Let’s assume for a moment that we compared number of hours studied by a group of college students to their final exam scores. We might assume that those who studied longer hours would score higher on the final exam. That is considered a positive correlation.
Now, let’s think about hours exercised per week by a group of college students, and how that might relate to percent body fat. More hours exercised would reasonably lead to a lower percent body fat, right? (Actually, that’s more of a thesis question, but for the sake of my example let’s say yes.) That is considered a negative correlation.
Further reading here.
Yes, you really have to do all those tests.
Much of statistical analysis is based on the assumption that you have a lot of data to work with and the data follow a normal distribution. Beyond that, though, there are reasons we can’t just work up a t-test and a Pearson correlation without examining the data set first.
Non-parametric statistical tests are appropriate in different instances. This article from Boston U School of Public Health is a good place to start if you’re wondering.
In any instance, it’s always a good idea to run a normality test (Kolmogorov-Smirnov or Shapiro-Wilk, depending on sample size) before further analysis.
Wondering what statistical test to plow through in R, SPSS, or STATA? Here’s a handy decision flowchart and matching instructions for these software packages. I use it sometimes to double-check my thought process (much like I still use Andy Field’s introductory SPSS textbook, dutifully marked up and full of Post-It Notes).
No matter how accomplished you might be in statistical analysis, it’s good to have something to jog your memory.