# Types of statistical tests

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## 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)