A decision tree for statistics is helpful for determining the correct inferential or descriptive statistical test to use to analyze and report your data. There are so many types of statistical analyses that sometimes, it's hard to pick the best-fitting one for your data.
Before you choose an inferential statistic to use, you should know two important pieces of information:
1) What is the purpose of your research?
2) What kind of data do you have?
The purpose of the research question can be answered in one of three ways. Are you describing the data? Are you examining a relationship between variables? Or are you comparing groups and analyzing group differences?
These are your commonly reported measures - mean, median, mode, range, standard deviation. They do not have any analytical benefit, but descriptive measures are useful for simply describing what the data looks like. Descriptive statistics are usually reported alongside an inferential test, but different inferential statistics use different descriptives. For instance, chi-squared tests measure categorical dependent variables, so they report frequencies and percentages to describe the data.
Relationship tests are used to analyze relationships between variables, not to compare differences. The most common type of relationship study is a correlation, which shows the relationship between two variables. It is important to remember that correlation is not equal to causation; just because you find a strong relationship between two variables does not mean that one is caused by another. To examine causation, you have to meet the expectations for experimentation - manipulation of a variable, maintenance of a control group and experimental group(s), random assignment to each condition - and use a parametric or non-parametric test.
These are a classification of tests used to compare group differences and find significance. If you are comparing groups and looking at group differences, you also have to ask yourself whether your data abides by parametric assumptions:
Is your data normally distributed? (normality assumption)
Do all comparison groups have equal standard deviations? (homogeneity of variance assumption)
Are all of your groups measured on the same interval or ratio scale?
If these assumptions are met, then a parametric test is for you!
These are a different classification of group comparison tests and are used when the assumptions for parametric tests are not met. This could include data that is reported on an ordinal scale and data that uses categorical dependent variables, like the chi-squared test.
Gravetter, F. J., & Wallnau, L. B. (2013). Statistics for the Behavioral Sciences. Wadsworth, CA: Cengage Learning.