# Understanding Statistics and Statistical Myths

## Kicab Castaneda-Mendez

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## Opis: Understanding Statistics and Statistical Myths - Kicab Castaneda-Mendez

Addressing more than 30 statistical myths, this book explains how to understand statistics rather than how to do statistics. In the book, six characters have 30 discussions on various topics taught in a fictional course intended to teach students how to apply statistics to improve processes. Readers follow along and learn as the students apply what they learn to a project in which they are team members. Each discussion will helps readers understand why certain statements are not always true under all conditions, as well as when they contradict other myths.Myth 1: Two Types of Data-Attribute/Discrete and Measurement/Continuous Background Measurement Requires Scale Gauges or Instruments vs. No Gauges Discrete, Categorical, Attribute versus Continuous, Variable: Degree of Information Creating Continuous Measures by Changing the "Thing" Measured Discrete versus Continuous: Half Test Nominal, Ordinal, Interval, Ratio Measurement to Compare Scale Type versus Data Type Scale Taxonomy Purpose of Data Classification Myth 2: Proportions and Percentages Are Discrete Data Background Denominator for Proportions and Percentages Probabilities Classification of Proportions, Percentages, and Probabilities Myth 3: s = [SIGMA(Xi- x)2/(n- 1)] The Correct Formula for Sample Standard Deviation Background Correctness of Estimations Estimators and Estimates Properties of Estimators Myth 4: Sample Standard Deviation [SIGMA(Xi-x)2/(n- 1)] Is Unbiased Background Degrees of Freedom t Distribution Definition of Bias Removing Bias and Control Charts Myth 5: Variances Can Be Added but Not Standard Deviations Background Sums of Squares and Square Roots: Pythagorean Theorem Functions and Operators Random Variables Independence of Factors Other Properties Myth 6: Parts and Operators for an MSA Do Not Have to Be Randomly Selected Background Types of Analyses of Variance Making Measurement System Look Better than It Is: Selecting Parts to Cover the Range of Process Variation Selecting Both Good and Bad Parts Myth 7: % Study (% Contribution, Number of Distinct Categories) Is the Best Criterion for Evaluating a Measurement System for Process Improvement Background % Contribution versus % Study P/T Ratio versus % Study Distinguishing between Good and Bad Parts Distinguishing Parts That Are Different Myth 8: Only Sigma Can Compare Different Processes and Metrics Background Sigma and Specifications Sigma as a Percentage Myth 9: Capability Is Not Percent/Proportion of Good Units Background Capability Indices: Frequency Meeting Specifications Capability: Actual versus Potential Capability Indices Process Capability Time-Dependent Meaning of Capability: Short-Cut Calculations Myth 10: p = Probability of Making an Error Background Only Two Types of Errors Definition of an Error about Deciding What Is True Calculation of p and Evidence for a Hypothesis Probability of Making an Error for a Particular Case Probability of Data Given Ho versus Probability of Ho Given Data Non-probabilistic Decisions Myth 11: Need More Data for Discrete Data than Continuous Data Analysis Background Discrete Examples When n = 1 Factors That Determine Sample Size Relevancy of Data Myth 12: Nonparametric Tests Are Less Powerful than Parametric Tests Background Distribution Free versus Nonparametric Comparing Power for the Same Conditions Different Formulas for Testing the Same Hypotheses Assumptions of Tests Comparing Power for the Same Characteristic Converting Quantitative Data to Qualitative Data Myth 13: Sample Size of 30 Is Acceptable (for Statistical Significance) Background A Rationale for n = 30 Contradictory Rules of Thumb Uses of Data Sample Size as a Function of Alpha, Beta, Delta, and Sigma Sample Size for Practical Use Sample Size and Statistical Significance Myth 14: Can Only Fail to Reject Ho, Can Never Accept Ho Background Proving Theories: Sufficient versus Necessary Prove versus Accept versus Fail to Reject: Actions Innocent versus Guilty: Problems with Example Two-Choice Testing Significance Testing and Confidence Intervals Hypothesis Testing and Power Null Hypothesis of => or <= Practical Cases Which Hypothesis Has the Equal Sign? Bayesian Statistics: Probability of Hypothesis Myth 15: Control Limits Are +-3 Standard Deviations from the Center Line Background Standard Error versus Standard Deviation Within- versus between-Subgroup Variation: How Control Charts Work I Chart of Individuals Myth 16: Control Chart Limits Are Empirical Limits Background Definition of Empirical Empirical Limits versus Limits Justified Empirically Shewhart's Evidence of Limits Being Empirical Wheeler's Empirical Rule Empirical Justification for a Purpose Myth 17: Control Chart Limits Are Not Probability Limits Background Association of Probabilities and Control Chart Limits Can Control Limits Be Probability Limits? False Alarm Rates for All Special