Which statistical test should you use?
This article will help you choose the right statistical test for your data.
What is a statistical test?
A statistical test is a way to evaluate the evidence the data provides against a hypothesis. This hypothesis is called the null hypothesis and is often referred to as H0. Under H0, data are generated by random processes. In other words, the controlled processes (the experimental manipulations for example) do not affect the data. Usually, H0 is a statement of equality (equality between averages or between variances or between a correlation coefficient and zero, for example).
A guide to choosing an appropriate test according to the situation
XLSTAT provides a high number of statistical tests. We have drawn the grid below to guide you through the choice of an appropriate statistical test according to your question, the type of your variables (i.e., categorical variables, binary, continuous) and the distribution of data. The guide proposes a formulation of the null hypothesis, as well as a concrete example in each situation. In columns Parametric tests and Nonparametric tests, you may click on the link to view a detailed tutorial related to the proposed test including a data file. Conditions of validity of parametric tests are listed in the paragraph following the grid. When available, nonparametric equivalents are proposed. In some situations, parametric tests do not exist and so only nonparametric solutions are proposed.
For a more theoretical background on statistical testing, please read the below articles:

What is a difference between paired and independent samples tests?

What is the difference between a parametric and a nonparametric test?

What is the difference between a twotailed and a onetailed test?

How to interpret the output of a statistical test: the significance level alpha and the pvalue
The grid
The displayed tests are the most commonly used tests in statistics. They are all available in XLSTAT. Please notice that the list is not exhaustive, and that many other situations / tests exist. Please scroll down to see the grid.
Test family  Question  Data  Null Hypothesis  Example  Parametric tests  Conditions of validity (parametric tests)  Nonparametric equivalents 

