The following section includes a series of statistical inference tests performed using the basic install of R. By default, the page will present the whole series, but you can limit the number of tests by selecting the different key words:
  • Means: tests that compare means
  • 1 Population, 2 Populations, n Populations: tests used to compare, 1, 2 or n Populations.
  • Parametric and Non-Parametric: tests that use distribution parameters (mean, variance, etc.) for the inference vs tests that do not uses these parameters.

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Means, 2 Populations

t-test for difference in means (2 samples, equal variances)

This test is used to test if 2 samples were taken from normal populations with equal means (assuming that these two populations have equal, although unknown variances).
Non-Parametric, Normality

Shapiro-Wilks test of normality

This test is used to test if a samples was taken from a populations with a normal distribution.
Means, 2 Populations

Welch test for difference in means (2 samples, unequal variances)

This test is used to test if 2 samples were taken from normal populations with equal means (assuming that these two populations have unequal and unknown variances).
Correlation, 2 Populations, Non-Parametric

Correlation tests (2 variables)

This test is used to test if 2 variables are correlated (H0 R = 0) using 1 of 3 correlation coefficients (Pearson, Spearman’s rank correlation and Kendall’s rank correlation)
1 Population, Means

One sample t-test for a hypothesised mean ( 1 sample)

This test is used to test if the mean of a population is equal to a predefined hypothetical mean. There only a single sample from the population.
2 Populations, Non-Parametric,

Wilcoxon signed rank test for paired samples ( 2 samples)

This test is used to test two paired samples have been extracted from population with similar values.
2 Populations, Non-Parametric

Mann-Whitney-Wilcoxon test ( 2 samples)

This test is used to test if two samples have been extracted from the same population, or populations with similar values.
k Populations

Bartlett’s test for heteroscedasticity (k samples)

This test is used to test if k samples have been extracted from populations with equal variances.
k Populations, Non-Parametric

Flinger-Killeen’s test for heteroscedasticity (k samples)

This test is used to test if k samples have been extracted from populations with equal variances.
k Populations, Non-Parametric

Chi-square (Goodness of Fit)

This test is used to test if a series of observed frequencies match another series of theoretical frequencies determined by a underlying model,
2 Populations, Non-Parametric

Binomial test

The binomial test is used to test if the frequencies of observations of a binary event (success/ failure) follows a binomial model.
2 Populations, Non-Parametric

Chi-square (Independence)

This test is used to assess if the frequencies of observations in two categorical variables are independent of each other,
2 Populations, Non-Parametric

McNemar (Concordance of paired frequencies)

This test is used to assess if the frequencies of observations in two linked categorical variables are independent of each other,