Cause Patterns Wheeler Uses Probability Limits Other Uses of Probability Limits Myth 18: +-3 Sigma Limits Are the Most Economical Control Chart Limits Background Evidence for 3-Standard Error Limits Being Economically Best Evidence against 3-Standard Error Limits Being the Best Economically Counterexamples: Simple Cost Model Other Out-of-Control Rules-Assignable Causes Shewhart Didn't Find but Exist Small Changes Are Not Critical to Detect versus Taguchi's Loss Function Importance of Subgroup Size and Frequency on Economic Value of Control Chart Limits Purpose to Detect Lack of Control-3-Standard Error Limits Misplaced Myth 19: Statistical Inferences Are Inductive Inferences Background Reasoning: Validity and Soundness Induction versus Deduction Four Cases of Inductive Inferences Statistical Inferences: Probability Distributions Inferences about Population Parameters Deductive Statistical Inferences: Hypothesis Testing Deductive Statistical Inferences: Estimation Real-World Cases of Statistical Inferences Myth 20: There Is One Universe or Population If Data Are Homogeneous Background Definition of Homogeneous Is Displaying Stability Required for Universes to Exist? Are There Always Multiple Universes If Data Display Instability? Is There Only One Universe If Data Appropriately Plotted Display Stability? Control Chart Framework: Valid and Invalid Conclusions Myth 21: Control Charts Are Analytic Studies Background Enumerative versus Analytic Distinguishing Characteristics Enumerative Problem, Study, and Solution Analytic Problem, Study, and Solution Procedures for Enumerative and Analytic Studies Are Control Charts Enumerative or Analytic Studies? Cause-Effect Relationship An Analytic Study Answers "When?" Myth 22: Control Charts Are Not Tests of Hypotheses Background Definition and Structure of Hypothesis Test Control Chart as a General Hypothesis Test Statistical Hypothesis Testing: Alpha and p Analysis of Means Shewhart's View on Control Charts as Tests of Hypotheses Deming's Argument: No Definable, Finite, Static Population Woodall's Two Phases of Control Chart Use Finite, Static Universe Control Charts as Nonparametric Tests of Hypotheses Utility of Viewing Control Charts as Statistical Hypothesis Tests Is the Process in Control? versus What Is the Probability the Process Changed? Myth 23: Process Needs to Be Stable to Calculate Process Capability Background Stability and Capability: Dependent or Independent? Actual Performance and Potential Capability versus Stability Process Capability: Reliability of Estimates Control Charts Are Fallible Capable: 100% or Less than 100% Meeting Specifications Process Capability: "Best" Performance versus Sustainability Cp versus P/T Random Sampling Response Surface Studies Myth 24: Specifications Don't Belong on Control Charts Background Run Charts Charts of Individual Values Confusion Having Both Control and Specification Limits on Charts Stability, Performance, and Capability Specifications on Averages and Variation Myth 25: Identify and Eliminate Assignable Causes of Variation Background Assignable Causes versus Process Change Is Increase in Process Variation Always Bad? Good Assignable Causes Myth 26: Process Needs to Be Stable before You Can Improve It Background History of Improvement before the 1920s Control Chart Fallibility Stabilizing a Process and Improving It Stability Required versus Four States of a Process Shewhart's Counterexample Myth 27: Stability (Homogeneity) Is Required to Establish a Baseline Background Purpose of Baseline Just-Do-It Projects Natural Processes Processes Whose Output We Want to Be "Out of Control" Meaning of "Meaningless" Daily Comparisons "True" Process Average: Process, Outputs, Characteristics, and Measures Ways to Compare Universe or Population and Descriptive Statistics Random Sampling When Is Homogeneity/Stability Not Required or Unimportant? Myth 28: A Process Must Be Stable to Be Predictable Background Types of Predictions: Interpolation and Extrapolation Interpolation: Stability versus Instability Conditional Predictions Extrapolation: Stability versus Instability Fallibility of Control Chart Stability Control Charts in Daily Life Statistical versus Causal Control Myth 29: Adjusting a Process Based on a Single Defect Is Tampering, Causing Increased Process Variation Background Definition of Tampering Zero versus One versus Multiple Defects to Define Tampering Role of Theory and Understanding When Adjusting Defects Arise from Special Causes: Anomalies Control Limits versus Specification Limits Actions for Common Cause Signals versus Special Cause Signals Is Reducing Common Cause Variation Always Good? Fundamental Change versus Tampering Funnel Exercise: Counterexample Myth 30: No Assumptions Required When the Data Speak for Themselves Background Simpson's Paradox Math and Descriptive Statistics: Adding versus Aggregating Inferences versus Facts: Conditions for Paradoxes Assumptions for Modeling Assumptions for Causal Inferences Assumptions for Inferences from Reasons Epilogue References Index

