Types of Statistical Tests
Now that you have looked at the distribution of your data and perhaps conducted some descriptive statistics to find out the mean, median or mode, it is time to make some inferences about the data. As previously covered in the module, inferential statistics are the set of statistical tests we use to make inferences about data. These statistical tests allow us to make inferences because they can tell us if the pattern we are observing is real or just due to chance.
How do you know what kind of test to use?
Types of statistical tests: There are a wide range of statistical tests. The decision of which statistical test to use depends on the research design, the distribution of the data, and the type of variable. In general, if the data is normally distributed you will choose from parametric tests. If the data is nonnormal you choose from the set of nonparametric tests. Below is a table listing just a few common statistical tests and their use
Type of Test: 
Use: 
Correlational 
These tests look for an association between variables 
Pearson correlation 
Tests for the strength of the association between two continuous variables 
Spearman correlation 
Tests for the strength of the association between two ordinal variables (does not rely on the assumption of normal distributed data) 
Chisquare 
Tests for the strength of the association between two categorical variables 
Comparison of Means: look for the difference between the means of variables  
Paired Ttest 
Tests for difference between two related variables 
Independent Ttest 
Tests for difference between two independent variables 
ANOVA 
Tests the difference between group means after any other variance in the outcome variable is accounted for 
Regression: assess if change in one variable predicts change in another variable 

Simple regression 
Tests how change in the predictor variable predicts the level of change in the outcome variable 
Multiple regression 
Tests how change in the combination of two or more predictor variables predict the level of change in the outcome variable 
Nonparametric: are used when the data does not meet assumptions required for parametric tests 

Wilcoxon ranksum test 
Tests for difference between two independent variables  takes into account magnitude and direction of difference 
Wilcoxon signrank test 
Tests for difference between two related variables  takes into account magnitude and direction of difference 
Sign test 
Tests if two related variables are different – ignores magnitude of change, only takes into account direction 
Click here for a printable PDF version of this table.