13 14 Typical service levels in contracts: 99% Good is 3.8 Sigma 95% Good is 3.1 Sigma 90% Good is 2.8 Sigma
A focus on defects allows apple-to-apple comparisons across industries. The average company operates at a four Sigma level, producing thousands of defects. A process that is operating at Six Sigma generates fewer than 3.4 defects per million. Culturally, this means near-flawless execution
What is Six Sigma?
Think of measurements occurring at three stages of the process: outputs, process, and inputs. Output measures are used to determine how well customer CTQs are met. The letter “Y” is often used to signify output measures, and is often referred to as the “Project Y.” Independent Variables (Xs): The input variables and in process variables that determine the performance of the dependent variable (Y). When the appropriate independent variables are measured and tracked, they can be used to predict the dependent (Y) variable. Process measures are internal to your process and include key leverage points for improving output (Y) measures. Meaningful process measures will correlate with output measures. The symbol for process measures is the letter “X”. Input measures represent measures of the key CTQs placed on suppliers. Input measures not only indicate supplier performance, but also correlate to output measures. Just like process measures, the symbol for input measures is the letter “X”. Dependent Variables (Ys): Measure of the outcome or output of the process being observed or improved. CTQ: Critical to Quality
Steps in Hypothesis Testing Define the Problem & State the Objectives Establish the Hypotheses State the Null Hypothesis (Ho) State the Alternative Hypothesis (Ha) Decide on appropriate statistical test State the Alpha level (usually 5%). State the Beta level (usually 10-20%) Establish the Effect Size (Delta). Establish the Sample Size. Develop the Sampling Plan. Select Samples. Conduct test and collect data. Determine the probability of the calculated test statistic occurring by chance = P-value If P-value is less than test statistic (usually .05), reject Ho and accept Ha. If P-value is greater than the test statistic (usually .05), don’t reject Ho Replicate results and translate statistical conclusion to practical solution HYPOTHESIS TESTING: HOW IT WORKS Data is collected A test statistic is calculated based on a signal-to-noise (SNR) ratio of this data If Ho is true (no difference between and ), then the SNR is very small forces the test to yield a high “p-value” If Ha is true (real difference between and ), then the SNR will be large forces the “p-value” to be small The “p-value” is the probability of the null hypothesis occurring by chance The p-value is based on an assumed or actual reference distribution (either normal, t-distribution, chi-square, or F-distribution)
Steps in Hypothesis Testing Define the Problem & State the Objectives Establish the Hypotheses State the Null Hypothesis (Ho) State the Alternative Hypothesis (Ha) Decide on appropriate statistical test State the Alpha level (usually 5%). State the Beta level (usually 10-20%) Establish the Effect Size (Delta). Establish the Sample Size. Develop the Sampling Plan. Select Samples. Conduct test and collect data. Determine the probability of the calculated test statistic occurring by chance = P-value If P-value is less than test statistic (usually .05), reject Ho and accept Ha. If P-value is greater than the test statistic (usually .05), don’t reject Ho Replicate results and translate statistical conclusion to practical solution HYPOTHESIS TESTING: HOW IT WORKS Data is collected A test statistic is calculated based on a signal-to-noise (SNR) ratio of this data If Ho is true (no difference between and ), then the SNR is very small forces the test to yield a high “p-value” If Ha is true (real difference between and ), then the SNR will be large forces the “p-value” to be small The “p-value” is the probability of the null hypothesis occurring by chance The p-value is based on an assumed or actual reference distribution (either normal, t-distribution, chi-square, or F-distribution)
Plant Process Process Procedure People Environment Measurement Materials “ Y” Describing variation is a first step to reducing it. The next step is to investigate the sources of variation. There are two fundamental sources or types of variation. The first type is due to the inherent interaction of all the possible sources of variation (common cause). The second type is due to especially large influences by one of the possible sources of variation (special cause). Cause & Effect – Alternate Categories – Use What Works For Your Team:
Understanding the source of variation is important to devising a sound strategy for process control and improvement. The source of variation has important consequences for the type of actions required. When a process exhibits special cause variation , the appropriate action is to investigate those specific data points related to the special cause signals. In most cases the investigation will reveal important causal factors (Xs) related to the special cause(s). The results of the investigation should be integrated into an action plan for addressing the special causes immediately . When a process exhibits common cause variation , the appropriate action is to investigate all of the data points. Finding the “vital few” causal factors (Xs) that explain common cause variation is more difficult than finding causal factors for special causes because they are not as obvious. The tools in the Analyze phase of DMAIC focuse on this more challenging investigation.