## Szczegóły: Understanding Statistics and Statistical Myths - Kicab Castaneda-Mendez

Tytuł: Understanding Statistics and Statistical Myths
Autor: Kicab Castaneda-Mendez
Producent: Productivity Press Inc
ISBN: 9781498727457
Rok produkcji: 2015
Ilość stron: 585
Oprawa: Twarda

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# Understanding Statistics and Statistical Myths

## Kicab Castaneda-Mendez

Addressing more than 30 statistical myths, this book explains how to understand statistics rather than how to do statistics. In the book, six characters have 30 discussions on various topics taught in a fictional course intended to teach students how to apply statistics to improve processes. Readers follow along and learn as the students apply what they learn to a project in which they are team members. Each discussion will helps readers understand why certain statements are not always true under all conditions, as well as when they contradict other myths.Myth 1: Two Types of Data-Attribute/Discrete and Measurement/Continuous Background Measurement Requires Scale Gauges or Instruments vs. No Gauges Discrete, Categorical, Attribute versus Continuous, Variable: Degree of Information Creating Continuous Measures by Changing the "Thing" Measured Discrete versus Continuous: Half Test Nominal, Ordinal, Interval, Ratio Measurement to Compare Scale Type versus Data Type Scale Taxonomy Purpose of Data Classification Myth 2: Proportions and Percentages Are Discrete Data Background Denominator for Proportions and Percentages Probabilities Classification of Proportions, Percentages, and Probabilities Myth 3: s = [SIGMA(Xi- x)2/(n- 1)] The Correct Formula for Sample Standard Deviation Background Correctness of Estimations Estimators and Estimates Properties of Estimators Myth 4: Sample Standard Deviation [SIGMA(Xi-x)2/(n- 1)] Is Unbiased Background Degrees of Freedom t Distribution Definition of Bias Removing Bias and Control Charts Myth 5: Variances Can Be Added but Not Standard Deviations Background Sums of Squares and Square Roots: Pythagorean Theorem Functions and Operators Random Variables Independence of Factors Other Properties Myth 6: Parts and Operators for an MSA Do Not Have to Be Randomly Selected Background Types of Analyses of Variance Making Measurement System Look Better than It Is: Selecting Parts to Cover the Range of Process Variation Selecting Both Good and Bad Parts Myth 7: % Study (% Contribution, Number of Distinct Categories) Is the Best Criterion for Evaluating a Measurement System for Process Improvement Background % Contribution versus % Study P/T Ratio versus % Study Distinguishing between Good and Bad Parts Distinguishing Parts That Are Different Myth 8: Only Sigma Can Compare Different Processes and Metrics Background Sigma and Specifications Sigma as a Percentage Myth 9: Capability Is Not Percent/Proportion of Good Units Background Capability Indices: Frequency Meeting Specifications Capability: Actual versus Potential Capability Indices Process Capability Time-Dependent Meaning of Capability: Short-Cut Calculations Myth 10: p = Probability of Making an Error Background Only Two Types of Errors Definition of an Error about Deciding What Is True Calculation of p and Evidence for a Hypothesis Probability of Making an Error for a Particular Case Probability of Data Given Ho versus Probability of Ho Given Data Non-probabilistic Decisions Myth 11: Need More Data for Discrete Data than Continuous Data Analysis Background Discrete Examples When n = 1 Factors That Determine Sample Size Relevancy of Data