The histogram plots the frequency of events where categories are ordered by x-values. If the data are continuous, they can
be "binned" to create the cut points for the histogram. There is no best number of bins and different bin sizes can reveal
different features of the data. Sometimes experimentation with different bins sizes can highlight the salient points of the
data. A histogram shows the shape of the data distribution, which is useful for checking the assumption of normality of the
data. A popular method for testing normality is the Andersen-Darling method, which can be found in most statistical software.
Figure 5 shows how two data sets can be compared. The top graphic shows the two separate histograms; in the bottom graph,
the two distributions have been overlaid.
Figure 5. Two examples showing different ways to compare data sets. In the bottom graph, the two distributions have been
CONVERTING QUANTITATIVE TO QUALITATIVE DATA
Typically, continuous data are converted to qualitative or binary response. For example, the specification for pH is between
6.9 and 7.1 but we code values within the limits as pass and those outside the limits as fail. Though this makes for an easier
disposition of the lot, it does not allow for extensive data analysis during an investigation. Another common problem with
data analysis occurs when the measurement system is inadequate so data is binned into a few unique values. For example, we
measure a weight to the closest 0.1 mg, although the measurement device can measure to the closest 0.01 mg. This is commonly
done to adhere to significant figures in a specification, but can lead to poor data analysis.
Data presentation should be designed to ensure the correct conclusions. Though graphical methods give an overview of the data,
more rigorous statistical methods help to separate normal variability from special cause variability. The key to a good graphical
presentation is to select the method that best fits the data.
Steven Walfish is the president of Statistical Outsourcing Services, Olney, MD, 301.325.3129, email@example.com