Parametric tests are classical statistical test that need the data to have normal distribution. For data that is not normally distributed, there are 2 options. One is to transform the data using functions like log to convert it to normal distribution and then apply parametric test. The second option is to use nonparametric test that do not assume the data to be normally distributed. Following table shows main parametric and nonparametric tests that are done in different situations:
Situation 
Parametric Test 
Nonparametric test 

Correlation between 2 numeric variables 
Pearson's correlation 
Spearman's or Kendall's correlation 
Comparing 2 series of numeric values (paired or unpaired) 
Student's ttest 
Mann Whitney U test or Wilcoxan test 
Comparing multiple groups of numeric values 
ANOVA (analysis of variance) 
KruskalWallis test 
Tables of categorical variables 
Chisquared test 
Fisher's Exact test 


