## Saturday, June 13, 2009

### Histograms in Excel

Histograms are very useful charts for displaying the distribution of a numerical measurement. The idea is to bucket the numerical measurement into intervals, and then to display the frequency (or percentage) of records in each interval.

Two ways to generate a histogram in Excel are:
1. Create a pivot table, with the measurement of interest in the Column area, and Count of that measurement (or any measurement) in the Data area. Then, right-click the column area and "Group and Show Detail >  Group" will create the intervals. Now simply click the chart wizard to create the matching chart. You will still need to do some fixing to get a legal histogram (explanation below).
2. Using the Data Analysis add-in (which is usually available with ordinary installation and only requires enabling it in the Tools>Add-ins menu): the Histogram function here will only create the frequency table (the name "Histogram" is misleading!). Then, you will need to create a bar chart that reads from this table, and fix it to create a legal histogram (explanation below).
Needed Fix: Histogram vs. Bar Chart
Background: Histograms and bar charts might appear similar, because in both cases the bar heights denote frequency (or percentage). However, they are different in a fundamental way: Bar charts are meant for displaying categorical measurements, while histograms are meant for displaying numerical measurements. This is reflected by the fact that in bar charts the x-axis conveys categories (e.g., "red", "blue", "green"), whereas in histograms the x-axis conveys the numerical intervals. Hence, in bar charts the order of the bars is unimportant and we can change the "red" bar with the "green" bar. In contrast, in histograms the interval order cannot be changed: the interval 20-30 can only be located between the interval 10-20 and the interval 30-40.

To convey this difference between bar charts and histograms, a major feature of a histogram is that there are no gaps between the bars (making the neighboring intervals "glue" to each other). The entire "shape" of the touching bars conveys important information, not only the single bars. Hence, the default chart that Excel creates using either of the two methods above will not be a legal and useful histogram unless you remove those gaps. To do that, double-click on any of the bars, and in the Options tab reduce the Gap to 0.

Method comparison:
The pivot-table method is much faster and yields a chart that is linked to the pivot table and is interactive. It also does not require the Data Analysis add-in. However,
there is a serious flaw with the pivot table method: if some of the intervals contain 0 records, then those intervals will be completely absent from the pivot table, which means that the chart will be missing "bars" of height zero for those intervals! The resulting histogram will therefore be wrong!

Ji Hee said...

It is interesting. I just made a bar chart to analyze a survey result today, and I transformed the continuous data to categorical data. I could make a histogram, but I thought it was clear enough to show people a bar chart for a simple survey.

Galit Shmueli said...

I guess it depends on the number of different values that you have. If it is a 5-point scale question, then showing a bar chart with 5 bars is reasonable and useful. Note, though, that such a bar chart would emphasize the ordinal nature of the data. If you want to emphasize the "interval scale" feel, a histogram is better.

ErikC said...