Types of statistical tests

Background

• There are many statistical tests used for biomedical research. The type of test to be used depends on the type of data, population type, distribution, and number of groups.
• This article lists 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, Interquartile 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