# How To Think Statistically With Six Sigma

 By: tjacowski
 The data gathering exercise results in quantitative data in abundance. How you want to analyze it depends broadly on your plan to arrive at the solution. Nevertheless, it depends on three fundamental questions. But as a precursor to these questions, one must keep in mind that the larger purpose of using wide ranging interacting data is to understand the processes, problems and the best possible solutions as applied to Six Sigma implementation.Six Sigma: Statistical ThinkingStatistical thinking involves the tendency to want to study the complete contextual situation when a wide ranging statistical inputs and control factors of several natures may be interacting simultaneously to produce a particular output.To understand the principle better, one can begin with the one factor at a time (OFAT) theory, which refers to the natural tendency of the investigator to change only one factor at a time and 'record' the results until all other factors are tested this way. The results need to be put in place in the natural logical manner that would have occurred had the study been conducted in the opposite of OFAT.The Fundamental Question As we discussed earlier, there are three fundamental questions that need to be addressed in the order that the data is analyzed.1.Whether the level of the measurement of the variables is known? If yes;a.Nominal or Crude Ordinalb.Good Ordinal or Interval or Ratio2.Size of the sample is another consideration. What kinds and how many of them are being considered?a.One sample onlyb.Two samples; Specify either dependent or independentc.Multiple samples; Specify either dependent or independent3.What are my anticipations about the statements on data that I will be able to make?a.Define the sample data but without generalizing to the larger batch sizei.Discuss each factor such as distribution, central tendency and variation in the context of a single variable.ii.Discuss the relationship between two or more variables if that is the case.b.Now, moving away a bit, generalize the samples to the batch size from which they were drawn. The process of statistical inference or hypothesis testing, as this is called, relies on the probability theory to determine the risk of an inaccurate generalization.i.For a single variable, discuss the various factors in the same way as in the above case.ii.For two or more samples discuss the differences between them concerning whether they are independent or dependent?iii.Relationship between two variables and again the relationship shared between more variables.In continuance with the discussion, the choice for adopting the appropriate statistical technique and going ahead with the task on hand rests with the answers to the above questions. Nevertheless, the philosophy of effective statistical thinking and action on a further course is better based on the following guiding principles:1.In a system all reactions occur in interconnected processes2.Variation is part and parcel of all processes3.The key to success lies in understanding and reducing variationsStatistical thinking succeeds in paving the way for a holistic approach to the deployment of Six Sigma. It can't be thought of in isolation.