How to interpret a box plot?

I have some data in which there are 5 categorical explanatory variables (concern, breath, weath, sleep, act) and 1 continuous response variable (tto). In addition, every categorical explanatory variable is divided into 5 levels which show how strong a person feels about it. level 1 and level 5 show the perfect and worst states respectively.

I was advised to create a box plot to see the relationship between the explanatory variables and the response variable. The plot is given below. However, I do not know how to read a box plot. Can any one please help me interpret it.

• You probably have read the Wikipedia article: en.wikipedia.org/wiki/Boxplot Could you explain more clearly what you are not understanding? – Stephan Kolassa Jan 18 '13 at 21:01
• Yes, I have. So I know the basic staff. However, I do not know how to use them on this. I mean there are lots of plots here and I have to choose the important figures. For example, in every category above, the plots of level 5 is the longest. What does that mean? What effect does it have on tto? Another example would be that why are there lots of points? I know they represent the outliers, but do not know how to expand this – Günal Jan 18 '13 at 21:15
• A related question which covers the limitations of what you can interpret from a box plot: Will two distributions with identical 5-number summaries always have the same shape? – Silverfish Jan 31 '15 at 21:04

2 Answers

Interpretation of the box plot (alternatively box and whisker plot) rests in understanding that it provides a graphical representation of a five number summary, i.e. minimum, 1st quartile, median, 3rd quartile and maximum. The box encompasses 50% of the observations. The ends of the whiskers (vertical lines emanating from the top and bottom of the box) typically show where the minimum and maximum lie. However, where possible outliers exist (sometimes assessed based on 1.5 $\times$ interquartile range) points are added, as is the case for your figure.

It may be useful for you to look at a histogram or density plots on specific categories of the data as that may help you understand what the box plot is saying.

@Glen_b rightly indicates that left skew is evident and the central tendency for the 5th level of strength of feeling is lower than the others. It is difficult however to see whether that difference would be statistically significant or not.

Here's a basic summary of what's there:

1. All the distributions appear left-skew, "jammed up" against the upper bound of 1.0, with many low 'outliers' tailing off toward the bottom.
2. The 5th category in each plot seems to sit lower than the others. Sometimes the 4th category is also low.
3. All 5 variables (concern, breath, weath, sleep, act) seem to have broadly similar patterns.