Why is it important to know the source of variation and treat it according to the appropriate strategy? Because not reacting appropriately to the type of variation present in a process can seriously impact customer satisfaction and the amount of variation and defects, and it can increase costs. Appropriately reacting to the source of variation in a process provides the correct economic balance between overreacting and under-reacting to variation from a process.
With Rolled Throughput Yield, we want to know the probability of successive steps in a process which is defect-free. Since we want the combination of several individual probabilities, we multiply the individual probabilities from each step (as we did in the form example). Key points : “ Sigma” is average of all the operations. Golf operations could be departments in your factory or steps in the commercial process. .7581 18 is 0.7% chance of a 3 golfer making par on 18 holes. .9999864 18 is a 99.97% chance of a 6 golfer making par 18 holes.
Here is another way to look at the relation between complexity, sigma level and rolled throughput yield.
Statistical Properties of Measurement Systems Measurement system statistical control Comparing measurement system variability to process variability Comparing measurement system variability to specification limits Increments of measurementsrelative to process variability or specification limits - 1 to 10 rule Measurement system statistical property changes must be small versus process variation and specification limits
Accuracy and Precision Suppose we take numerous measurements on a single unit of product and then compute the average. The extent to which the average agrees with the “true” value is called the accuracy, or systematic error, of the measurement system. The spread of the values around the average is called the precision, or repeatability, of the system. A measurement system can be precise but inaccurate, or accurate but imprecise. Ideally, both accuracy and precision are desired. While we normally think of accuracy and precision in the context of meters and gauges, it is important to note that these concepts also apply to human-sensing data. For example, a group of five checkers might examine the same piece of paperwork and come up with a different number of errors (lack of precision). Furthermore, they might all fail to identify a specific error (lack of accuracy). Calibration programs for test equipment, training classes for checkers, automation, foolproofing, and ongoing audits are techniques for assuring accurate and precise data. For more on the topics of accuracy, precision, and human inspector error, see Section 23 of Juran’s Quality Control Handbook, 5th Edition (Section 18 in QCH4).
From Qualpro: Some things are obvious Some things are obvious once the data are organized Some things require more sophisticated tools Some things which are obvious are not true! Think Directional: Going through the levels of analysis most efficiently “directs” you to the most effective solution for your project. This is a series of logical paths that when the current level of analysis is not yielding the root cause(s) then directs you to the next level of analysis. NOT ALL PROBLEMS REQUIRE LEVEL 6 ANALYSIS – NOT MANY PROBLEMS REVEAL ROOT CAUSES FROM LEVEL 1 ANALYSIS.
