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1 Did your project reduce variation or shift the mean? How do you demonstrate improvements statistically? 2 VIII-47 The question one needs to ask during a project is whether the changes made as the result of a Black Belt project have made a difference in the process. The question is, “Has the project made a difference, and if so, how confident are we that the difference is statistically significant?” We strive for 95% confidence or better (α=.05). 3 VIII-47 A hypothesis is: Examples: ◦ a tentative explanation for an observation that can be tested by further investigation. ◦ taken to be true for the purpose of investigation; an assumption. ◦ Average gas mileage differs depending on type A or B gas. ◦ Probability of death in auto accidents differs depending on seat belt usage. ◦ The type of aspirin determines the amount of pain relief. ◦ A Six Sigma Black Belt project produced significant results with regard to mean and/or standard deviation improvement. 4 VIII-47 We set up 2 hypotheses ◦ H0 is called the null hypothesis what is being tested must contain an = assumed to be true ◦ H1 is called the alternate hypothesis Based on the data we collect, we must decide in favor of either H0 or H1. Which does the evidence support? ◦ You can only reject null, or fail to reject null 5 VIII-47 Define the problem and state objectives State a “Null Hypothesis” (Ho) State the “Alternative Hypothesis” (H1) Establish significance level (a) and determine the critical value Collect sample data Calculate test statistic and/or p-value DECIDE: What does the evidence suggest? Reject Ho? or Fail to reject Ho? 6 VIII-47 Set up the statapult and reduce obvious variation Pick a factor that you would like to test ◦ Ball type ◦ Operator ◦ Etc Pick at least 3 different treatments (levels) Record data with at least 5 data points each population Analyze 7 VIII-83 Set up the statapult and reduce obvious variation Pick two factors that you would like to test ◦ ◦ ◦ ◦ Ball type Operator Pull back angle Etc. Pick at least 2 different levels for each factor Record at least 5 data points each Analyze 8 VIII-87