## Monday, 29 August 2011

### Box Plots..What language is that?

Ok rule of thumb for today! Use Hierarchical Clustering when number of objects to be clustered is less than 50 and K- Means Clustering when the objects are more than 50.

Suppose the number of objects in my analysis is more than 50 and I have to use K-Means clustering. How do I actually go about doing this?!!

Simple, I decide my objective of clustering, select the variables and cluster them. I will hopefully get a number of clusters with enough number of cases in each to make the clusters significant (AND they’ll be identifiably different from each other!!).

But what about all those clusters that I see in there with number of cases that read the dreaded number 1 and 2 and bla bla bla...What do I do about those?

First find out if they are outliers. Start by taking a smart and logical guess as to which variable out of the clustered ones could be the reason for them being outliers. Then create a box plot for that variable and identify and eliminate the outliers.

Remake the clusters, do their profiling in order to understand the difference in between the groups and then make suggestions and draw conclusions to satisfy the objective.

Ok so all of that sounds manageable, pretty simple in fact once I get the hang of it, except for that one little thing called box plot! If only that made more sense, I’m sure I could ace this!!

Lets look at Box Plots!

In 1977, John Tukey published an efficient method for displaying a five-number data summary. The graph is called a boxplot (also known as a box and whisker plot) and summarizes the following statistical measures:

• median
• upper and lower quartiles
• minimum and maximum data values
Box Plot

The plot may be drawn either vertically as in the above diagram, or horizontally.

Interpreting a Boxplot

The boxplot is interpreted as follows:

• The box itself contains the middle 50% of the data. The upper edge (hinge) of the box indicates the 75th percentile of the data set, and the lower hinge indicates the 25th percentile. The range of the middle two quartiles is known as the inter-quartile range.
• The line in the box indicates the median value of the data.
• If the median line within the box is not equidistant from the hinges, then the data is skewed.
• The ends of the vertical lines or "whiskers" indicate the minimum and maximum data values, unless outliers are present in which case the whiskers extend to a maximum of 1.5 times the inter-quartile range.
• The points outside the ends of the whiskers are outliers or suspected outliers.

Boxplot Enhancements

Beyond the basic information, boxplots sometimes are enhanced to convey additional information:

• The mean and its confidence interval can be shown using a diamond shape in the box.
• The expected range of the median can be shown using notches in the box.
• The width of the box can be varied in proportion to the log of the sample size.

Boxplots have the following strengths:

• Graphically display a variable's location and spread at a glance.
• Provide some indication of the data's symmetry and skewness.
• Unlike many other methods of data display, boxplots show outliers.
• By using a boxplot for each categorical variable side-by-side on the same graph, one quickly can compare data sets.

One drawback of boxplots is that they tend to emphasize the tails of a distribution, which are the least certain points in the data set. They also hide many of the details of the distribution. Displaying a histogram in conjunction with the boxplot helps in this regard, and both are important tools for exploratory data analysis.

Alright that was informative! Those weird boxes with lines and stars at odd places definitely make more sense to me now. Kind of like learning a new language...

Hope it helped!!

Priyanka Bagla (13029)..

Finance_Group6