Myth 12: Nonparametric Tests Are Less Powerful than Parametric Tests Background Distribution Free versus Nonparametric Comparing Power for the Same Conditions Different Formulas for Testing the Same Hypotheses Assumptions of Tests Comparing Power for the Same Characteristic Converting Quantitative Data to Qualitative Data Myth 13: Sample Size of 30 Is Acceptable (for Statistical Significance) Background A Rationale for n = 30 Contradictory Rules of Thumb Uses of Data Sample Size as a Function of Alpha, Beta, Delta, and Sigma Sample Size for Practical Use Sample Size and Statistical Significance Myth 14: Can Only Fail to Reject Ho, Can Never Accept Ho Background Proving Theories: Sufficient versus Necessary Prove versus Accept versus Fail to Reject: Actions Innocent versus Guilty: Problems with Example Two-Choice Testing Significance Testing and Confidence Intervals Hypothesis Testing and Power Null Hypothesis of => or <= Practical Cases Which Hypothesis Has the Equal Sign? Bayesian Statistics: Probability of Hypothesis Myth 15: Control Limits Are +-3 Standard Deviations from the Center Line Background Standard Error versus Standard Deviation Within- versus between-Subgroup Variation: How Control Charts Work I Chart of Individuals Myth 16: Control Chart Limits Are Empirical Limits Background Definition of Empirical Empirical Limits versus Limits Justified Empirically Shewhart's Evidence of Limits Being Empirical Wheeler's Empirical Rule Empirical Justification for a Purpose Myth 17: Control Chart Limits Are Not Probability Limits Background Association of Probabilities and Control Chart Limits Can Control Limits Be Probability Limits? False Alarm Rates for All Special Cause Patterns Wheeler Uses Probability Limits Other Uses of Probability Limits Myth 18: +-3 Sigma Limits Are the Most Economical Control Chart Limits Background Evidence for 3-Standard Error Limits Being Economically Best Evidence against 3-Standard Error Limits Being the Best Economically Counterexamples: Simple Cost Model Other Out-of-Control Rules-Assignable Causes Shewhart Didn't Find but Exist Small Changes Are Not Critical to Detect versus Taguchi's Loss Function Importance of Subgroup Size and Frequency on Economic Value of Control Chart Limits Purpose to Detect Lack of Control-3-Standard Error Limits Misplaced Myth 19: Statistical Inferences Are Inductive Inferences Background Reasoning: Validity and Soundness Induction versus Deduction Four Cases of Inductive Inferences Statistical Inferences: Probability Distributions Inferences about Population Parameters Deductive Statistical Inferences: Hypothesis Testing Deductive Statistical Inferences: Estimation Real-World Cases of Statistical Inferences Myth 20: There Is One Universe or Population If Data Are Homogeneous Background Definition of Homogeneous Is Displaying Stability Required for Universes to Exist? Are There Always Multiple Universes If Data Display Instability? Is There Only One Universe If Data Appropriately Plotted Display Stability? Control Chart Framework: Valid and Invalid Conclusions Myth 21: Control Charts Are Analytic Studies Background Enumerative versus Analytic Distinguishing Characteristics Enumerative Problem, Study, and Solution Analytic Problem, Study, and Solution Procedures for Enumerative and Analytic Studies Are Control Charts Enumerative or Analytic Studies? Cause-Effect Relationship An Analytic Study Answers "When?" Myth 22: Control Charts Are Not Tests of Hypotheses Background Definition and Structure of Hypothesis Test Control Chart as a General Hypothesis