Significance Level, (ALPHA): We would like there to be less than 10% chance that these observations could have occurred randomly ( = .10). Maybe we would like there to be less than 5% chance that the difference in observations occurred randomly ( = .05). Or, conservatively, we want there to be less than 1% chance that the difference in observations occurred randomly ( = .01). This alpha level requires two things: an assumption of no difference (Ho), and a reference distribution of some sort
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Six Sigma Orientation Presented By: Joseph Duhig University Medical Center Alliance / Methodist Healthcare November 21, 2003 The Century of Quality “ We are headed into the next century which will focus on quality… we are leaving one that has been focused on productivity” Dr. Joseph M. Juran
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SIX SIGMA <ul><li>Sigma, , is a letter in the Greek alphabet. It is used as a symbol to denote the standard deviation of a process (standard deviation is a measure of variation). </li></ul><ul><li>A process with “six sigma” capability means having six standard deviations between the process mean and either specification limit. Essentially, process variation is reduced so that no more than 3.4 parts per million fall outside the specification limits. Hence, as a metric, the higher the number of sigma’s, the better. </li></ul><ul><li>The “Six Sigma” term is also used to refer to a: </li></ul><ul><ul><li>-- philosophy </li></ul></ul><ul><ul><li>--goal </li></ul></ul><ul><ul><li>--methodology </li></ul></ul><ul><ul><li>to drive out waste, and improve the quality, cost and time performance of any business. </li></ul></ul>
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What is Six Sigma? 2 3 4 5 6 308,537 66,807 6,210 Sigma Defects per Million Opportunities 233 3.4 . 3 to 6 20,000 Times Improvement... A True Quantum Leap (99.99966% good) (99.98% good) (99.4% good) (93.3% good) (69.1% good)
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Six Sigma Benchmarks 1,000,000 100,000 10,000 1,000 100 3 4 5 6 7 2 Sigma (Short Term) Scale of Measure Restaurant Bills Doctor Prescription Writing Domestic Airline Fatality Rate (0.43 PPM) IRS Tax Advice (phone in) Airline Baggage Handling Average Company Best-in-Class 1 10 1 Defects per Million
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Getting To Six Sigma - Some Examples Six Sigma 99.99966% Good • 20,000 lost articles of mail per hour • Unsafe drinking water for almost 15 minutes each day • 5,000 incorrect surgical operations per week • Two short or long landings at most major airports each day • 200,000 wrong drug prescriptions each year <ul><li>• Seven articles lost per hour </li></ul><ul><li>• One unsafe minute every </li></ul><ul><li>seven months </li></ul><ul><li>1.7 incorrect operations per week </li></ul><ul><li>One short or long landing every </li></ul><ul><li>five years </li></ul><ul><li>• 68 wrong prescriptions per year </li></ul>3.8 Sigma 99% Good
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THE CENTURY OF QUALITY “ We are headed into the next century which will focus on quality… we are leaving one that has been focused on productivity” Dr. Joseph M. Juran
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WHAT IS SIX SIGMA QUALITY? Quality Product Features Freedom from Deficiencies That Customers Want Design for Six Sigma At Six Sigma Levels Improve to Six Sigma
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METHODOLOGY DEFINE Identify, prioritize, and select the right project(s) MEASURE Identify key product characteristics & process parameters, understand processes, and measure performance ANALYZE Identify the key (causative) process determinants IMPROVE Establish prediction model and optimize performance CONTROL Hold the gains
