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Benchmark Six Sigma Expert View by Venugopal R If the question had been “During which phases of DMIAC TOH (Test Of Hypothesis) is largely made use of?” then the answer would be very obvious. Having asked to identify the phase where TOH does not find an application, we need to put some thoughts on every phase. My discussion here is not to be taken as a counter for any of the other responses, but may be viewed as a thought inciter. TOH is a statistical tool that will help to compare a characteristic of a population with that of another population or standard and take a decision whether we have sufficient reason to believe they are equal or not…. The decision is based on evaluation of few samples that represent the population. The phases of DMAIC that predominantly use the TOH are Analyse and Improve, and hence I will keep these 2 phases aside and look at others. DEFINE phase is where the business case has to be evolved and the management buy-in obtained. For example, if we need to decide on taking a project on improving the market share of a product for a segment of customer across geographies; we may use TOH in the form of Chi-square comparison with a competitor’s product while trying to get a management approval for the business case. MEASURE PHASE is where the Measurements systems need to be finalized and the baseline measurements need to be done. An important aspect of measure phase is to carry out a Measurement Systems Analysis. MSA practices use ANOVA, which is built upon TOH principle, for determining the existence of parameters like linearity, bias etc. As indicated, I am skipping discussion on Analyse and Improve phases, which are most popular for use of TOH. CONTROL phase is where the focus is on monitoring & ensuring sustenance of the gains. The Control plans, Mistake proofing are very prevalent methods here. Control charts that would have been initiated during the Measure phase, continue to be used for monitoring performance in this phase. Usage of control charts is possible when we obtain sample data points periodically. There could be certain situations where we may have practical difficulties in using a control chart. For example, consider a project whose objective is to improve Training effectiveness. Here, we can monitor the sustained effectiveness, only as and when the training happens. Another example could be a project whose objective is to improve the cycle time to ‘go live’ for New Product Development Process. Here, we can monitor the sustained effectiveness only when the next new product is developed and launched. Wouldn't TOH find suitable application for comparing the performance indicators of an improved process with previous / or with a standard to assure sustenance, in such situations? Let me conclude this discussion with the thought…. “TOH is well known to be applied during Analyse and Improve phases – however, aren't there situations in other phases, where it could find useful application for practical decision making?” I look forward to see the views by others on this question.

Six Sigma gains it's edge over other Quality Management System as it uses data driven approach for problem solving. Statistics forms an integral part of Six Sigma methodology as many of it's tools refers to statistics for logical conclusions. We essentially have two branches in Statistics - Descriptive and Inferential. Descriptive Statistics helps work on collecting, analyzing and presenting information as mean, standard deviation, variation, percentage, proportion etc. While Descriptive Statistics helps with description of data, it will not manifest itself with any inferences. Inferences about data is very important for decision making and it is Inferential Statistics which helps us with the same. To answer above question on the approach for decision making using few samples, it is Inferential Statistics that helps us analyze sample data and predict the behavior of population. Further, Inferential statistics helps us establish the relationship between independent variables (X, Cause) and the outcome (Y, Effect) and also help identify the critical X which needs to be focused to improve the Y. Inferential Statistics is strongly associated with Hypothesis testing. Hypothesis testing is performed on Sample and whenever we do a Hypothesis testing, we ask below questions on whatever we saw in the sample Is It True? Is it Common Cause? Is it Pure Chance? Let us see how to perform a Hypothesis testing which is key for Inferential Statistics. Step 1. Define the Business Problem in a data driven format i.e. Y=f(X) Step 2. Select and appropriate or apt Hypothesis Test that we need to perform on the problem. We will see this in detail in next section. What drives the selection of test is basis the type of data defining both X and Y i.e. if the data type is discrete or continuous. Step 3. Make the Statistical Hypothesis Statement ; H0 = Null Hypothesis = No Change, No Impact or Difference; HA=Alternate Hypothesis = New argument holds good basis the business case. Step 4. Run the test on Sample data using tools like Minitab Step 5. Calculate the "P" value - which will be an output from the tool Step 6. Compare "P" value with "alpha" [Alpha is called as Type I error and acceptable level is generally kept at 5% or 0.05] Step 7. Do Statistical conclusion i.e. if P is greater than alpha, your Null Hypothesis holds good else your alternate hypothesis will hold good. Step 8. Do a Business Inference i.e. if Null Hypothesis holds good than the input sample is treated as non-critical x. Alternatively, if your alternate hypothesis holds good, we should treat the input as critical x. W.r.t Step 2, on selecting the apt test, below inputs should serve as guiding pointers Output Y is Discrete and Input X is Discrete in 2 categories, we need to use 2 proportion test Output Y is Discrete and Input X is Discrete in multiple categories, we need to use Chi-square test Output Y is Continuous and Input X is Discrete in 2 categories, we need to use 2-sample t-test Output Y is Continuous and Input X is Discrete in more than 2 categories, we need to use ANOVA Output Y is Continuous and Input X is Continuous we need to use Regression Analysis. In summary, Inferential Statistics is used draw conclusions on the larger population by taking a sample from the same and also try to establish relationship between the input and output.