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Sample Size Determination  Deliverable 10A
Analyze Module Roadmap Define 1D – Define VOC, VOB, and CTQ’s 2D – Define Project Boundaries 3D – Quantify Project Value 4D – Develop Project Mgmt. Plan Measure 5M – Document Process 6M – Prioritize List of X’s 7M – Create Data Collection Plan 8M – Validate Measurement System 9M – Establish Baseline Process Cap. Analyze  10A – Determine Critical X’s Improve 12I – Prioritized List of Solutions 13I – Pilot Best Solution Control 14C – Create Control System 15C – Finalize Project Documentation Green 11G – Identify Root Cause Relationships Queue 1 Queue 2
Objectives – Sample Size ,[object Object],[object Object],[object Object]
Key Variables in Sample Size ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Alpha Risk  (  ) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Beta Risk (  )  ,[object Object],[object Object],[object Object],[object Object],[object Object]
Delta (  )  ,[object Object],[object Object],[object Object],[object Object],[object Object]
Signal to Noise Ratio ,[object Object],[object Object],[object Object],Low   High   
Minitab Versus Excel ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Calculating Sample Size in Minitab ,[object Object],Enter multiple values with a space between values for any/all of these (Minitab will calculate the value for the third parameter)
Wastewater Sample Size Example ,[object Object]
Wastewater Sample Size Example Stat > power and sample size > 2-Sample t
Minitab Output Power and Sample Size  2-Sample t Test Testing mean 1 = mean 2 (versus not =) Calculating power for mean 1 = mean 2 + difference Alpha = 0.05 Assumed standard deviation = 5 Sample Target Difference Size Power Actual Power 10 7 0.9 0.929070 The sample size is for each group.
Wastewater Sample Size – Pt. 2 ,[object Object],Power and Sample Size  2-Sample t Test Testing mean 1 = mean 2 (versus not =) Calculating power for mean 1 = mean 2 + difference Alpha = 0.05 Assumed standard deviation = 5 Sample Size Power Difference 10 0.9 7.66846 15 0.9 6.13222 20 0.9 5.25996 25 0.9 4.67878 The sample size is for each group. Notice how sample size increases dramatically as the difference to detect becomes smaller and smaller.
Class Exercise ,[object Object],10 min
Homework - Back to Pat’s Invoice Problem ,[object Object]
Selecting Data for the Stat Test ,[object Object],[object Object],[object Object],[object Object],[object Object]
Generating Random Data ,[object Object],[object Object]
Selecting Data at Random ,[object Object],[object Object]
Randomly Selected Data This procedure works equally well with text or numerical values (a wonderful way to select the sequence for Black Belts to present their projects in class).
Learning Check – Sample Size ,[object Object],[object Object],[object Object]

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A04 Sample Size

  • 1. Sample Size Determination Deliverable 10A
  • 2. Analyze Module Roadmap Define 1D – Define VOC, VOB, and CTQ’s 2D – Define Project Boundaries 3D – Quantify Project Value 4D – Develop Project Mgmt. Plan Measure 5M – Document Process 6M – Prioritize List of X’s 7M – Create Data Collection Plan 8M – Validate Measurement System 9M – Establish Baseline Process Cap. Analyze 10A – Determine Critical X’s Improve 12I – Prioritized List of Solutions 13I – Pilot Best Solution Control 14C – Create Control System 15C – Finalize Project Documentation Green 11G – Identify Root Cause Relationships Queue 1 Queue 2
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  • 12. Wastewater Sample Size Example Stat > power and sample size > 2-Sample t
  • 13. Minitab Output Power and Sample Size 2-Sample t Test Testing mean 1 = mean 2 (versus not =) Calculating power for mean 1 = mean 2 + difference Alpha = 0.05 Assumed standard deviation = 5 Sample Target Difference Size Power Actual Power 10 7 0.9 0.929070 The sample size is for each group.
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  • 20. Randomly Selected Data This procedure works equally well with text or numerical values (a wonderful way to select the sequence for Black Belts to present their projects in class).
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Editor's Notes

  1. Power and Sample Size Test for One Proportion Testing proportion = 0.1 (versus not = 0.1) Alpha = 0.05 Alternative Sample Target Proportion Size Power Actual Power 0.12 2523 0.9 0.900079 0.15 438 0.9 0.900409 0.20 122 0.9 0.901723 0.25 59 0.9 0.903729