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INPUT Project Mission Statement Define Define customers & CTQ’s <ul><li>Prioritized list of customers/segments </li></ul><ul><li>Prioritized list of CTQ’s </li></ul>Define process to be improved <ul><li>High level Process Map </li></ul>Define Project Charter <ul><li>Project Charter </li></ul>Measure Establish Project Y’s Identify possible X’s Plan Data Collection <ul><li>Data Collection Plan </li></ul>Validate Measurement System Determine Process Capability <ul><li>Baseline Six Sigma values </li></ul>Analyze Improve Control Develop and test hypotheses on the sources variation and cause-effect relationships <ul><li>Stated theory (s) </li></ul><ul><li>Hypothesis testing results </li></ul>Develop the list of vital few causes of process performance <ul><li>List of “vital few” variations that account for the majority of variation in performance </li></ul><ul><li>Quantified $ Opportunity </li></ul><ul><li>List of possible solutions to test or operating parameters for experimentation </li></ul>Generate Solution Alternatives <ul><li>List of possible risks evaluated for level of seriousness and corresponding abatement actions as needed. </li></ul>Assess Risk <ul><li>Results of DOE and/or pilot and/or simulation </li></ul>Test Solution Alternatives. Select Solution(s) to optimize performance <ul><li>SPC charts in place </li></ul><ul><li>Feedback mechanisms and Mistake Proofing devices implemented </li></ul>Design and implement sustainable feedback mechanisms and methods to achieve self control for dominant variables. <ul><li>Updated Standard Operating Procedures (SOP), Process Maps, FMEA </li></ul><ul><li>Preventative Maintenance Plans </li></ul><ul><li>Personnel trained </li></ul>Control Plans and Documentation. <ul><li>Final project report </li></ul><ul><li>Audit plan </li></ul>Document Project work. Close Project Module <ul><li>Deliverables </li></ul><ul><li>Possible Tools </li></ul><ul><li>VOC Continuum, Surveys, </li></ul><ul><li>Interviews </li></ul><ul><li>List of Possible Xs </li></ul><ul><li>List of Project Ys </li></ul><ul><li>Reliable Measurement System </li></ul><ul><li>ANOVA, tests for equal variance, regression, t-tests, tests for proportions, contingency tables, non-parametric tests, Detailed Process Map, C&E Diagram, FMEA, Pareto </li></ul><ul><li>Designed Experiments, Pilots, Simulations </li></ul><ul><li>Performance Measurement Matrix </li></ul><ul><li>Detailed Process Map, C&E Diagram, FMEA </li></ul><ul><li>Gage R&R, Discrete Data Measure Analysis </li></ul>
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SIX SIGMA TOOLBOX Analysis of Variance (ANOVA) Box Plots Brainstorming Cause-effect Diagrams Correlation & Regression Design Of Experiments Evolutionary Operation (EVOP) FMECA Graphs and Charts Histograms Hypothesis Testing Lean Manufacturing (Lean Enterprise) Measurement System Analysis Mistake Proofing Pareto Analysis Process Capability Studies Process Control Plans Process Flow Diagrams Quality Function Deployment Response Surface Methods Scatter Diagrams Standard Operating Procedures (SOPs) Statistical Process Control Stratification
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Why We Need Six Sigma in Healthcare Presented By: Joseph Duhig University Medical Center Alliance / Methodist Healthcare November 21, 2003 The Century of Quality “ We are headed into the next century which will focus on quality… we are leaving one that has been focused on productivity” Dr. Joseph M. Juran
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GOOD NEWS <ul><li>Incredible Advances in Medicine </li></ul><ul><li>2 Million Articles/20,000 Journals/Year </li></ul><ul><li>Applying this knowledge is like: </li></ul><ul><li>“Trying to drink water from a fire hose” </li></ul>BAD NEWS The average time from discovery of knowledge until that knowledge is in wide-spread use is over 17 years
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The IOM Roundtable <ul><li>“… Serious and widespread quality problems exist throughout American medicine. These problems… occur in small and large communities alike, in all parts of the country, and with approximately equal frequency in managed care and fee-for-service systems of care. Very large numbers of Americans are harmed as a result….” </li></ul>Source: 2002 Institute for Healthcare Improvement The call to action...
