Statistics Tip of the Week: Always plot the data first. Calculated statistics alone can be misleading.
It's been said that the first 3 laws of statistics are:
1. Plot the data.
2. Plot the data.
3. Plot the data.
Others say the same thing using different words:
1. Draw a picture.
2. Draw a picture.
3. Draw a picture.
Let's say we have a couple of sets of (x,y) data, and we want to fit Regression models to them. For Simple Linear Regression, we would first have to establish a Linear Correlation. If we just calculated the Correlation Coefficient, r, it would tell us that both the datasets graphed below have a very strong Linear Correlation.
We can see how that would apply for the data set pictured on the left. But the one on the right is definitely not linear. We would be better off with non-linear regression, using a Polynomial model.
This kind of thing happens more frequently than one might think. So, always plot the data first; calculated statistics alone can be misleading. And a picture of the data helps give you a more intuitive understanding of the data that you are analyzing.
Andrew A. (Andy) Jawlik is the author of the book, Statistics from A to Z -- Confusing Concepts Clarified, published by Wiley.