Test Statistical Hypothesis Testing: Alpha and p Analysis of Means Shewhart's View on Control Charts as Tests of Hypotheses Deming's Argument: No Definable, Finite, Static Population Woodall's Two Phases of Control Chart Use Finite, Static Universe Control Charts as Nonparametric Tests of Hypotheses Utility of Viewing Control Charts as Statistical Hypothesis Tests Is the Process in Control? versus What Is the Probability the Process Changed? Myth 23: Process Needs to Be Stable to Calculate Process Capability Background Stability and Capability: Dependent or Independent? Actual Performance and Potential Capability versus Stability Process Capability: Reliability of Estimates Control Charts Are Fallible Capable: 100% or Less than 100% Meeting Specifications Process Capability: "Best" Performance versus Sustainability Cp versus P/T Random Sampling Response Surface Studies Myth 24: Specifications Don't Belong on Control Charts Background Run Charts Charts of Individual Values Confusion Having Both Control and Specification Limits on Charts Stability, Performance, and Capability Specifications on Averages and Variation Myth 25: Identify and Eliminate Assignable Causes of Variation Background Assignable Causes versus Process Change Is Increase in Process Variation Always Bad? Good Assignable Causes Myth 26: Process Needs to Be Stable before You Can Improve It Background History of Improvement before the 1920s Control Chart Fallibility Stabilizing a Process and Improving It Stability Required versus Four States of a Process Shewhart's Counterexample Myth 27: Stability (Homogeneity) Is Required to Establish a Baseline Background Purpose of Baseline Just-Do-It Projects Natural Processes Processes Whose Output We Want to Be "Out of Control" Meaning of "Meaningless" Daily Comparisons "True" Process Average: Process, Outputs, Characteristics, and Measures Ways to Compare Universe or Population and Descriptive Statistics Random Sampling When Is Homogeneity/Stability Not Required or Unimportant? Myth 28: A Process Must Be Stable to Be Predictable Background Types of Predictions: Interpolation and Extrapolation Interpolation: Stability versus Instability Conditional Predictions Extrapolation: Stability versus Instability Fallibility of Control Chart Stability Control Charts in Daily Life Statistical versus Causal Control Myth 29: Adjusting a Process Based on a Single Defect Is Tampering, Causing Increased Process Variation Background Definition of Tampering Zero versus One versus Multiple Defects to Define Tampering Role of Theory and Understanding When Adjusting Defects Arise from Special Causes: Anomalies Control Limits versus Specification Limits Actions for Common Cause Signals versus Special Cause Signals Is Reducing Common Cause Variation Always Good? Fundamental Change versus Tampering Funnel Exercise: Counterexample Myth 30: No Assumptions Required When the Data Speak for Themselves Background Simpson's Paradox Math and Descriptive Statistics: Adding versus Aggregating Inferences versus Facts: Conditions for Paradoxes Assumptions for Modeling Assumptions for Causal Inferences Assumptions for Inferences from Reasons Epilogue References Index

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## Szczegóły: Understanding Statistics and Statistical Myths - Kicab Castaneda-Mendez

Tytuł: Understanding Statistics and Statistical Myths
Autor: Kicab Castaneda-Mendez
Producent: Productivity Press Inc
ISBN: 9781498727457
Rok produkcji: 2015
Ilość stron: 585
Oprawa: Twarda

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