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What is Wrong?? <ul><li>OVERUSE (of procedures, medications, visits that cannot help) </li></ul><ul><li>UNDERUSE (of procedures, medications, visits that can help) </li></ul><ul><li>MISUSE (errors of execution) </li></ul>Source: 2002 Institute for Healthcare Improvement
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Examples of OVERUSE <ul><li>30% of children receive excessive antibiotics for ear infections </li></ul><ul><li>20% to 50% of many surgical operations are unnecessary </li></ul><ul><li>50% of X-rays in back pain patients are unnecessary </li></ul>Source: 2002 Institute for Healthcare Improvement
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Examples of UNDERUSE <ul><li>50% of elderly fail to receive pneumococcal vaccine </li></ul><ul><li>50% of heart attack victims fail to receive beta-blockers </li></ul><ul><li>27% of high blood pressure is adequately treated </li></ul>Source: 2002 Institute for Healthcare Improvement
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Examples of MISUSE <ul><li>7% of hospital patients experience a serious medication error </li></ul><ul><li>44,000-98,000 Americans die in hospitals each year due to injuries in care </li></ul>Source: 2002 Institute for Healthcare Improvement
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What the IOM Said…. <ul><li>The patient safety problem is large. </li></ul><ul><li>It (usually) isn’t the fault of health care workers. </li></ul><ul><li>Most patient injuries are due to system failures. </li></ul>Source: 2002 Institute for Healthcare Improvement
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How Hazardous is Health Care? ( Leape) Total lives lost per year DANGEROUS (>1/1000) REGULATED ULTRA-SAFE (<1/100K) Number of encounters for each fatality Source: 2002 Institute of Healthcare Improvement Healthcare Driving Scheduled Airlines Chartered Flights Chemical Manufacturing Mountain Climbing Bungee Jumping European Railroads Nuclear Power
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Core Conclusions <ul><li>There are serious problems in quality and safety. --Between the health care we have and the care we could have lies not just a gap but a chasm. </li></ul><ul><li>The problems come from poor systems…not bad people --In its current form, habits, and environment, American health care is incapable of providing the public with the quality health care it expects and deserves. </li></ul><ul><li>We can fix it…but it will require changes. </li></ul>Source: 2002 Institute for Healthcare Improvement
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“The First Law of Improvement” <ul><li>Every system is perfectly designed to achieve exactly the results it gets </li></ul>Source: 2002 Institute for Healthcare Improvement Quality is a system property
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Why Six Sigma? <ul><li>Safe </li></ul><ul><li>Timely </li></ul><ul><li>Efficient </li></ul><ul><li>Effective </li></ul><ul><li>Equitable </li></ul><ul><li>Patient-centered </li></ul>Variation is the Key : Six Sigma is all about understanding variation in providing care that is:
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How is Six Sigma different from traditional Performance Improvement Approaches <ul><li>Strategically Deployed </li></ul><ul><li>Financially Focused </li></ul><ul><li>Trained Professionals vs. Good Intentioned Amateurs </li></ul><ul><li>Statistically Based Y = f(x) </li></ul><ul><li>Project Management is Built-in </li></ul><ul><li>Measurement System is Validated </li></ul><ul><li>Focus on Mistake Proofing – Failure Modes and Effects Analysis (FMEA) </li></ul>
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The Business Case – Doing Well by Doing Good Six Sigma Impact on Net Income Decreased # of cases Decreased LOS Decreased # units/case Decreased cost/unit Shared Risk Per Diem Per Case Discounted FFS Six Sigma Results
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PROJECT FOCUS <ul><li>Process </li></ul><ul><li>Problems and Symptoms </li></ul><ul><li>Process outputs </li></ul><ul><li>Response variable, Y </li></ul><ul><li>Independent variables, X i </li></ul><ul><li>Process inputs </li></ul><ul><li>The Vital Few determinants </li></ul><ul><li>Causes </li></ul><ul><li>Mathematical relationship </li></ul>Y X’s Measure Analyze Improve Control Process Characterization Process Optimization Goal: Y = f ( x ) Define The right project(s), the right team(s)
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PROCESS CONTEXT FOR MEASUREMENT Y = f(X 1 , X 2 ,... , X n ) Measures P S I O C Process Map Suppliers Inputs Process Outputs Customers Measures Measures CTQs
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AHRQ Medicare SMR vs. Standardised Charge, 1997 (Random Sample 250 Hospitals Plotted) Source: 2002 Institute for Healthcare Improvement
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The cohorts had similar baseline health across quintiles But were treated differently . Per-capita Medicare Spending 1996 2000 Ratio: High to Low: 1.61 1.58 $ 3,922 $ 4,439 $ 4,940 $ 5,444 $ 6,304 $ 5,229 $ 5.692 $ 6,069 $ 6,614 $ 8,283
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Glucose Levels of Diabetic Cardiac Surgery Patients
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SOURCES OF VARIATION People Process Process Place Procedure Provisions Measurement Patrons “ Y” 5 P’s + 1 M
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COMMON vs. SPECIAL CAUSES Measurements Common or Special ? CONTROL Sustain The Improvements Measurements Common Causes MEASURE ANALYZE Investigate all of the variation Develop solutions for the “vital few” process and input Xs IMPROVE Develop solutions for special causes and implement as appropriate IMPROVE Special Causes MEASURE Investigate specific data points ANALYZE
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COMMON vs. SPECIAL CAUSES Two Types Of Mistakes How you treat variation . . . Common Causes Special Causes Common Causes Special Causes Mistake 1 Tampering (increases variation) Focus on fundamental process change Mistake 2 Underreacting (missed prevention) Focus on investigating special causes What the variation really is...