Compare locations*  Compare an observed mean to a theoretical one  Measurements on one sample and 1 theoretical mean (1 number)  Observed mean = theoretical mean  Compare an observed pollution rate to a standard value  Onesample ttest  2  One sample Wilcoxon signed rank test 
Compare two observed means (independent samples)  Measurements on two samples  means* are identical  Compare hemoglobin concentration between two groups of patients  ttest on two independent samples  1 ; 3 ; 5  MannWhitney's test  
Test the equivalence between two samples  Measurements on two samples  means* are different  Check if the effect of medication A is the same as the effect of medication B on the concentration of a molecule in mice  Equivalence test (TOST)  1 ; 3 ; 5  
Compare several observed means (independent samples)  Measurements on several samples  means* are identical  Compare corn yields according to 4 different fertilizers  Analysis Of Variance (ANOVA)  1 ; 3 ; 4 ; 6  KruskalWallis test ; Mood's test  
Compare two observed means (dependent measurements)  Two series of quantitative measurements on the same units (beforeafter…)  means* are identical  Compare the mean hemoglobin concentration before and after a treatment has been applied on a group of patients  ttest on two paired samples  10  Wilcoxon's test  
Compare several observed means (dependent measurements)  Several series of quantitative measurements on the same units  means* are identical  Follow the concentration of a trace element in a group of plants across time  Repeated measures Analysis of Variance (ANOVA) , mixed models  10 ; Sphericity  Friedman's test for complete block designs; Durbin, SkillingsMack's test for incomplete block designs; Page test for cases where series scores are expected to increase or to decrease (across time for example)  
Compare series of binary data  Compare series of binary data (dependent measurements)  Several series of binary measurements on the same units  Locations* are identical  A group of assessors (units) evaluate the presence/absence of an attribute in a group of products  McNemar's test (for 2 series); Cochran's Q test (for more than 2 series)  
Compare variances  Compare 2 variances (could be used to test assumption 3)  Measurements on two samples  variance(1) = variance(2)  Compare the natural dispersion of size in 2 different varieties of a fruit  Fisher's test  
Compare several variances (could be used to test assumption 3)  Measurements on several samples  variance(1) = variance(2) = variance(n)  Compare the natural dispersion of size in several different varieties of a fruit  Levene's test  
Compare proportions  Compare an observed proportion to a theoretical one  1 observed proportion with its associated sample size, one theoretical proportion  observed proportion = theoretical proportion  Compare the proportion of a female group to a proportion of 0.5 in a sample  Tests for one proportion (chisquare test)  
Compare observed proportions to each other  Sample size associated to every category  proportion(1) = proportion(2) = proportion(n)  Compare the proportions of different eye colors in a sample  Chisquare test  
Compare observed proportions to theoretical ones  Sample size and theoretical proportion associated to every category  observed proportions = theoretical proportions  Compare the proportions of observed F1xF1 crossbreeding frequencies to Mendelian frequencies (1/2, 1/4, 1/2)  Multinomial GoodnessOfFit test  
Association tests  Test the association between two qualitative variables  Contingency table or two qualitative variables  variable 1 & variable 2 are independent  Is the presence of a trace element linked to the presence of another trace element?  Chisquare test on contengency table  1 ; 9  Exact Fisher test ;Monte Carlo method 
Test the association between two qualitative variables across several strata  Several contingency tables or two qualitative variables with a stratum identificator  variable 1 & variable 2 are independent  Is the presence of a trace element linked to the presence of another trace element? Assessed over several sites (strata)  CochranMantelHaenszel (CMH) test  
Test the association between two quantitative variables  Measurements of two quantitative variables on the same sample  variable 1 & variable 2 are independent  Does plant biomass change with soil Pb content?  Pearson's correlation test  7 ; 8  Spearman's correlation test  
Test the association between a binary variable and a quantitative one  Measurements on one binary variable and one quantitative variable  the two variables are independent  Is the concentration of a molecule in rats linked to the rats' sex (M/F)?  Biserial correlation test  Normality of the quantitative variable  
Test the association between a series of proportions and an ordinal variable  Contingency table or proportions and sample sizes  Proportions do not change according to the ordinal variable  Did birth rates change from year to year during the last decade?  CochranArmitage trend test  
Test the association between two tables of quantitative variables  Two tables of quantitative variables  Tables are independent  Does the evaluation of a series of products on a series of attributes change from a panel to another?  RV coefficient test  
Test the association between two proximity matrices  Two proximity matrices  Proximity matrices are independent  Is geographic distance between populations of bees correlated with genetic distance?  Mantel's test  
Time series tests  Test the presence of a trend across time  One series of data sorted by date (time series)  There is no trend across time for the measured variable  Did stock value change across the last 10 years?  MannKendall trend test  
Tests on distributions  Compare an observed distribution to a theoretical one  Measurements of a quantitative variable on one sample; parameters of the theoretical distribution  The observed and the theoretical distributions are the same  Do the salaries of a company follow a normal distribution with mean 2500 and standard deviation 150?  KolmogorovSmirnov's test  
Compare two observed distributions  Measurements of a quantitative variable on two samples  The two samples follow the same distribution  Is the distribution of human weight the same in those two geographical regions?  KolmogorovSmirnov's test  
Test the normality of a series of measurements (could be used to test assumptions 2, 4, 7)  Measurements on one sample  The sample follows a normal distribution  Is the observed sample distribution significantly different from a normal distribution?  Normality tests  
Tests for outliers  Test for outliers  Measurements on one sample  The sample does not contain an outlier (following the normal distribution)  Is this data point an outlier?  Dixon's test / Grubbs test  Boxplot (not a statistical test) 
*Locations are means in parametric tests and mean ranks in nonparametric equivalents.
Conditions of validity of parametric tests
Validity conditions we propose are rules of thumb. There are no precise rules in literature. We strongly advise to refer to your fields’ specific recommendations.

Measurements are independent

The population from which the sample was extracted follows a normal distribution (assumed or verified)

Samples have equal variances

The residuals are normally distributed (assumed or verified)

At least 20 individuals per sample, or normality of the population of every sample verified or assumed

At least 20 individuals in the whole experiment, or normality of residuals assumed or verified

Every variable is normally distributed

At least 20 individuals in the sample (recommended)

Theoretical frequencies should not be < 5 in all of the table cells

Differences between series should follow normal distributions
How to run statistical tests in XLSTAT?
In XLSTAT, you can access any of the above tests in any solution. Simply choose the appropiate test in the main ribbon (see below), select your data and get the results in a few clicks. If you do not have XLSTAT, download for free our 14Day version to run your own test.
For each test, you may choose to display several outcomes such as descriptive statistics, detailed results, confidence intervals.
Furthermore, we offer a wide range of charts to help you visualize the results of statistical tests and quicker draw conclusions. See an example below for a twosample ttest and ztest.
Go further
Read our guide Which statistical model should you choose to learn how to choose the right model for your analysis (i.e., linear regression, logistic regression, regression trees) when you want to study the relationship between two or several variables and make predictions.
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