Two or More Independent Samples (Groups) (one independent/predictor variable)
Scale/Type of	#of Samples (Groups)	Requirement	Test
Ratio or Interval(continuous/numerical)	2	Normal distribution or n>30 and Equal variances	T test
		normal distribution or n>30	Welch's T test
			Rank Sum Test
	>2	Normal distribution or n>30 Homogeneous variance	Analysis of Variance (ANOVA)
			Kruskal-Wallis Test
Ordinal (ranks) or Discrete Numerical	2		Rank Sum Test
	>2		Kruskal-Wallis Test
Nominal (categories)	2		Fisher's Exact test Chi Squared
	2	Expected values >5	Chi Squared
			Relative Risk (Rate Ratio)
			Odds Ratio
	≥2	Expected values >5	Chi Squared

Comparison of Two or More Independent Samples (Groups) (one independent/predictor variable)
Scale/Type of	#of Samples (Groups)	Requirement	Test
Ratio or Interval(continuous/numerical)	2	Normal distribution or n>30 and Equal variances	Paired T test
			Wilcoxon Signed Rank test
	2	Normal distribution or n>30 and Equal variances	Repeated Measures ANOVA
			Friedman 2-Way ANOVA
Nominal (categories)	2	>20 discordant pairs	McNemar's Chi Squared
			McNemar's Chi Squared (Exact Method)

See Also

• statistical power

Authors

Jeff Rogers, Ann Huang, Ross Donaldson, Neil Young