Methods and tools for graphically displaying data such as Box Plots, Pareto Charts and Multi-Vari Charts are used widely in business improvement, particularly where Six Sigma methods are employed. But the relationship between those and more advanced statistics is often misunderstood.
Graphical Display Methods
All of those graphical type tools are designed to help us to locate a source of variation by distinguishing values as they relate to different categorical variables. For example a box plot can be used to display and visually compare the performance of different shifts in a production plan or the heights of people by country of origin.
However there is a limitation with these methods, they rely entirely on visual interpretation.
When we are studying values as a part of problem solving and results show clear distinctions within any category, provided our sample data set is representative of the population we can focus on the obvious source of our problem with a high degree of confidence that any improvement will make a difference.
For example, if we observe in our Pareto Chart that 90 percent of all lost time relates to hand injuries, or we see in our stratified box plots that all coffee made on a Monday is outside the required temperature range while all other days are inside, we don’t need some rocket scientist to come along and tell us whether or not any difference we observe is significant.
However, if the differences we observe between say coffee temperature results on the Monday and the rest of the week are quite overlapped and we cannot say with absolute confidence that the difference is not just because of sample variation, we must bring inferential statistics into play.
The role of inferential statistics comes to the fore when we work with samples. Its role is to minimise the risk of us focusing on one variable when in fact it was never a source of variation in the first place. We use inferential statistics to validate our hypothesis that a particular observed source of variation (based on a sample of data) is in fact a source of variation we should treat.
The diagram above shows common graphical techniques as well as statistical methods used to locate and validate sources of variation.
Do you need statistics in business?
If you work with sample data then the answer is a resounding yes.