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CALCULATING SIGMA - YIELD Suppose we say that there are 4 key characteristics which must be executed (without error) in order to par the hole. In this case, what is the probability of accomplishing the task error free? Rolled Yield .7581 .9999864 3 6 With Shifting Tee Shots .9331 .9999966 Fairway Shots .9331 .9999966 Chipping .9331 .9999966 Putting .9331 .9999966 Rolled Throughput Yield
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THE FUNDAMENTAL MSA QUESTION “ Is the variation (spread) of my measurement system too large to study the current level of process variation?” + = (Observed Variability) Total Variability Product Variability Process Variability Variation in the measurement process
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POSSIBLE SOURCES OF VARIATION To address actual process variability, the variation due to the measurement system must first be identified and separated from that of the process. Observed Process Variation Actual Process Variation Measurement Variation Long-term Process Variation Short-term Process Variation Repeatability Accuracy Stability Linearity Reproducibility
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LEVELS OF ANALYSIS Measure 1 Individual Experience Measure 2 Group Experience Analyze 3 Graphical Interpretation of Observed Data Analyze 4 Statistical Interpretation of Observed Data Improve 5 Graphical Interpretation of Experimental Data Improve 6 Statistical Interpretation of Experimental Data “ Think Directional”
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THE ANALYSIS TOOL DEPENDS ON THE QUESTION AND THE DATA TYPE Continuous Data Discrete Data Discrete Data Continuous Data X Y Variance Different ? Statistical: Test of Equal Variances Graphical: Stratified Box Plots Means Different ? Statistical: t-test; ANOVA Graphical: Histogram(s) How does change in X affect change in Y ? Statistical: Correlation /Regression Graphical: Scatter Plots How does change in X affect change in Y ? Statistical: Logistic Regression Are the outputs different ? Statistical: Chi Square, Proportion tests Graphical: Stratified Pareto Diagrams
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HYPOTHESIS TESTING DESCRIPTION <ul><li>Allows us to answer the practical question: </li></ul><ul><li>“ Is there a real difference between Dr. A and Dr. B ?” </li></ul><ul><li>A practical process problem is translated into a statistical hypothesis so that we may answer the question above. </li></ul><ul><li>In hypothesis testing, we use relatively small samples to answer questions about large populations. There is always a chance that we selected a sample that is not representative of the population - a “weird” sample. Therefore, there is always a chance that the conclusion obtained is wrong. </li></ul><ul><li>With some assumptions, i nferential statistics allows us to estimate the probability of getting a “weird” sample. Hypothesis testing quantifies the probability (P-Value) of a wrong conclusion. </li></ul>Data vs. Gut Feeling
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ALPHA & BETA RISK Truth Ho Ha Fail to Reject Ho Reject Ho Type I Error Type II Error Correct Decision Correct Decision Also called: Type II error Consumers’ Risk Also called: Type I error Producers’ Risk <ul><li> is the risk of finding a difference when there really isn’t one. </li></ul><ul><li> is the risk of not finding a difference when there really is one. </li></ul>
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